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| versions
list | update_date
timestamp[s] | authors_parsed
sequence |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0806.4735 | Shai Gutner | Noga Alon and Shai Gutner | Linear Time Algorithms for Finding a Dominating Set of Fixed Size in
Degenerated Graphs | null | Proc. of 13th COCOON (2007), 394-405 | null | null | cs.DS cs.DM | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | There is substantial literature dealing with fixed parameter algorithms for
the dominating set problem on various families of graphs. In this paper, we
give a $k^{O(dk)} n$ time algorithm for finding a dominating set of size at
most $k$ in a $d$-degenerated graph with $n$ vertices. This proves that the
dominating set problem is fixed-parameter tractable for degenerated graphs. For
graphs that do not contain $K_h$ as a topological minor, we give an improved
algorithm for the problem with running time $(O(h))^{hk} n$. For graphs which
are $K_h$-minor-free, the running time is further reduced to $(O(\log
h))^{hk/2} n$. Fixed-parameter tractable algorithms that are linear in the
number of vertices of the graph were previously known only for planar graphs.
For the families of graphs discussed above, the problem of finding an induced
cycle of a given length is also addressed. For every fixed $H$ and $k$, we show
that if an $H$-minor-free graph $G$ with $n$ vertices contains an induced cycle
of size $k$, then such a cycle can be found in O(n) expected time as well as in
$O(n \log n)$ worst-case time. Some results are stated concerning the
(im)possibility of establishing linear time algorithms for the more general
family of degenerated graphs.
| [
{
"version": "v1",
"created": "Sun, 29 Jun 2008 06:09:57 GMT"
}
] | 2008-12-18T00:00:00 | [
[
"Alon",
"Noga",
""
],
[
"Gutner",
"Shai",
""
]
] |
0806.4790 | Vladimir Braverman | Vladimir Braverman, Kai-Min Chung, Zhenming Liu, Michael Mitzenmacher,
Rafail Ostrovsky | AMS Without 4-Wise Independence on Product Domains | null | null | null | null | cs.DS | http://creativecommons.org/licenses/by/3.0/ | In their seminal work, Alon, Matias, and Szegedy introduced several sketching
techniques, including showing that 4-wise independence is sufficient to obtain
good approximations of the second frequency moment. In this work, we show that
their sketching technique can be extended to product domains $[n]^k$ by using
the product of 4-wise independent functions on $[n]$. Our work extends that of
Indyk and McGregor, who showed the result for $k = 2$. Their primary motivation
was the problem of identifying correlations in data streams. In their model, a
stream of pairs $(i,j) \in [n]^2$ arrive, giving a joint distribution $(X,Y)$,
and they find approximation algorithms for how close the joint distribution is
to the product of the marginal distributions under various metrics, which
naturally corresponds to how close $X$ and $Y$ are to being independent. By
using our technique, we obtain a new result for the problem of approximating
the $\ell_2$ distance between the joint distribution and the product of the
marginal distributions for $k$-ary vectors, instead of just pairs, in a single
pass. Our analysis gives a randomized algorithm that is a $(1 \pm \epsilon)$
approximation (with probability $1-\delta$) that requires space logarithmic in
$n$ and $m$ and proportional to $3^k$.
| [
{
"version": "v1",
"created": "Sun, 29 Jun 2008 21:34:28 GMT"
},
{
"version": "v2",
"created": "Fri, 15 May 2009 19:16:27 GMT"
},
{
"version": "v3",
"created": "Thu, 17 Sep 2009 16:21:56 GMT"
},
{
"version": "v4",
"created": "Tue, 5 Jan 2010 22:23:35 GMT"
},
{
"version": "v5",
"created": "Wed, 3 Feb 2010 14:19:09 GMT"
}
] | 2010-02-03T00:00:00 | [
[
"Braverman",
"Vladimir",
""
],
[
"Chung",
"Kai-Min",
""
],
[
"Liu",
"Zhenming",
""
],
[
"Mitzenmacher",
"Michael",
""
],
[
"Ostrovsky",
"Rafail",
""
]
] |
0806.4899 | Mordecai Golin | Mordecai Golin and Yan Zhang | A Dynamic Programming Approach To Length-Limited Huffman Coding | null | null | null | null | cs.DS cs.IT math.IT | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | The ``state-of-the-art'' in Length Limited Huffman Coding algorithms is the
$\Theta(ND)$-time, $\Theta(N)$-space one of Hirschberg and Larmore, where $D\le
N$ is the length restriction on the code. This is a very clever, very problem
specific, technique. In this note we show that there is a simple
Dynamic-Programming (DP) method that solves the problem with the same time and
space bounds. The fact that there was an $\Theta(ND)$ time DP algorithm was
previously known; it is a straightforward DP with the Monge property (which
permits an order of magnitude speedup). It was not interesting, though, because
it also required $\Theta(ND)$ space. The main result of this paper is the
technique developed for reducing the space. It is quite simple and applicable
to many other problems modeled by DPs with the Monge property. We illustrate
this with examples from web-proxy design and wireless mobile paging.
| [
{
"version": "v1",
"created": "Mon, 30 Jun 2008 14:13:18 GMT"
}
] | 2008-07-01T00:00:00 | [
[
"Golin",
"Mordecai",
""
],
[
"Zhang",
"Yan",
""
]
] |
0807.0038 | Changyong Zhang | Changyong Zhang | A Novel Mathematical Model for the Unique Shortest Path Routing Problem | 31 pages, 4 figures | null | null | null | math.OC cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Link weights are the principal parameters of shortest path routing protocols,
the most commonly used protocols for IP networks. The problem of optimally
setting link weights for unique shortest path routing is addressed. Due to the
complexity of the constraints involved, there exist challenges to formulate the
problem properly, so that a solution algorithm may be developed which could
prove to be more efficient than those already in existence. In this paper, a
novel complete formulation with a polynomial number of constraints is first
introduced and then mathematically proved to be correct. It is further
illustrated that the formulation has advantages over a prior one in terms of
both constraint structure and model size for a proposed decomposition method to
solve the problem.
| [
{
"version": "v1",
"created": "Mon, 30 Jun 2008 23:22:47 GMT"
},
{
"version": "v2",
"created": "Thu, 4 Mar 2010 06:54:04 GMT"
}
] | 2010-03-04T00:00:00 | [
[
"Zhang",
"Changyong",
""
]
] |
0807.0222 | Sariel Har-Peled | Sariel Har-Peled, S. Muthukrishnan | Range Medians | To appear in ESA 08 | null | null | null | cs.DS cs.OH | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We study a generalization of the classical median finding problem to batched
query case: given an array of unsorted $n$ items and $k$ (not necessarily
disjoint) intervals in the array, the goal is to determine the median in {\em
each} of the intervals in the array. We give an algorithm that uses $O(n\log n
+ k\log k \log n)$ comparisons and show a lower bound of $\Omega(n\log k)$
comparisons for this problem. This is optimal for $k=O(n/\log n)$.
| [
{
"version": "v1",
"created": "Tue, 1 Jul 2008 20:05:29 GMT"
}
] | 2008-07-02T00:00:00 | [
[
"Har-Peled",
"Sariel",
""
],
[
"Muthukrishnan",
"S.",
""
]
] |
0807.0644 | Neal E. Young | Christos Koufogiannakis and Neal E. Young | Greedy D-Approximation Algorithm for Covering with Arbitrary Constraints
and Submodular Cost | null | Algorithmica 66(1):113-152 (2013) | 10.1007/978-3-642-02927-1_53 | null | cs.DS cs.DC | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | This paper describes a simple greedy D-approximation algorithm for any
covering problem whose objective function is submodular and non-decreasing, and
whose feasible region can be expressed as the intersection of arbitrary (closed
upwards) covering constraints, each of which constrains at most D variables of
the problem. (A simple example is Vertex Cover, with D = 2.) The algorithm
generalizes previous approximation algorithms for fundamental covering problems
and online paging and caching problems.
| [
{
"version": "v1",
"created": "Fri, 4 Jul 2008 23:31:29 GMT"
},
{
"version": "v2",
"created": "Thu, 20 Nov 2008 01:26:09 GMT"
},
{
"version": "v3",
"created": "Fri, 8 May 2009 02:11:42 GMT"
},
{
"version": "v4",
"created": "Fri, 30 Dec 2011 17:40:35 GMT"
}
] | 2015-06-02T00:00:00 | [
[
"Koufogiannakis",
"Christos",
""
],
[
"Young",
"Neal E.",
""
]
] |
0807.0807 | Mustaq Ahmed | Mustaq Ahmed, Anna Lubiw | Shortest Paths Avoiding Forbidden Subpaths | 12 pages, 2 figures. Fixed a few typos, rephrased a few sentences,
and used the STACS style | Proceedings of the 26th International Symposium on Theoretical
Aspects of Computer Science (STACS), Freiburg, Germany, 2009, pp. 63-74 | null | null | cs.DM cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | In this paper we study a variant of the shortest path problem in graphs:
given a weighted graph G and vertices s and t, and given a set X of forbidden
paths in G, find a shortest s-t path P such that no path in X is a subpath of
P. Path P is allowed to repeat vertices and edges. We call each path in X an
exception, and our desired path a shortest exception-avoiding path. We
formulate a new version of the problem where the algorithm has no a priori
knowledge of X, and finds out about an exception x in X only when a path
containing x fails. This situation arises in computing shortest paths in
optical networks. We give an algorithm that finds a shortest exception avoiding
path in time polynomial in |G| and |X|. The main idea is to run Dijkstra's
algorithm incrementally after replicating vertices when an exception is
discovered.
| [
{
"version": "v1",
"created": "Fri, 4 Jul 2008 19:30:30 GMT"
},
{
"version": "v2",
"created": "Wed, 11 Feb 2009 16:49:43 GMT"
}
] | 2009-02-11T00:00:00 | [
[
"Ahmed",
"Mustaq",
""
],
[
"Lubiw",
"Anna",
""
]
] |
0807.0928 | Denis Charles X. | Denis Charles, Kumar Chellapilla | Bloomier Filters: A second look | 13 Pages, 3 figures, to appear in ESA - 2008 | null | null | null | cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | A Bloom filter is a space efficient structure for storing static sets, where
the space efficiency is gained at the expense of a small probability of
false-positives. A Bloomier filter generalizes a Bloom filter to compactly
store a function with a static support. In this article we give a simple
construction of a Bloomier filter. The construction is linear in space and
requires constant time to evaluate. The creation of our Bloomier filter takes
linear time which is faster than the existing construction. We show how one can
improve the space utilization further at the cost of increasing the time for
creating the data structure.
| [
{
"version": "v1",
"created": "Sun, 6 Jul 2008 19:45:37 GMT"
}
] | 2008-07-08T00:00:00 | [
[
"Charles",
"Denis",
""
],
[
"Chellapilla",
"Kumar",
""
]
] |
0807.1139 | Nitish Korula | Nitish Korula, Martin Pal | Algorithms for Secretary Problems on Graphs and Hypergraphs | 15 pages, 2 figures | null | null | null | cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We examine several online matching problems, with applications to Internet
advertising reservation systems. Consider an edge-weighted bipartite graph G,
with partite sets L, R. We develop an 8-competitive algorithm for the following
secretary problem: Initially given R, and the size of L, the algorithm receives
the vertices of L sequentially, in a random order. When a vertex l \in L is
seen, all edges incident to l are revealed, together with their weights. The
algorithm must immediately either match l to an available vertex of R, or
decide that l will remain unmatched.
Dimitrov and Plaxton show a 16-competitive algorithm for the transversal
matroid secretary problem, which is the special case with weights on vertices,
not edges. (Equivalently, one may assume that for each l \in L, the weights on
all edges incident to l are identical.) We use a similar algorithm, but
simplify and improve the analysis to obtain a better competitive ratio for the
more general problem. Perhaps of more interest is the fact that our analysis is
easily extended to obtain competitive algorithms for similar problems, such as
to find disjoint sets of edges in hypergraphs where edges arrive online. We
also introduce secretary problems with adversarially chosen groups. Finally, we
give a 2e-competitive algorithm for the secretary problem on graphic matroids,
where, with edges appearing online, the goal is to find a maximum-weight
acyclic subgraph of a given graph.
| [
{
"version": "v1",
"created": "Mon, 7 Jul 2008 22:51:46 GMT"
}
] | 2008-07-09T00:00:00 | [
[
"Korula",
"Nitish",
""
],
[
"Pal",
"Martin",
""
]
] |
0807.1277 | David Gamarnik | David Gamarnik and David Goldberg | Randomized greedy algorithms for independent sets and matchings in
regular graphs: Exact results and finite girth corrections | 24 pages | null | null | null | cs.DM cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We derive new results for the performance of a simple greedy algorithm for
finding large independent sets and matchings in constant degree regular graphs.
We show that for $r$-regular graphs with $n$ nodes and girth at least $g$, the
algorithm finds an independent set of expected cardinality $f(r)n -
O\big(\frac{(r-1)^{\frac{g}{2}}}{\frac{g}{2}!} n\big)$, where $f(r)$ is a
function which we explicitly compute. A similar result is established for
matchings. Our results imply improved bounds for the size of the largest
independent set in these graphs, and provide the first results of this type for
matchings. As an implication we show that the greedy algorithm returns a nearly
perfect matching when both the degree $r$ and girth $g$ are large. Furthermore,
we show that the cardinality of independent sets and matchings produced by the
greedy algorithm in \emph{arbitrary} bounded degree graphs is concentrated
around the mean. Finally, we analyze the performance of the greedy algorithm
for the case of random i.i.d. weighted independent sets and matchings, and
obtain a remarkably simple expression for the limiting expected values produced
by the algorithm. In fact, all the other results are obtained as
straightforward corollaries from the results for the weighted case.
| [
{
"version": "v1",
"created": "Tue, 8 Jul 2008 15:29:42 GMT"
}
] | 2008-07-09T00:00:00 | [
[
"Gamarnik",
"David",
""
],
[
"Goldberg",
"David",
""
]
] |
0807.1891 | Benjmain Moseley | Chandra Chekuri and Benjamin Moseley | Online Scheduling to Minimize the Maximum Delay Factor | null | null | null | null | cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | In this paper two scheduling models are addressed. First is the standard
model (unicast) where requests (or jobs) are independent. The other is the
broadcast model where broadcasting a page can satisfy multiple outstanding
requests for that page. We consider online scheduling of requests when they
have deadlines. Unlike previous models, which mainly consider the objective of
maximizing throughput while respecting deadlines, here we focus on scheduling
all the given requests with the goal of minimizing the maximum {\em delay
factor}.We prove strong lower bounds on the achievable competitive ratios for
delay factor scheduling even with unit-time requests.For the unicast model we
give algorithms that are $(1 + \eps)$-speed $O({1 \over \eps})$-competitive in
both the single machine and multiple machine settings. In the broadcast model
we give an algorithm for similar-sized pages that is $(2+ \eps)$-speed $O({1
\over \eps^2})$-competitive. For arbitrary page sizes we give an algorithm that
is $(4+\eps)$-speed $O({1 \over \eps^2})$-competitive.
| [
{
"version": "v1",
"created": "Fri, 11 Jul 2008 17:00:07 GMT"
}
] | 2008-07-14T00:00:00 | [
[
"Chekuri",
"Chandra",
""
],
[
"Moseley",
"Benjamin",
""
]
] |
0807.2120 | Robin Moser | Robin A. Moser | Derandomizing the Lovasz Local Lemma more effectively | 8 pages; added acknowledgement | null | null | null | cs.DS cs.CC | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | The famous Lovasz Local Lemma [EL75] is a powerful tool to non-constructively
prove the existence of combinatorial objects meeting a prescribed collection of
criteria. Kratochvil et al. applied this technique to prove that a k-CNF in
which each variable appears at most 2^k/(ek) times is always satisfiable
[KST93]. In a breakthrough paper, Beck found that if we lower the occurrences
to O(2^(k/48)/k), then a deterministic polynomial-time algorithm can find a
satisfying assignment to such an instance [Bec91]. Alon randomized the
algorithm and required O(2^(k/8)/k) occurrences [Alo91]. In [Mos06], we
exhibited a refinement of his method which copes with O(2^(k/6)/k) of them. The
hitherto best known randomized algorithm is due to Srinivasan and is capable of
solving O(2^(k/4)/k) occurrence instances [Sri08]. Answering two questions
asked by Srinivasan, we shall now present an approach that tolerates
O(2^(k/2)/k) occurrences per variable and which can most easily be
derandomized. The new algorithm bases on an alternative type of witness tree
structure and drops a number of limiting aspects common to all previous
methods.
| [
{
"version": "v1",
"created": "Mon, 14 Jul 2008 09:55:09 GMT"
},
{
"version": "v2",
"created": "Mon, 15 Sep 2008 13:57:58 GMT"
}
] | 2008-09-15T00:00:00 | [
[
"Moser",
"Robin A.",
""
]
] |
0807.2178 | Bernd G\"artner | Bernd G\"artner | Ranking Unit Squares with Few Visibilities | 4 pages, 2 EPS-figures | null | null | null | cs.CG cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Given a set of n unit squares in the plane, the goal is to rank them in space
in such a way that only few squares see each other vertically. We prove that
ranking the squares according to the lexicographic order of their centers
results in at most 3n-7 pairwise visibilities for n at least 4. We also show
that this bound is best possible, by exhibiting a set of n squares with at
least 3n-7 pairwise visibilities under any ranking.
| [
{
"version": "v1",
"created": "Mon, 14 Jul 2008 15:23:52 GMT"
}
] | 2008-07-15T00:00:00 | [
[
"Gärtner",
"Bernd",
""
]
] |
0807.2269 | Michel Rueher | Alexandre Goldsztejn (LINA), Claude Michel (I3S, Laboratoire I3S),
Michel Rueher (I3S, Laboratoire I3S) | An Efficient Algorithm for a Sharp Approximation of Universally
Quantified Inequalities | ACM symposium on Applied computing, Fortaleza, Ceara : Br\'esil
(2008) | null | null | null | cs.NA cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | This paper introduces a new algorithm for solving a sub-class of quantified
constraint satisfaction problems (QCSP) where existential quantifiers precede
universally quantified inequalities on continuous domains. This class of QCSPs
has numerous applications in engineering and design. We propose here a new
generic branch and prune algorithm for solving such continuous QCSPs. Standard
pruning operators and solution identification operators are specialized for
universally quantified inequalities. Special rules are also proposed for
handling the parameters of the constraints. First experimentation show that our
algorithm outperforms the state of the art methods.
| [
{
"version": "v1",
"created": "Tue, 15 Jul 2008 14:45:38 GMT"
}
] | 2008-07-16T00:00:00 | [
[
"Goldsztejn",
"Alexandre",
"",
"LINA"
],
[
"Michel",
"Claude",
"",
"I3S, Laboratoire I3S"
],
[
"Rueher",
"Michel",
"",
"I3S, Laboratoire I3S"
]
] |
0807.2330 | Antonios Symvonis | Tamara Mchedlidze, Antonios Symvonis | Optimal Acyclic Hamiltonian Path Completion for Outerplanar Triangulated
st-Digraphs (with Application to Upward Topological Book Embeddings) | null | null | null | null | cs.DS cs.DM | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Given an embedded planar acyclic digraph G, we define the problem of "acyclic
hamiltonian path completion with crossing minimization (Acyclic-HPCCM)" to be
the problem of determining an hamiltonian path completion set of edges such
that, when these edges are embedded on G, they create the smallest possible
number of edge crossings and turn G to a hamiltonian digraph. Our results
include:
--We provide a characterization under which a triangulated st-digraph G is
hamiltonian.
--For an outerplanar triangulated st-digraph G, we define the st-polygon
decomposition of G and, based on its properties, we develop a linear-time
algorithm that solves the Acyclic-HPCCM problem with at most one crossing per
edge of G.
--For the class of st-planar digraphs, we establish an equivalence between
the Acyclic-HPCCM problem and the problem of determining an upward 2-page
topological book embedding with minimum number of spine crossings. We infer
(based on this equivalence) for the class of outerplanar triangulated
st-digraphs an upward topological 2-page book embedding with minimum number of
spine crossings and at most one spine crossing per edge.
To the best of our knowledge, it is the first time that edge-crossing
minimization is studied in conjunction with the acyclic hamiltonian completion
problem and the first time that an optimal algorithm with respect to spine
crossing minimization is presented for upward topological book embeddings.
| [
{
"version": "v1",
"created": "Tue, 15 Jul 2008 10:12:03 GMT"
},
{
"version": "v2",
"created": "Thu, 24 Jul 2008 21:50:12 GMT"
}
] | 2008-07-25T00:00:00 | [
[
"Mchedlidze",
"Tamara",
""
],
[
"Symvonis",
"Antonios",
""
]
] |
0807.2496 | Ashish Goel | Ashish Goel and Kamesh Munagala | Hybrid Keyword Search Auctions | null | null | null | null | cs.GT cs.DS cs.IR | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Search auctions have become a dominant source of revenue generation on the
Internet. Such auctions have typically used per-click bidding and pricing. We
propose the use of hybrid auctions where an advertiser can make a
per-impression as well as a per-click bid, and the auctioneer then chooses one
of the two as the pricing mechanism. We assume that the advertiser and the
auctioneer both have separate beliefs (called priors) on the click-probability
of an advertisement. We first prove that the hybrid auction is truthful,
assuming that the advertisers are risk-neutral. We then show that this auction
is superior to the existing per-click auction in multiple ways: 1) It takes
into account the risk characteristics of the advertisers. 2) For obscure
keywords, the auctioneer is unlikely to have a very sharp prior on the
click-probabilities. In such situations, the hybrid auction can result in
significantly higher revenue. 3) An advertiser who believes that its
click-probability is much higher than the auctioneer's estimate can use
per-impression bids to correct the auctioneer's prior without incurring any
extra cost. 4) The hybrid auction can allow the advertiser and auctioneer to
implement complex dynamic programming strategies. As Internet commerce matures,
we need more sophisticated pricing models to exploit all the information held
by each of the participants. We believe that hybrid auctions could be an
important step in this direction.
| [
{
"version": "v1",
"created": "Wed, 16 Jul 2008 04:04:32 GMT"
},
{
"version": "v2",
"created": "Mon, 26 Jan 2009 01:00:16 GMT"
}
] | 2009-01-26T00:00:00 | [
[
"Goel",
"Ashish",
""
],
[
"Munagala",
"Kamesh",
""
]
] |
0807.2694 | Fei Li | Fei Li | Algorithms for Scheduling Weighted Packets with Deadlines in a Bounded
Queue | 19 pages. Appears in the Proceedings of the 28th IEEE International
Conference on Computer Communications (INFOCOM 2009) | null | null | null | cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Motivated by the Quality-of-Service (QoS) buffer management problem, we
consider online scheduling of packets with hard deadlines in a finite capacity
queue. At any time, a queue can store at most $b \in \mathbb Z^+$ packets.
Packets arrive over time. Each packet is associated with a non-negative value
and an integer deadline. In each time step, only one packet is allowed to be
sent. Our objective is to maximize the total value gained by the packets sent
by their deadlines in an online manner. Due to the Internet traffic's chaotic
characteristics, no stochastic assumptions are made on the packet input
sequences. This model is called a {\em finite-queue model}.
We use competitive analysis to measure an online algorithm's performance
versus an unrealizable optimal offline algorithm who constructs the worst
possible input based on the knowledge of the online algorithm. For the
finite-queue model, we first present a deterministic 3-competitive memoryless
online algorithm. Then, we give a randomized ($\phi^2 = ((1 + \sqrt{5}) / 2)^2
\approx 2.618$)-competitive memoryless online algorithm.
The algorithmic framework and its theoretical analysis include several
interesting features. First, our algorithms use (possibly) modified
characteristics of packets; these characteristics may not be same as those
specified in the input sequence. Second, our analysis method is different from
the classical potential function approach.
| [
{
"version": "v1",
"created": "Thu, 17 Jul 2008 04:58:30 GMT"
},
{
"version": "v2",
"created": "Wed, 12 Nov 2008 01:44:22 GMT"
},
{
"version": "v3",
"created": "Mon, 17 Nov 2008 22:32:16 GMT"
},
{
"version": "v4",
"created": "Sat, 7 Feb 2009 21:53:00 GMT"
}
] | 2009-02-09T00:00:00 | [
[
"Li",
"Fei",
""
]
] |
0807.3006 | Enoch Peserico | Enoch Peserico and Luca Pretto | The rank convergence of HITS can be slow | 5 pages, 1 figure. Keywords: algorithm analysis, information
retrieval, rank convergence | null | null | null | cs.DS cs.IR | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We prove that HITS, to "get right" h of the top k ranked nodes of an N>=2k
node graph, can require h^(Omega(N h/k)) iterations (i.e. a substantial Omega(N
h log(h)/k) matrix multiplications even with a "squaring trick"). Our proof
requires no algebraic tools and is entirely self-contained.
| [
{
"version": "v1",
"created": "Fri, 18 Jul 2008 16:42:57 GMT"
}
] | 2008-07-21T00:00:00 | [
[
"Peserico",
"Enoch",
""
],
[
"Pretto",
"Luca",
""
]
] |
0807.3026 | Ryan Williams | Ryan Williams | Finding paths of length k in O*(2^k) time | 7 pages. Revised version to appear in Information Processing Letters | Information Processing Letters, 109(6):315--318, February 2009 | null | null | cs.DS cs.DM | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We give a randomized algorithm that determines if a given graph has a simple
path of length at least k in O(2^k poly(n,k)) time.
| [
{
"version": "v1",
"created": "Fri, 18 Jul 2008 18:25:15 GMT"
},
{
"version": "v2",
"created": "Wed, 23 Jul 2008 18:54:40 GMT"
},
{
"version": "v3",
"created": "Sun, 9 Nov 2008 01:04:01 GMT"
}
] | 2010-01-05T00:00:00 | [
[
"Williams",
"Ryan",
""
]
] |
0807.3387 | Jeremy Sumner | J. G. Sumner and M. A. Charleston | Phylogenetic estimation with partial likelihood tensors | 20 pages, 7 figures, 3 tables | null | null | null | q-bio.QM cs.DS q-bio.PE | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We present an alternative method for calculating likelihoods in molecular
phylogenetics. Our method is based on partial likelihood tensors, which are
generalizations of partial likelihood vectors, as used in Felsenstein's
approach. Exploiting a lexicographic sorting and partial likelihood tensors, it
is possible to obtain significant computational savings. We show this on a
range of simulated data by enumerating all numerical calculations that are
required by our method and the standard approach.
| [
{
"version": "v1",
"created": "Tue, 22 Jul 2008 04:24:11 GMT"
}
] | 2008-07-23T00:00:00 | [
[
"Sumner",
"J. G.",
""
],
[
"Charleston",
"M. A.",
""
]
] |
0807.4234 | Stavros Nikolopoulos D. | Kyriaki Ioannidou and Stavros D. Nikolopoulos | Linear Coloring and Linear Graphs | 21 pages, 7 figures | null | null | null | cs.DM cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Motivated by the definition of linear coloring on simplicial complexes,
recently introduced in the context of algebraic topology \cite{Civan}, and the
framework through which it was studied, we introduce the linear coloring on
graphs. We provide an upper bound for the chromatic number $\chi(G)$, for any
graph $G$, and show that $G$ can be linearly colored in polynomial time by
proposing a simple linear coloring algorithm. Based on these results, we define
a new class of perfect graphs, which we call co-linear graphs, and study their
complement graphs, namely linear graphs. The linear coloring of a graph $G$ is
a vertex coloring such that two vertices can be assigned the same color, if
their corresponding clique sets are associated by the set inclusion relation (a
clique set of a vertex $u$ is the set of all maximal cliques containing $u$);
the linear chromatic number $\mathcal{\lambda}(G)$ of $G$ is the least integer
$k$ for which $G$ admits a linear coloring with $k$ colors. We show that linear
graphs are those graphs $G$ for which the linear chromatic number achieves its
theoretical lower bound in every induced subgraph of $G$. We prove inclusion
relations between these two classes of graphs and other subclasses of chordal
and co-chordal graphs, and also study the structure of the forbidden induced
subgraphs of the class of linear graphs.
| [
{
"version": "v1",
"created": "Sat, 26 Jul 2008 12:04:27 GMT"
}
] | 2008-07-29T00:00:00 | [
[
"Ioannidou",
"Kyriaki",
""
],
[
"Nikolopoulos",
"Stavros D.",
""
]
] |
0807.4368 | Dimitris Papamichail | Dimitris Papamichail and Georgios Papamichail | Improved Algorithms for Approximate String Matching (Extended Abstract) | 10 pages | null | null | null | cs.DS | http://creativecommons.org/licenses/by-nc-sa/3.0/ | The problem of approximate string matching is important in many different
areas such as computational biology, text processing and pattern recognition. A
great effort has been made to design efficient algorithms addressing several
variants of the problem, including comparison of two strings, approximate
pattern identification in a string or calculation of the longest common
subsequence that two strings share.
We designed an output sensitive algorithm solving the edit distance problem
between two strings of lengths n and m respectively in time
O((s-|n-m|)min(m,n,s)+m+n) and linear space, where s is the edit distance
between the two strings. This worst-case time bound sets the quadratic factor
of the algorithm independent of the longest string length and improves existing
theoretical bounds for this problem. The implementation of our algorithm excels
also in practice, especially in cases where the two strings compared differ
significantly in length. Source code of our algorithm is available at
http://www.cs.miami.edu/\~dimitris/edit_distance
| [
{
"version": "v1",
"created": "Mon, 28 Jul 2008 07:17:57 GMT"
}
] | 2008-07-29T00:00:00 | [
[
"Papamichail",
"Dimitris",
""
],
[
"Papamichail",
"Georgios",
""
]
] |
0807.4479 | Yago Ascasibar | Yago Ascasibar | FiEstAS sampling -- a Monte Carlo algorithm for multidimensional
numerical integration | 18 pages, 3 figures, submitted to Comp. Phys. Comm | null | 10.1016/j.cpc.2008.07.011 | null | astro-ph cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | This paper describes a new algorithm for Monte Carlo integration, based on
the Field Estimator for Arbitrary Spaces (FiEstAS). The algorithm is discussed
in detail, and its performance is evaluated in the context of Bayesian
analysis, with emphasis on multimodal distributions with strong parameter
degeneracies. Source code is available upon request.
| [
{
"version": "v1",
"created": "Mon, 28 Jul 2008 15:47:20 GMT"
}
] | 2009-11-13T00:00:00 | [
[
"Ascasibar",
"Yago",
""
]
] |
0807.4582 | Ashish Goel | Douglas E. Carroll and Ashish Goel | Lower Bounds for Embedding into Distributions over Excluded Minor Graph
Families | null | null | null | null | cs.DS cs.DM | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | It was shown recently by Fakcharoenphol et al that arbitrary finite metrics
can be embedded into distributions over tree metrics with distortion O(log n).
It is also known that this bound is tight since there are expander graphs which
cannot be embedded into distributions over trees with better than Omega(log n)
distortion.
We show that this same lower bound holds for embeddings into distributions
over any minor excluded family. Given a family of graphs F which excludes minor
M where |M|=k, we explicitly construct a family of graphs with treewidth-(k+1)
which cannot be embedded into a distribution over F with better than Omega(log
n) distortion. Thus, while these minor excluded families of graphs are more
expressive than trees, they do not provide asymptotically better approximations
in general. An important corollary of this is that graphs of treewidth-k cannot
be embedded into distributions over graphs of treewidth-(k-3) with distortion
less than Omega(log n).
We also extend a result of Alon et al by showing that for any k, planar
graphs cannot be embedded into distributions over treewidth-k graphs with
better than Omega(log n) distortion.
| [
{
"version": "v1",
"created": "Tue, 29 Jul 2008 07:52:57 GMT"
}
] | 2008-07-30T00:00:00 | [
[
"Carroll",
"Douglas E.",
""
],
[
"Goel",
"Ashish",
""
]
] |
0807.4626 | Assaf Naor | Subhash Khot and Assaf Naor | Approximate kernel clustering | null | null | null | null | cs.DS cs.CC math.FA | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | In the kernel clustering problem we are given a large $n\times n$ positive
semi-definite matrix $A=(a_{ij})$ with $\sum_{i,j=1}^na_{ij}=0$ and a small
$k\times k$ positive semi-definite matrix $B=(b_{ij})$. The goal is to find a
partition $S_1,...,S_k$ of $\{1,... n\}$ which maximizes the quantity $$
\sum_{i,j=1}^k (\sum_{(i,j)\in S_i\times S_j}a_{ij})b_{ij}. $$ We study the
computational complexity of this generic clustering problem which originates in
the theory of machine learning. We design a constant factor polynomial time
approximation algorithm for this problem, answering a question posed by Song,
Smola, Gretton and Borgwardt. In some cases we manage to compute the sharp
approximation threshold for this problem assuming the Unique Games Conjecture
(UGC). In particular, when $B$ is the $3\times 3$ identity matrix the UGC
hardness threshold of this problem is exactly $\frac{16\pi}{27}$. We present
and study a geometric conjecture of independent interest which we show would
imply that the UGC threshold when $B$ is the $k\times k$ identity matrix is
$\frac{8\pi}{9}(1-\frac{1}{k})$ for every $k\ge 3$.
| [
{
"version": "v1",
"created": "Tue, 29 Jul 2008 10:40:55 GMT"
},
{
"version": "v2",
"created": "Tue, 9 Dec 2008 20:48:32 GMT"
}
] | 2008-12-09T00:00:00 | [
[
"Khot",
"Subhash",
""
],
[
"Naor",
"Assaf",
""
]
] |
0807.5111 | Atish Das Sarma | Atish Das Sarma, Amit Deshpande, Ravi Kannan | Finding Dense Subgraphs in G(n,1/2) | 6 pages | null | null | null | cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Finding the largest clique is a notoriously hard problem, even on random
graphs. It is known that the clique number of a random graph G(n,1/2) is almost
surely either k or k+1, where k = 2log n - 2log(log n) - 1. However, a simple
greedy algorithm finds a clique of size only (1+o(1))log n, with high
probability, and finding larger cliques -- that of size even (1+ epsilon)log n
-- in randomized polynomial time has been a long-standing open problem. In this
paper, we study the following generalization: given a random graph G(n,1/2),
find the largest subgraph with edge density at least (1-delta). We show that a
simple modification of the greedy algorithm finds a subset of 2log n vertices
whose induced subgraph has edge density at least 0.951, with high probability.
To complement this, we show that almost surely there is no subset of 2.784log n
vertices whose induced subgraph has edge density 0.951 or more.
| [
{
"version": "v1",
"created": "Thu, 31 Jul 2008 17:12:25 GMT"
},
{
"version": "v2",
"created": "Mon, 22 Sep 2008 15:23:43 GMT"
}
] | 2008-09-22T00:00:00 | [
[
"Sarma",
"Atish Das",
""
],
[
"Deshpande",
"Amit",
""
],
[
"Kannan",
"Ravi",
""
]
] |
0808.0084 | Frederic Magniez | Frederic Magniez, Ashwin Nayak, Peter C. Richter, and Miklos Santha | On the hitting times of quantum versus random walks | null | null | null | null | quant-ph cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | In this paper we define new Monte Carlo type classical and quantum hitting
times, and we prove several relationships among these and the already existing
Las Vegas type definitions. In particular, we show that for some marked state
the two types of hitting time are of the same order in both the classical and
the quantum case.
Further, we prove that for any reversible ergodic Markov chain $P$, the
quantum hitting time of the quantum analogue of $P$ has the same order as the
square root of the classical hitting time of $P$. We also investigate the
(im)possibility of achieving a gap greater than quadratic using an alternative
quantum walk.
Finally, we present new quantum algorithms for the detection and finding
problems. The complexities of both algorithms are related to the new,
potentially smaller, quantum hitting times. The detection algorithm is based on
phase estimation and is particularly simple. The finding algorithm combines a
similar phase estimation based procedure with ideas of Tulsi from his recent
theorem for the 2D grid. Extending his result, we show that for any
state-transitive Markov chain with unique marked state, the quantum hitting
time is of the same order for both the detection and finding problems.
| [
{
"version": "v1",
"created": "Fri, 1 Aug 2008 14:45:51 GMT"
}
] | 2018-03-22T00:00:00 | [
[
"Magniez",
"Frederic",
""
],
[
"Nayak",
"Ashwin",
""
],
[
"Richter",
"Peter C.",
""
],
[
"Santha",
"Miklos",
""
]
] |
0808.0148 | James Lee | Punyashloka Biswal, James R. Lee, Satish Rao | Eigenvalue bounds, spectral partitioning, and metrical deformations via
flows | Minor revisions | null | null | null | cs.DS cs.CG math.MG math.SP | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We present a new method for upper bounding the second eigenvalue of the
Laplacian of graphs. Our approach uses multi-commodity flows to deform the
geometry of the graph; we embed the resulting metric into Euclidean space to
recover a bound on the Rayleigh quotient. Using this, we show that every
$n$-vertex graph of genus $g$ and maximum degree $d$ satisfies $\lambda_2(G) =
O((g+1)^3 d/n)$. This recovers the $O(d/n)$ bound of Spielman and Teng for
planar graphs, and compares to Kelner's bound of $O((g+1) poly(d)/n)$, but our
proof does not make use of conformal mappings or circle packings. We are thus
able to extend this to resolve positively a conjecture of Spielman and Teng, by
proving that $\lambda_2(G) = O(d h^6 \log h/n)$ whenever $G$ is $K_h$-minor
free. This shows, in particular, that spectral partitioning can be used to
recover $O(\sqrt{n})$-sized separators in bounded degree graphs that exclude a
fixed minor. We extend this further by obtaining nearly optimal bounds on
$\lambda_2$ for graphs which exclude small-depth minors in the sense of
Plotkin, Rao, and Smith. Consequently, we show that spectral algorithms find
small separators in a general class of geometric graphs.
Moreover, while the standard "sweep" algorithm applied to the second
eigenvector may fail to find good quotient cuts in graphs of unbounded degree,
our approach produces a vector that works for arbitrary graphs. This yields an
alternate proof of the result of Alon, Seymour, and Thomas that every
excluded-minor family of graphs has $O(\sqrt{n})$-node balanced separators.
| [
{
"version": "v1",
"created": "Fri, 1 Aug 2008 16:45:16 GMT"
},
{
"version": "v2",
"created": "Sat, 9 Aug 2008 15:54:35 GMT"
}
] | 2008-08-09T00:00:00 | [
[
"Biswal",
"Punyashloka",
""
],
[
"Lee",
"James R.",
""
],
[
"Rao",
"Satish",
""
]
] |
0808.0159 | Eli Ben-Naim | T. Antal, D. ben-Avraham, E. Ben-Naim, P.L. Krapivsky | Front Propagation with Rejuvenation in Flipping Processes | 10 pages, 9 figures, 4 tables | J. Phys. A 41, 465002 (2008) | 10.1088/1751-8113/41/46/465002 | null | cond-mat.stat-mech cs.DS math.PR | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We study a directed flipping process that underlies the performance of the
random edge simplex algorithm. In this stochastic process, which takes place on
a one-dimensional lattice whose sites may be either occupied or vacant,
occupied sites become vacant at a constant rate and simultaneously cause all
sites to the right to change their state. This random process exhibits rich
phenomenology. First, there is a front, defined by the position of the
left-most occupied site, that propagates at a nontrivial velocity. Second, the
front involves a depletion zone with an excess of vacant sites. The total
excess D_k increases logarithmically, D_k ~ ln k, with the distance k from the
front. Third, the front exhibits rejuvenation -- young fronts are vigorous but
old fronts are sluggish. We investigate these phenomena using a quasi-static
approximation, direct solutions of small systems, and numerical simulations.
| [
{
"version": "v1",
"created": "Fri, 1 Aug 2008 17:44:13 GMT"
}
] | 2008-10-16T00:00:00 | [
[
"Antal",
"T.",
""
],
[
"ben-Avraham",
"D.",
""
],
[
"Ben-Naim",
"E.",
""
],
[
"Krapivsky",
"P. L.",
""
]
] |
0808.0163 | Daniel A. Spielman | Joshua Batson, Daniel A. Spielman, Nikhil Srivastava | Twice-Ramanujan Sparsifiers | null | null | null | null | cs.DS cs.DM | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We prove that every graph has a spectral sparsifier with a number of edges
linear in its number of vertices. As linear-sized spectral sparsifiers of
complete graphs are expanders, our sparsifiers of arbitrary graphs can be
viewed as generalizations of expander graphs.
In particular, we prove that for every $d>1$ and every undirected, weighted
graph $G=(V,E,w)$ on $n$ vertices, there exists a weighted graph
$H=(V,F,\tilde{w})$ with at most $\ceil{d(n-1)}$ edges such that for every $x
\in \R^{V}$, \[ x^{T}L_{G}x \leq x^{T}L_{H}x \leq
(\frac{d+1+2\sqrt{d}}{d+1-2\sqrt{d}})\cdot x^{T}L_{G}x \] where $L_{G}$ and
$L_{H}$ are the Laplacian matrices of $G$ and $H$, respectively. Thus, $H$
approximates $G$ spectrally at least as well as a Ramanujan expander with
$dn/2$ edges approximates the complete graph. We give an elementary
deterministic polynomial time algorithm for constructing $H$.
| [
{
"version": "v1",
"created": "Fri, 1 Aug 2008 18:19:17 GMT"
},
{
"version": "v2",
"created": "Mon, 1 Dec 2008 19:13:09 GMT"
},
{
"version": "v3",
"created": "Wed, 18 Nov 2009 07:27:03 GMT"
}
] | 2009-11-18T00:00:00 | [
[
"Batson",
"Joshua",
""
],
[
"Spielman",
"Daniel A.",
""
],
[
"Srivastava",
"Nikhil",
""
]
] |
0808.0298 | Dmitrii V. Pasechnik | Edith Elkind and Dmitrii V. Pasechnik | Computing the nucleolus of weighted voting games | LaTeX, 12 pages, COMSOC-2008 workshop | Proceedings of SODA 2009, pp. 327-335 | 10.1145/1496770.1496807 | null | cs.GT cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Weighted voting games (WVG) are coalitional games in which an agent's
contribution to a coalition is given by his it weight, and a coalition wins if
its total weight meets or exceeds a given quota. These games model
decision-making in political bodies as well as collaboration and surplus
division in multiagent domains. The computational complexity of various
solution concepts for weighted voting games received a lot of attention in
recent years. In particular, Elkind et al.(2007) studied the complexity of
stability-related solution concepts in WVGs, namely, of the core, the least
core, and the nucleolus. While they have completely characterized the
algorithmic complexity of the core and the least core, for the nucleolus they
have only provided an NP-hardness result. In this paper, we solve an open
problem posed by Elkind et al. by showing that the nucleolus of WVGs, and, more
generally, k-vector weighted voting games with fixed k, can be computed in
pseudopolynomial time, i.e., there exists an algorithm that correctly computes
the nucleolus and runs in time polynomial in the number of players and the
maximum weight. In doing so, we propose a general framework for computing the
nucleolus, which may be applicable to a wider of class of games.
| [
{
"version": "v1",
"created": "Sun, 3 Aug 2008 05:22:47 GMT"
}
] | 2010-10-21T00:00:00 | [
[
"Elkind",
"Edith",
""
],
[
"Pasechnik",
"Dmitrii V.",
""
]
] |
0808.0540 | Paul Tarau | Paul Tarau | Executable Set Theory and Arithmetic Encodings in Prolog | Unpublished draft | null | null | null | cs.LO cs.DM cs.DS cs.MS cs.SC | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | The paper is organized as a self-contained literate Prolog program that
implements elements of an executable finite set theory with focus on
combinatorial generation and arithmetic encodings. The complete Prolog code is
available at http://logic.csci.unt.edu/tarau/research/2008/pHFS.zip . First,
ranking and unranking functions for some "mathematically elegant" data types in
the universe of Hereditarily Finite Sets with Urelements are provided,
resulting in arithmetic encodings for powersets, hypergraphs, ordinals and
choice functions. After implementing a digraph representation of Hereditarily
Finite Sets we define {\em decoration functions} that can recover well-founded
sets from encodings of their associated acyclic digraphs. We conclude with an
encoding of arbitrary digraphs and discuss a concept of duality induced by the
set membership relation. In the process, we uncover the surprising possibility
of internally sharing isomorphic objects, independently of their language level
types and meanings.
| [
{
"version": "v1",
"created": "Tue, 5 Aug 2008 04:59:56 GMT"
}
] | 2009-09-29T00:00:00 | [
[
"Tarau",
"Paul",
""
]
] |
0808.0753 | Paul Tarau | Paul Tarau | Ranking Catamorphisms and Unranking Anamorphisms on Hereditarily Finite
Datatypes | unpublished draft | null | null | null | cs.SC cs.DM cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Using specializations of unfold and fold on a generic tree data type we
derive unranking and ranking functions providing natural number encodings for
various Hereditarily Finite datatypes.
In this context, we interpret unranking operations as instances of a generic
anamorphism and ranking operations as instances of the corresponding
catamorphism.
Starting with Ackerman's Encoding from Hereditarily Finite Sets to Natural
Numbers we define pairings and tuple encodings that provide building blocks for
a theory of Hereditarily Finite Functions.
The more difficult problem of ranking and unranking Hereditarily Finite
Permutations is then tackled using Lehmer codes and factoradics.
The self-contained source code of the paper, as generated from a literate
Haskell program, is available at
\url{http://logic.csci.unt.edu/tarau/research/2008/fFUN.zip}.
Keywords: ranking/unranking, pairing/tupling functions, Ackermann encoding,
hereditarily finite sets, hereditarily finite functions, permutations and
factoradics, computational mathematics, Haskell data representations
| [
{
"version": "v1",
"created": "Wed, 6 Aug 2008 00:54:05 GMT"
}
] | 2008-08-07T00:00:00 | [
[
"Tarau",
"Paul",
""
]
] |
0808.0754 | Paul Tarau | Paul Tarau | A Functional Hitchhiker's Guide to Hereditarily Finite Sets, Ackermann
Encodings and Pairing Functions | unpublished draft | null | null | null | cs.MS cs.DM cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | The paper is organized as a self-contained literate Haskell program that
implements elements of an executable finite set theory with focus on
combinatorial generation and arithmetic encodings. The code, tested under GHC
6.6.1, is available at http://logic.csci.unt.edu/tarau/research/2008/fSET.zip .
We introduce ranking and unranking functions generalizing Ackermann's
encoding to the universe of Hereditarily Finite Sets with Urelements. Then we
build a lazy enumerator for Hereditarily Finite Sets with Urelements that
matches the unranking function provided by the inverse of Ackermann's encoding
and we describe functors between them resulting in arithmetic encodings for
powersets, hypergraphs, ordinals and choice functions. After implementing a
digraph representation of Hereditarily Finite Sets we define {\em decoration
functions} that can recover well-founded sets from encodings of their
associated acyclic digraphs. We conclude with an encoding of arbitrary digraphs
and discuss a concept of duality induced by the set membership relation.
Keywords: hereditarily finite sets, ranking and unranking functions,
executable set theory, arithmetic encodings, Haskell data representations,
functional programming and computational mathematics
| [
{
"version": "v1",
"created": "Wed, 6 Aug 2008 01:05:09 GMT"
}
] | 2008-08-07T00:00:00 | [
[
"Tarau",
"Paul",
""
]
] |
0808.0760 | Paul Tarau | Paul Tarau | Declarative Combinatorics: Boolean Functions, Circuit Synthesis and BDDs
in Haskell | unpublished draft | null | null | null | cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We describe Haskell implementations of interesting combinatorial generation
algorithms with focus on boolean functions and logic circuit representations.
First, a complete exact combinational logic circuit synthesizer is described
as a combination of catamorphisms and anamorphisms.
Using pairing and unpairing functions on natural number representations of
truth tables, we derive an encoding for Binary Decision Diagrams (BDDs) with
the unique property that its boolean evaluation faithfully mimics its
structural conversion to a a natural number through recursive application of a
matching pairing function.
We then use this result to derive ranking and unranking functions for BDDs
and reduced BDDs.
Finally, a generalization of the encoding techniques to Multi-Terminal BDDs
is provided.
The paper is organized as a self-contained literate Haskell program,
available at http://logic.csci.unt.edu/tarau/research/2008/fBDD.zip .
Keywords: exact combinational logic synthesis, binary decision diagrams,
encodings of boolean functions, pairing/unpairing functions, ranking/unranking
functions for BDDs and MTBDDs, declarative combinatorics in Haskell
| [
{
"version": "v1",
"created": "Wed, 6 Aug 2008 01:41:51 GMT"
}
] | 2008-08-07T00:00:00 | [
[
"Tarau",
"Paul",
""
]
] |
0808.0980 | Gregory Gutin | Peter Dankelmann, Gregory Gutin, Eun Jung Kim | On Complexity of Minimum Leaf Out-branching Problem | null | null | null | null | cs.DS cs.CC | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Given a digraph $D$, the Minimum Leaf Out-Branching problem (MinLOB) is the
problem of finding in $D$ an out-branching with the minimum possible number of
leaves, i.e., vertices of out-degree 0. Gutin, Razgon and Kim (2008) proved
that MinLOB is polynomial time solvable for acyclic digraphs which are exactly
the digraphs of directed path-width (DAG-width, directed tree-width,
respectively) 0. We investigate how much one can extend this polynomiality
result. We prove that already for digraphs of directed path-width (directed
tree-width, DAG-width, respectively) 1, MinLOB is NP-hard. On the other hand,
we show that for digraphs of restricted directed tree-width (directed
path-width, DAG-width, respectively) and a fixed integer $k$, the problem of
checking whether there is an out-branching with at most $k$ leaves is
polynomial time solvable.
| [
{
"version": "v1",
"created": "Thu, 7 Aug 2008 08:41:48 GMT"
}
] | 2008-08-08T00:00:00 | [
[
"Dankelmann",
"Peter",
""
],
[
"Gutin",
"Gregory",
""
],
[
"Kim",
"Eun Jung",
""
]
] |
0808.1108 | Nicolas Bock | Nicolas Bock and Emanuel H. Rubensson and Pawe{\l} Sa{\l}ek and Anders
M. N. Niklasson and Matt Challacombe | Cache oblivious storage and access heuristics for blocked matrix-matrix
multiplication | Fixed typos | null | null | null | cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We investigate effects of ordering in blocked matrix--matrix multiplication.
We find that submatrices do not have to be stored contiguously in memory to
achieve near optimal performance. Instead it is the choice of execution order
of the submatrix multiplications that leads to a speedup of up to four times
for small block sizes. This is in contrast to results for single matrix
elements showing that contiguous memory allocation quickly becomes irrelevant
as the blocksize increases.
| [
{
"version": "v1",
"created": "Thu, 7 Aug 2008 22:49:29 GMT"
},
{
"version": "v2",
"created": "Fri, 15 Aug 2008 14:34:31 GMT"
}
] | 2008-08-15T00:00:00 | [
[
"Bock",
"Nicolas",
""
],
[
"Rubensson",
"Emanuel H.",
""
],
[
"Sałek",
"Paweł",
""
],
[
"Niklasson",
"Anders M. N.",
""
],
[
"Challacombe",
"Matt",
""
]
] |
0808.1128 | Mihai Patrascu | Timothy M. Chan and Mihai Patrascu and Liam Roditty | Dynamic Connectivity: Connecting to Networks and Geometry | Full version of a paper to appear in FOCS 2008 | null | null | null | cs.DS cs.CG | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Dynamic connectivity is a well-studied problem, but so far the most
compelling progress has been confined to the edge-update model: maintain an
understanding of connectivity in an undirected graph, subject to edge
insertions and deletions. In this paper, we study two more challenging, yet
equally fundamental problems.
Subgraph connectivity asks to maintain an understanding of connectivity under
vertex updates: updates can turn vertices on and off, and queries refer to the
subgraph induced by "on" vertices. (For instance, this is closer to
applications in networks of routers, where node faults may occur.)
We describe a data structure supporting vertex updates in O (m^{2/3})
amortized time, where m denotes the number of edges in the graph. This greatly
improves over the previous result [Chan, STOC'02], which required fast matrix
multiplication and had an update time of O(m^0.94). The new data structure is
also simpler.
Geometric connectivity asks to maintain a dynamic set of n geometric objects,
and query connectivity in their intersection graph. (For instance, the
intersection graph of balls describes connectivity in a network of sensors with
bounded transmission radius.)
Previously, nontrivial fully dynamic results were known only for special
cases like axis-parallel line segments and rectangles. We provide similarly
improved update times, O (n^{2/3}), for these special cases. Moreover, we show
how to obtain sublinear update bounds for virtually all families of geometric
objects which allow sublinear-time range queries, such as arbitrary 2D line
segments, d-dimensional simplices, and d-dimensional balls.
| [
{
"version": "v1",
"created": "Thu, 7 Aug 2008 22:16:15 GMT"
}
] | 2008-08-11T00:00:00 | [
[
"Chan",
"Timothy M.",
""
],
[
"Patrascu",
"Mihai",
""
],
[
"Roditty",
"Liam",
""
]
] |
0808.1246 | Mugurel Ionut Andreica | Mugurel Ionut Andreica, Romulus Andreica, Angela Andreica | Minimum Dissatisfaction Personnel Scheduling | Some of the algorithmic techniques presented in this paper were later
used by the first author for developing solutions to several algorithmic
contest tasks (see the attached zip archive for some examples) | ARA Congress, Boston : United States (2008) | null | null | cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | In this paper we consider two problems regarding the scheduling of available
personnel in order to perform a given quantity of work, which can be
arbitrarily decomposed into a sequence of activities. We are interested in
schedules which minimize the overall dissatisfaction, where each employee's
dissatisfaction is modeled as a time-dependent linear function. For the two
situations considered we provide a detailed mathematical analysis, as well as
efficient algorithms for determining optimal schedules.
| [
{
"version": "v1",
"created": "Fri, 8 Aug 2008 17:15:34 GMT"
},
{
"version": "v2",
"created": "Mon, 21 Jan 2013 17:26:48 GMT"
}
] | 2013-01-22T00:00:00 | [
[
"Andreica",
"Mugurel Ionut",
""
],
[
"Andreica",
"Romulus",
""
],
[
"Andreica",
"Angela",
""
]
] |
0808.1671 | Shuchi Chawla | Shuchi Chawla and Jason Hartline and Robert Kleinberg | Algorithmic Pricing via Virtual Valuations | A preliminary version of this work appeared at the ACM EC'07
conference. The current version contains improved results and simpler
algorithms | null | null | null | cs.GT cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Algorithmic pricing is the computational problem that sellers (e.g., in
supermarkets) face when trying to set prices for their items to maximize their
profit in the presence of a known demand. Guruswami et al. (2005) propose this
problem and give logarithmic approximations (in the number of consumers) when
each consumer's values for bundles are known precisely. Subsequently several
versions of the problem have been shown to have poly-logarithmic
inapproximability. This problem has direct ties to the important open question
of better understanding the Bayesian optimal mechanism in multi-parameter
settings; however, logarithmic approximations are inadequate for this purpose.
It is therefore of vital interest to consider special cases where constant
approximations are possible. We consider the unit-demand variant of this
problem. Here a consumer has a valuation for each different item and their
value for a set of items is simply the maximum value they have for any item in
the set. We assume that the preferences of the consumers are drawn from a
distribution, the standard assumption in economics; furthermore, the setting of
a specific set of customers with known preferences, which is employed in all
prior work in algorithmic pricing, is a special case of this general problem,
where there is a discrete Bayesian distribution for preferences specified by
picking one consumer uniformly from the given set of consumers. Our work
complements these existing works by considering the case where the consumer's
valuations for the different items are independent random variables. Our main
result is a constant approximation that makes use of an interesting connection
between this problem and the concept of virtual valuations from the
single-parameter Bayesian optimal mechanism design literature.
| [
{
"version": "v1",
"created": "Tue, 12 Aug 2008 18:08:21 GMT"
}
] | 2008-08-13T00:00:00 | [
[
"Chawla",
"Shuchi",
""
],
[
"Hartline",
"Jason",
""
],
[
"Kleinberg",
"Robert",
""
]
] |
0808.1766 | Ping Li | Ping Li | The Optimal Quantile Estimator for Compressed Counting | null | null | null | null | cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Compressed Counting (CC) was recently proposed for very efficiently computing
the (approximate) $\alpha$th frequency moments of data streams, where $0<\alpha
<= 2$. Several estimators were reported including the geometric mean estimator,
the harmonic mean estimator, the optimal power estimator, etc. The geometric
mean estimator is particularly interesting for theoretical purposes. For
example, when $\alpha -> 1$, the complexity of CC (using the geometric mean
estimator) is $O(1/\epsilon)$, breaking the well-known large-deviation bound
$O(1/\epsilon^2)$. The case $\alpha\approx 1$ has important applications, for
example, computing entropy of data streams.
For practical purposes, this study proposes the optimal quantile estimator.
Compared with previous estimators, this estimator is computationally more
efficient and is also more accurate when $\alpha> 1$.
| [
{
"version": "v1",
"created": "Wed, 13 Aug 2008 01:38:45 GMT"
}
] | 2008-08-14T00:00:00 | [
[
"Li",
"Ping",
""
]
] |
0808.1771 | Ping Li | Ping Li | A Very Efficient Scheme for Estimating Entropy of Data Streams Using
Compressed Counting | null | null | null | null | cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Compressed Counting (CC)} was recently proposed for approximating the
$\alpha$th frequency moments of data streams, for $0<\alpha \leq 2$. Under the
relaxed strict-Turnstile model, CC dramatically improves the standard algorithm
based on symmetric stable random projections}, especially as $\alpha\to 1$. A
direct application of CC is to estimate the entropy, which is an important
summary statistic in Web/network measurement and often serves a crucial
"feature" for data mining. The R\'enyi entropy and the Tsallis entropy are
functions of the $\alpha$th frequency moments; and both approach the Shannon
entropy as $\alpha\to 1$. A recent theoretical work suggested using the
$\alpha$th frequency moment to approximate the Shannon entropy with
$\alpha=1+\delta$ and very small $|\delta|$ (e.g., $<10^{-4}$).
In this study, we experiment using CC to estimate frequency moments, R\'enyi
entropy, Tsallis entropy, and Shannon entropy, on real Web crawl data. We
demonstrate the variance-bias trade-off in estimating Shannon entropy and
provide practical recommendations. In particular, our experiments enable us to
draw some important conclusions:
(1) As $\alpha\to 1$, CC dramatically improves {\em symmetric stable random
projections} in estimating frequency moments, R\'enyi entropy, Tsallis entropy,
and Shannon entropy. The improvements appear to approach "infinity."
(2) Using {\em symmetric stable random projections} and $\alpha = 1+\delta$
with very small $|\delta|$ does not provide a practical algorithm because the
required sample size is enormous.
| [
{
"version": "v1",
"created": "Wed, 13 Aug 2008 03:05:33 GMT"
},
{
"version": "v2",
"created": "Thu, 21 Aug 2008 17:36:19 GMT"
}
] | 2008-08-21T00:00:00 | [
[
"Li",
"Ping",
""
]
] |
0808.1787 | Arnab Bhattacharyya | Arnab Bhattacharyya, Elena Grigorescu, Kyomin Jung, Sofya
Raskhodnikova, David P. Woodruff | Transitive-Closure Spanners | Extended abstract with appendices | null | null | null | cs.DS cs.CC | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Given a directed graph G = (V,E) and an integer k>=1, a
k-transitive-closure-spanner (k-TC-spanner) of G is a directed graph H = (V,
E_H) that has (1) the same transitive-closure as G and (2) diameter at most k.
These spanners were implicitly studied in access control, data structures, and
property testing, and properties of these spanners have been rediscovered over
the span of 20 years. The main goal in each of these applications is to obtain
the sparsest k-TC-spanners. We bring these diverse areas under the unifying
framework of TC-spanners.
We initiate the study of approximability of the size of the sparsest
k-TC-spanner for a given directed graph. We completely resolve the
approximability of 2-TC-spanners, showing that it is Theta(log n) unless P =
NP. For k>2, we present a polynomial-time algorithm that finds a k-TC-spanner
with size within O((n log n)^{1-1/k}) of the optimum. Our algorithmic
techniques also yield algorithms with the best-known approximation ratio for
well-studied problems on directed spanners when k>3: DIRECTED k-SPANNER,
CLIENT/SERVER DIRECTED k-SPANNER, and k-DIAMETER SPANNING SUBGRAPH. For
constant k>=3, we show that the size of the sparsest k-TC-spanner is hard to
approximate with 2^{log^{1-eps} n} ratio unless NP \subseteq DTIME(n^{polylog
n}}). Finally, we study the size of the sparsest k-TC-spanners for H-minor-free
graph families. Combining our constructions with our insight that 2-TC-spanners
can be used for designing property testers, we obtain a monotonicity tester
with O(log^2 n /eps) queries for any poset whose transitive reduction is an
H-minor free digraph, improving the Theta(sqrt(n) log n/eps)-queries required
of the tester due to Fischer et al (2002).
| [
{
"version": "v1",
"created": "Wed, 13 Aug 2008 06:44:10 GMT"
}
] | 2008-08-14T00:00:00 | [
[
"Bhattacharyya",
"Arnab",
""
],
[
"Grigorescu",
"Elena",
""
],
[
"Jung",
"Kyomin",
""
],
[
"Raskhodnikova",
"Sofya",
""
],
[
"Woodruff",
"David P.",
""
]
] |
0808.2017 | Ittai Abraham | Ittai Abraham, Yair Bartal, and Ofer Neiman | Nearly Tight Low Stretch Spanning Trees | null | null | null | null | cs.DS cs.DM | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We prove that any graph $G$ with $n$ points has a distribution $\mathcal{T}$
over spanning trees such that for any edge $(u,v)$ the expected stretch $E_{T
\sim \mathcal{T}}[d_T(u,v)/d_G(u,v)]$ is bounded by $\tilde{O}(\log n)$. Our
result is obtained via a new approach of building ``highways'' between portals
and a new strong diameter probabilistic decomposition theorem.
| [
{
"version": "v1",
"created": "Thu, 14 Aug 2008 15:58:55 GMT"
}
] | 2008-08-15T00:00:00 | [
[
"Abraham",
"Ittai",
""
],
[
"Bartal",
"Yair",
""
],
[
"Neiman",
"Ofer",
""
]
] |
0808.2222 | Andrew McGregor | Alexandr Andoni, Andrew McGregor, Krzysztof Onak, Rina Panigrahy | Better Bounds for Frequency Moments in Random-Order Streams | 4 pages | null | null | null | cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Estimating frequency moments of data streams is a very well studied problem
and tight bounds are known on the amount of space that is necessary and
sufficient when the stream is adversarially ordered. Recently, motivated by
various practical considerations and applications in learning and statistics,
there has been growing interest into studying streams that are randomly
ordered. In the paper we improve the previous lower bounds on the space
required to estimate the frequency moments of a randomly ordered streams.
| [
{
"version": "v1",
"created": "Sat, 16 Aug 2008 00:43:14 GMT"
}
] | 2008-08-19T00:00:00 | [
[
"Andoni",
"Alexandr",
""
],
[
"McGregor",
"Andrew",
""
],
[
"Onak",
"Krzysztof",
""
],
[
"Panigrahy",
"Rina",
""
]
] |
0808.2953 | Paul Tarau | Paul Tarau | Declarative Combinatorics: Isomorphisms, Hylomorphisms and Hereditarily
Finite Data Types in Haskell | unpublished draft, revision 3, added various new encodings, with
focus on primes and multisets, now 104 pages | null | null | null | cs.PL cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | This paper is an exploration in a functional programming framework of {\em
isomorphisms} between elementary data types (natural numbers, sets, multisets,
finite functions, permutations binary decision diagrams, graphs, hypergraphs,
parenthesis languages, dyadic rationals, primes, DNA sequences etc.) and their
extension to hereditarily finite universes through {\em hylomorphisms} derived
from {\em ranking/unranking} and {\em pairing/unpairing} operations.
An embedded higher order {\em combinator language} provides any-to-any
encodings automatically.
Besides applications to experimental mathematics, a few examples of ``free
algorithms'' obtained by transferring operations between data types are shown.
Other applications range from stream iterators on combinatorial objects to
self-delimiting codes, succinct data representations and generation of random
instances.
The paper covers 59 data types and, through the use of the embedded
combinator language, provides 3540 distinct bijective transformations between
them.
The self-contained source code of the paper, as generated from a literate
Haskell program, is available at
\url{http://logic.csci.unt.edu/tarau/research/2008/fISO.zip}.
{\bf Keywords}: Haskell data representations, data type isomorphisms,
declarative combinatorics, computational mathematics, Ackermann encoding,
G\"{o}del numberings, arithmetization, ranking/unranking, hereditarily finite
sets, functions and permutations, encodings of binary decision diagrams, dyadic
rationals, DNA encodings
| [
{
"version": "v1",
"created": "Thu, 21 Aug 2008 16:47:38 GMT"
},
{
"version": "v2",
"created": "Mon, 20 Oct 2008 18:47:59 GMT"
},
{
"version": "v3",
"created": "Tue, 9 Dec 2008 01:28:15 GMT"
},
{
"version": "v4",
"created": "Mon, 19 Jan 2009 19:39:51 GMT"
}
] | 2009-01-19T00:00:00 | [
[
"Tarau",
"Paul",
""
]
] |
0808.3197 | Ming-Zhe Chen | Ming-Zhe Chen | On the Monotonicity of Work Function in k-Server Conjecture | 3 pages, corrected typos | null | null | null | cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | This paper presents a mistake in work function algorithm of k-server
conjecture. That is, the monotonicity of the work function is not always true.
| [
{
"version": "v1",
"created": "Sun, 24 Aug 2008 15:37:35 GMT"
}
] | 2008-08-26T00:00:00 | [
[
"Chen",
"Ming-Zhe",
""
]
] |
0808.3331 | Gregory Karagiorgos | Gregory Karagiorgos, Dimitrios Poulakis | Efficient algorithms for the basis of finite Abelian groups | 11 pages | null | null | null | cs.DS cs.CC | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Let $G$ be a finite abelian group $G$ with $N$ elements. In this paper we
give a O(N) time algorithm for computing a basis of $G$. Furthermore, we obtain
an algorithm for computing a basis from a generating system of $G$ with $M$
elements having time complexity $O(M\sum_{p|N} e(p)\lceil
p^{1/2}\rceil^{\mu(p)})$, where $p$ runs over all the prime divisors of $N$,
and $p^{e(p)}$, $\mu(p)$ are the exponent and the number of cyclic groups which
are direct factors of the $p$-primary component of $G$, respectively. In case
where $G$ is a cyclic group having a generating system with $M$ elements, a
$O(MN^{\epsilon})$ time algorithm for the computation of a basis of $G$ is
obtained.
| [
{
"version": "v1",
"created": "Mon, 25 Aug 2008 11:01:15 GMT"
}
] | 2008-08-26T00:00:00 | [
[
"Karagiorgos",
"Gregory",
""
],
[
"Poulakis",
"Dimitrios",
""
]
] |
0808.3881 | Paul Bonsma | Paul Bonsma, Felix Breuer | Counting Hexagonal Patches and Independent Sets in Circle Graphs | null | null | null | null | cs.DM cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | A hexagonal patch is a plane graph in which inner faces have length 6, inner
vertices have degree 3, and boundary vertices have degree 2 or 3. We consider
the following counting problem: given a sequence of twos and threes, how many
hexagonal patches exist with this degree sequence along the outer face? This
problem is motivated by the study of benzenoid hydrocarbons and fullerenes in
computational chemistry. We give the first polynomial time algorithm for this
problem. We show that it can be reduced to counting maximum independent sets in
circle graphs, and give a simple and fast algorithm for this problem.
| [
{
"version": "v1",
"created": "Thu, 28 Aug 2008 10:39:10 GMT"
},
{
"version": "v2",
"created": "Wed, 15 Jul 2009 15:27:00 GMT"
}
] | 2009-07-15T00:00:00 | [
[
"Bonsma",
"Paul",
""
],
[
"Breuer",
"Felix",
""
]
] |
0808.4134 | Daniel A. Spielman | Daniel A. Spielman and Shang-Hua Teng | Spectral Sparsification of Graphs | This revision addresses comments of the referees. In particular, we
have completely re-written the proof of the main graph partitioning theorem
in section 8 | null | null | null | cs.DS cs.DM | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We introduce a new notion of graph sparsificaiton based on spectral
similarity of graph Laplacians: spectral sparsification requires that the
Laplacian quadratic form of the sparsifier approximate that of the original.
This is equivalent to saying that the Laplacian of the sparsifier is a good
preconditioner for the Laplacian of the original. We prove that every graph has
a spectral sparsifier of nearly linear size. Moreover, we present an algorithm
that produces spectral sparsifiers in time $\softO{m}$, where $m$ is the number
of edges in the original graph. This construction is a key component of a
nearly-linear time algorithm for solving linear equations in
diagonally-dominant matrcies. Our sparsification algorithm makes use of a
nearly-linear time algorithm for graph partitioning that satisfies a strong
guarantee: if the partition it outputs is very unbalanced, then the larger part
is contained in a subgraph of high conductance.
| [
{
"version": "v1",
"created": "Fri, 29 Aug 2008 17:17:29 GMT"
},
{
"version": "v2",
"created": "Fri, 19 Sep 2008 14:20:42 GMT"
},
{
"version": "v3",
"created": "Tue, 20 Jul 2010 20:48:36 GMT"
}
] | 2010-07-22T00:00:00 | [
[
"Spielman",
"Daniel A.",
""
],
[
"Teng",
"Shang-Hua",
""
]
] |
0809.0188 | Marek Karpinski | Piotr Berman, Bhaskar DasGupta and Marek Karpinski | Approximating Transitivity in Directed Networks | null | null | null | null | cs.CC cs.DM cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We study the problem of computing a minimum equivalent digraph (also known as
the problem of computing a strong transitive reduction) and its maximum
objective function variant, with two types of extensions. First, we allow to
declare a set $D\subset E$ and require that a valid solution $A$ satisfies
$D\subset A$ (it is sometimes called transitive reduction problem). In the
second extension (called $p$-ary transitive reduction), we have integer edge
labeling and we view two paths as equivalent if they have the same beginning,
ending and the sum of labels modulo $p$. A solution $A\subseteq E$ is valid if
it gives an equivalent path for every original path. For all problems we
establish the following: polynomial time minimization of $|A|$ within ratio
1.5, maximization of $|E-A|$ within ratio 2, MAX-SNP hardness even of the
length of simple cycles is limited to 5. Furthermore, we believe that the
combinatorial technique behind the approximation algorithm for the minimization
version might be of interest to other graph connectivity problems as well.
| [
{
"version": "v1",
"created": "Mon, 1 Sep 2008 08:58:32 GMT"
}
] | 2008-09-02T00:00:00 | [
[
"Berman",
"Piotr",
""
],
[
"DasGupta",
"Bhaskar",
""
],
[
"Karpinski",
"Marek",
""
]
] |
0809.0400 | Xuan Cai | Xuan Cai | Canonical Coin Systems for Change-Making Problems | 7 pages | null | null | null | cs.DS cs.DM | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | The Change-Making Problem is to represent a given value with the fewest coins
under a given coin system. As a variation of the knapsack problem, it is known
to be NP-hard. Nevertheless, in most real money systems, the greedy algorithm
yields optimal solutions. In this paper, we study what type of coin systems
that guarantee the optimality of the greedy algorithm. We provide new proofs
for a sufficient and necessary condition for the so-called \emph{canonical}
coin systems with four or five types of coins, and a sufficient condition for
non-canonical coin systems, respectively. Moreover, we present an $O(m^2)$
algorithm that decides whether a tight coin system is canonical.
| [
{
"version": "v1",
"created": "Tue, 2 Sep 2008 11:04:19 GMT"
},
{
"version": "v2",
"created": "Sat, 21 Mar 2009 16:12:55 GMT"
}
] | 2009-03-21T00:00:00 | [
[
"Cai",
"Xuan",
""
]
] |
0809.0460 | Shipra Agrawal | Shipra Agrawal, Amin Saberi, Yinyu Ye | Stochastic Combinatorial Optimization under Probabilistic Constraints | null | null | null | null | cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | In this paper, we present approximation algorithms for combinatorial
optimization problems under probabilistic constraints. Specifically, we focus
on stochastic variants of two important combinatorial optimization problems:
the k-center problem and the set cover problem, with uncertainty characterized
by a probability distribution over set of points or elements to be covered. We
consider these problems under adaptive and non-adaptive settings, and present
efficient approximation algorithms for the case when underlying distribution is
a product distribution. In contrast to the expected cost model prevalent in
stochastic optimization literature, our problem definitions support
restrictions on the probability distributions of the total costs, via
incorporating constraints that bound the probability with which the incurred
costs may exceed a given threshold.
| [
{
"version": "v1",
"created": "Tue, 2 Sep 2008 16:07:42 GMT"
}
] | 2008-09-03T00:00:00 | [
[
"Agrawal",
"Shipra",
""
],
[
"Saberi",
"Amin",
""
],
[
"Ye",
"Yinyu",
""
]
] |
0809.0949 | Michael Baer | Michael B. Baer | Efficient Implementation of the Generalized Tunstall Code Generation
Algorithm | 5 pages, 5 figures, accepted to ISIT 2009 | null | null | null | cs.IT cs.DS math.IT | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | A method is presented for constructing a Tunstall code that is linear time in
the number of output items. This is an improvement on the state of the art for
non-Bernoulli sources, including Markov sources, which require a (suboptimal)
generalization of Tunstall's algorithm proposed by Savari and analytically
examined by Tabus and Rissanen. In general, if n is the total number of output
leaves across all Tunstall trees, s is the number of trees (states), and D is
the number of leaves of each internal node, then this method takes O((1+(log
s)/D) n) time and O(n) space.
| [
{
"version": "v1",
"created": "Fri, 5 Sep 2008 05:14:10 GMT"
},
{
"version": "v2",
"created": "Thu, 30 Apr 2009 19:58:44 GMT"
},
{
"version": "v3",
"created": "Fri, 8 May 2009 00:10:57 GMT"
}
] | 2009-05-08T00:00:00 | [
[
"Baer",
"Michael B.",
""
]
] |
0809.1171 | Cheng-Wei Luo | Cheng-Wei Luo, Hsiao-Fei Liu, Peng-An Chen, and Kun-Mao Chao | Minkowski Sum Selection and Finding | 23 pages, 10 figures, accepted by ISAAC 2008 | null | null | null | cs.DS cs.CG | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | For the \textsc{Minkowski Sum Selection} problem with linear objective
functions, we obtain the following results: (1) optimal $O(n\log n)$ time
algorithms for $\lambda=1$; (2) $O(n\log^2 n)$ time deterministic algorithms
and expected $O(n\log n)$ time randomized algorithms for any fixed $\lambda>1$.
For the \textsc{Minkowski Sum Finding} problem with linear objective functions
or objective functions of the form
$f(x,y)=\frac{by}{ax}$, we construct optimal $O(n\log n)$ time algorithms for
any fixed $\lambda\geq 1$.
| [
{
"version": "v1",
"created": "Sat, 6 Sep 2008 14:31:49 GMT"
}
] | 2008-09-09T00:00:00 | [
[
"Luo",
"Cheng-Wei",
""
],
[
"Liu",
"Hsiao-Fei",
""
],
[
"Chen",
"Peng-An",
""
],
[
"Chao",
"Kun-Mao",
""
]
] |
0809.1681 | Rafael Laufer | Rafael Laufer and Leonard Kleinrock | Multirate Anypath Routing in Wireless Mesh Networks | 13 pages, 8 figures | IEEE INFOCOM 2009 | 10.1109/INFCOM.2009.5061904 | UCLA-CSD-TR080025 | cs.NI cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | In this paper, we present a new routing paradigm that generalizes
opportunistic routing in wireless mesh networks. In multirate anypath routing,
each node uses both a set of next hops and a selected transmission rate to
reach a destination. Using this rate, a packet is broadcast to the nodes in the
set and one of them forwards the packet on to the destination. To date, there
is no theory capable of jointly optimizing both the set of next hops and the
transmission rate used by each node. We bridge this gap by introducing a
polynomial-time algorithm to this problem and provide the proof of its
optimality. The proposed algorithm runs in the same running time as regular
shortest-path algorithms and is therefore suitable for deployment in link-state
routing protocols. We conducted experiments in a 802.11b testbed network, and
our results show that multirate anypath routing performs on average 80% and up
to 6.4 times better than anypath routing with a fixed rate of 11 Mbps. If the
rate is fixed at 1 Mbps instead, performance improves by up to one order of
magnitude.
| [
{
"version": "v1",
"created": "Tue, 9 Sep 2008 21:49:04 GMT"
}
] | 2010-11-01T00:00:00 | [
[
"Laufer",
"Rafael",
""
],
[
"Kleinrock",
"Leonard",
""
]
] |
0809.1715 | Bodo Manthey | Bodo Manthey and Heiko R\"oglin | Improved Smoothed Analysis of the k-Means Method | To be presented at the 20th ACM-SIAM Symposium on Discrete Algorithms
(SODA 2009) | null | null | null | cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | The k-means method is a widely used clustering algorithm. One of its
distinguished features is its speed in practice. Its worst-case running-time,
however, is exponential, leaving a gap between practical and theoretical
performance. Arthur and Vassilvitskii (FOCS 2006) aimed at closing this gap,
and they proved a bound of $\poly(n^k, \sigma^{-1})$ on the smoothed
running-time of the k-means method, where n is the number of data points and
$\sigma$ is the standard deviation of the Gaussian perturbation. This bound,
though better than the worst-case bound, is still much larger than the
running-time observed in practice.
We improve the smoothed analysis of the k-means method by showing two upper
bounds on the expected running-time of k-means. First, we prove that the
expected running-time is bounded by a polynomial in $n^{\sqrt k}$ and
$\sigma^{-1}$. Second, we prove an upper bound of $k^{kd} \cdot \poly(n,
\sigma^{-1})$, where d is the dimension of the data space. The polynomial is
independent of k and d, and we obtain a polynomial bound for the expected
running-time for $k, d \in O(\sqrt{\log n/\log \log n})$.
Finally, we show that k-means runs in smoothed polynomial time for
one-dimensional instances.
| [
{
"version": "v1",
"created": "Wed, 10 Sep 2008 07:00:38 GMT"
}
] | 2008-09-11T00:00:00 | [
[
"Manthey",
"Bodo",
""
],
[
"Röglin",
"Heiko",
""
]
] |
0809.1810 | Felipe Cruz | Felipe A. Cruz, L. A. Barba | Characterization of the errors of the FMM in particle simulations | 34 pages, 38 images | Int. J. Num. Meth. Engrg., 79(13):1577-1604 (2009) | 10.1002/nme.2611 | null | cs.DS physics.comp-ph | http://creativecommons.org/licenses/by/3.0/ | The Fast Multipole Method (FMM) offers an acceleration for pairwise
interaction calculation, known as $N$-body problems, from $\mathcal{O}(N^2)$ to
$\mathcal{O}(N)$ with $N$ particles. This has brought dramatic increase in the
capability of particle simulations in many application areas, such as
electrostatics, particle formulations of fluid mechanics, and others. Although
the literature on the subject provides theoretical error bounds for the FMM
approximation, there are not many reports of the measured errors in a suite of
computational experiments. We have performed such an experimental
investigation, and summarized the results of about 1000 calculations using the
FMM algorithm, to characterize the accuracy of the method in relation with the
different parameters available to the user. In addition to the more standard
diagnostic of the maximum error, we supply illustrations of the spatial
distribution of the errors, which offers visual evidence of all the
contributing factors to the overall approximation accuracy: multipole
expansion, local expansion, hierarchical spatial decomposition (interaction
lists, local domain, far domain). This presentation is a contribution to any
researcher wishing to incorporate the FMM acceleration to their application
code, as it aids in understanding where accuracy is gained or compromised.
| [
{
"version": "v1",
"created": "Wed, 10 Sep 2008 15:06:08 GMT"
}
] | 2011-09-21T00:00:00 | [
[
"Cruz",
"Felipe A.",
""
],
[
"Barba",
"L. A.",
""
]
] |
0809.1895 | Benjamin Birnbaum | Yossi Azar, Benjamin Birnbaum, Anna R. Karlin, and C. Thach Nguyen | Thinking Twice about Second-Price Ad Auctions | null | null | null | null | cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Recent work has addressed the algorithmic problem of allocating advertisement
space for keywords in sponsored search auctions so as to maximize revenue, most
of which assume that pricing is done via a first-price auction. This does not
realistically model the Generalized Second Price (GSP) auction used in
practice, in which bidders pay the next-highest bid for keywords that they are
allocated. Towards the goal of more realistically modeling these auctions, we
introduce the Second-Price Ad Auctions problem, in which bidders' payments are
determined by the GSP mechanism. We show that the complexity of the
Second-Price Ad Auctions problem is quite different than that of the more
studied First-Price Ad Auctions problem. First, unlike the first-price variant,
for which small constant-factor approximations are known, it is NP-hard to
approximate the Second-Price Ad Auctions problem to any non-trivial factor,
even when the bids are small compared to the budgets. Second, this discrepancy
extends even to the 0-1 special case that we call the Second-Price Matching
problem (2PM). Offline 2PM is APX-hard, and for online 2PM there is no
deterministic algorithm achieving a non-trivial competitive ratio and no
randomized algorithm achieving a competitive ratio better than 2. This
contrasts with the results for the analogous special case in the first-price
model, the standard bipartite matching problem, which is solvable in polynomial
time and which has deterministic and randomized online algorithms achieving
better competitive ratios. On the positive side, we provide a 2-approximation
for offline 2PM and a 5.083-competitive randomized algorithm for online 2PM.
The latter result makes use of a new generalization of a result on the
performance of the "Ranking" algorithm for online bipartite matching.
| [
{
"version": "v1",
"created": "Wed, 10 Sep 2008 23:33:47 GMT"
}
] | 2008-09-12T00:00:00 | [
[
"Azar",
"Yossi",
""
],
[
"Birnbaum",
"Benjamin",
""
],
[
"Karlin",
"Anna R.",
""
],
[
"Nguyen",
"C. Thach",
""
]
] |
0809.1902 | Manor Mendel | Manor Mendel, Chaya Schwob | Fast C-K-R Partitions of Sparse Graphs | 15 pages, title changed, a small error in the running time was fixed.
Many errors in English were eliminated | Chicago J. Theoretical Comp. Sci., 2009(2), 2009 | null | null | cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We present fast algorithms for constructing probabilistic embeddings and
approximate distance oracles in sparse graphs. The main ingredient is a fast
algorithm for sampling the probabilistic partitions of Calinescu, Karloff, and
Rabani in sparse graphs.
| [
{
"version": "v1",
"created": "Thu, 11 Sep 2008 02:10:29 GMT"
},
{
"version": "v2",
"created": "Wed, 9 Sep 2009 02:47:44 GMT"
}
] | 2009-09-09T00:00:00 | [
[
"Mendel",
"Manor",
""
],
[
"Schwob",
"Chaya",
""
]
] |
0809.1906 | Shiva Kintali | Shiva Kintali | Betweenness Centrality : Algorithms and Lower Bounds | null | null | null | null | cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | One of the most fundamental problems in large scale network analysis is to
determine the importance of a particular node in a network. Betweenness
centrality is the most widely used metric to measure the importance of a node
in a network. In this paper, we present a randomized parallel algorithm and an
algebraic method for computing betweenness centrality of all nodes in a
network. We prove that any path-comparison based algorithm cannot compute
betweenness in less than O(nm) time.
| [
{
"version": "v1",
"created": "Thu, 11 Sep 2008 02:49:07 GMT"
},
{
"version": "v2",
"created": "Sun, 19 Oct 2008 04:24:21 GMT"
}
] | 2008-10-19T00:00:00 | [
[
"Kintali",
"Shiva",
""
]
] |
0809.2075 | Jittat Fakcharoenphol | Jittat Fakcharoenphol, Boonserm Kijsirikul | Low congestion online routing and an improved mistake bound for online
prediction of graph labeling | 5 pages | null | null | null | cs.DS cs.DM cs.LG | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | In this paper, we show a connection between a certain online low-congestion
routing problem and an online prediction of graph labeling. More specifically,
we prove that if there exists a routing scheme that guarantees a congestion of
$\alpha$ on any edge, there exists an online prediction algorithm with mistake
bound $\alpha$ times the cut size, which is the size of the cut induced by the
label partitioning of graph vertices. With previous known bound of $O(\log n)$
for $\alpha$ for the routing problem on trees with $n$ vertices, we obtain an
improved prediction algorithm for graphs with high effective resistance.
In contrast to previous approaches that move the graph problem into problems
in vector space using graph Laplacian and rely on the analysis of the
perceptron algorithm, our proof are purely combinatorial. Further more, our
approach directly generalizes to the case where labels are not binary.
| [
{
"version": "v1",
"created": "Thu, 11 Sep 2008 19:32:49 GMT"
},
{
"version": "v2",
"created": "Fri, 12 Sep 2008 07:02:37 GMT"
}
] | 2008-09-12T00:00:00 | [
[
"Fakcharoenphol",
"Jittat",
""
],
[
"Kijsirikul",
"Boonserm",
""
]
] |
0809.2097 | Hsiao-Fei Liu | Hsiao-Fei Liu, Peng-An Chen, and Kun-Mao Chao | Algorithms for Locating Constrained Optimal Intervals | An earlier version of the second part of this work appeared in
Proceedings of the 18th International Symposium on Algorithms and
Computation, Japan, 2007 | null | null | null | cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | In this work, we obtain the following new results.
1. Given a sequence $D=((h_1,s_1), (h_2,s_2) ..., (h_n,s_n))$ of number
pairs, where $s_i>0$ for all $i$, and a number $L_h$, we propose an O(n)-time
algorithm for finding an index interval $[i,j]$ that maximizes
$\frac{\sum_{k=i}^{j} h_k}{\sum_{k=i}^{j} s_k}$ subject to $\sum_{k=i}^{j} h_k
\geq L_h$.
2. Given a sequence $D=((h_1,s_1), (h_2,s_2) ..., (h_n,s_n))$ of number
pairs, where $s_i=1$ for all $i$, and an integer $L_s$ with $1\leq L_s\leq n$,
we propose an $O(n\frac{T(L_s^{1/2})}{L_s^{1/2}})$-time algorithm for finding
an index interval $[i,j]$ that maximizes $\frac{\sum_{k=i}^{j}
h_k}{\sqrt{\sum_{k=i}^{j} s_k}}$ subject to $\sum_{k=i}^{j} s_k \geq L_s$,
where $T(n')$ is the time required to solve the all-pairs shortest paths
problem on a graph of $n'$ nodes. By the latest result of Chan \cite{Chan},
$T(n')=O(n'^3 \frac{(\log\log n')^3}{(\log n')^2})$, so our algorithm runs in
subquadratic time $O(nL_s\frac{(\log\log L_s)^3}{(\log L_s)^2})$.
| [
{
"version": "v1",
"created": "Thu, 11 Sep 2008 20:12:08 GMT"
}
] | 2008-09-15T00:00:00 | [
[
"Liu",
"Hsiao-Fei",
""
],
[
"Chen",
"Peng-An",
""
],
[
"Chao",
"Kun-Mao",
""
]
] |
0809.2489 | Petteri Kaski | Andreas Bj\"orklund, Thore Husfeldt, Petteri Kaski, Mikko Koivisto | The fast intersection transform with applications to counting paths | 11 pages | null | null | null | cs.DS cs.DM | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We present an algorithm for evaluating a linear ``intersection transform'' of
a function defined on the lattice of subsets of an $n$-element set. In
particular, the algorithm constructs an arithmetic circuit for evaluating the
transform in ``down-closure time'' relative to the support of the function and
the evaluation domain. As an application, we develop an algorithm that, given
as input a digraph with $n$ vertices and bounded integer weights at the edges,
counts paths by weight and given length $0\leq\ell\leq n-1$ in time
$O^*(\exp(n\cdot H(\ell/(2n))))$, where $H(p)=-p\log p-(1-p)\log(1-p)$, and the
notation $O^*(\cdot)$ suppresses a factor polynomial in $n$.
| [
{
"version": "v1",
"created": "Mon, 15 Sep 2008 11:15:05 GMT"
}
] | 2008-09-16T00:00:00 | [
[
"Björklund",
"Andreas",
""
],
[
"Husfeldt",
"Thore",
""
],
[
"Kaski",
"Petteri",
""
],
[
"Koivisto",
"Mikko",
""
]
] |
0809.2554 | Kanat Tangwongsan | Anupam Gupta and Kanat Tangwongsan | Simpler Analyses of Local Search Algorithms for Facility Location | null | null | null | null | cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We study local search algorithms for metric instances of facility location
problems: the uncapacitated facility location problem (UFL), as well as
uncapacitated versions of the $k$-median, $k$-center and $k$-means problems.
All these problems admit natural local search heuristics: for example, in the
UFL problem the natural moves are to open a new facility, close an existing
facility, and to swap a closed facility for an open one; in $k$-medians, we are
allowed only swap moves. The local-search algorithm for $k$-median was analyzed
by Arya et al. (SIAM J. Comput. 33(3):544-562, 2004), who used a clever
``coupling'' argument to show that local optima had cost at most constant times
the global optimum. They also used this argument to show that the local search
algorithm for UFL was 3-approximation; their techniques have since been applied
to other facility location problems.
In this paper, we give a proof of the $k$-median result which avoids this
coupling argument. These arguments can be used in other settings where the Arya
et al. arguments have been used. We also show that for the problem of opening
$k$ facilities $F$ to minimize the objective function $\Phi_p(F) = \big(\sum_{j
\in V} d(j, F)^p\big)^{1/p}$, the natural swap-based local-search algorithm is
a $\Theta(p)$-approximation. This implies constant-factor approximations for
$k$-medians (when $p=1$), and $k$-means (when $p = 2$), and an $O(\log
n)$-approximation algorithm for the $k$-center problem (which is essentially $p
= \log n$).
| [
{
"version": "v1",
"created": "Mon, 15 Sep 2008 15:42:47 GMT"
}
] | 2008-09-16T00:00:00 | [
[
"Gupta",
"Anupam",
""
],
[
"Tangwongsan",
"Kanat",
""
]
] |
0809.2858 | Christophe Paul | Stephane Bessy and Christophe Paul and Anthony Perez | Polynomial kernels for 3-leaf power graph modification problems | Submitted | null | 10.1007/978-3-642-10217-2_10 | null | cs.DM cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | A graph G=(V,E) is a 3-leaf power iff there exists a tree T whose leaves are
V and such that (u,v) is an edge iff u and v are at distance at most 3 in T.
The 3-leaf power graph edge modification problems, i.e. edition (also known as
the closest 3-leaf power), completion and edge-deletion, are FTP when
parameterized by the size of the edge set modification. However polynomial
kernel was known for none of these three problems. For each of them, we provide
cubic kernels that can be computed in linear time for each of these problems.
We thereby answer an open problem first mentioned by Dom, Guo, Huffner and
Niedermeier (2005).
| [
{
"version": "v1",
"created": "Wed, 17 Sep 2008 06:16:37 GMT"
},
{
"version": "v2",
"created": "Wed, 17 Sep 2008 20:10:57 GMT"
}
] | 2015-05-13T00:00:00 | [
[
"Bessy",
"Stephane",
""
],
[
"Paul",
"Christophe",
""
],
[
"Perez",
"Anthony",
""
]
] |
0809.2957 | Sergi Elizalde | Sergi Elizalde, Peter Winkler | Sorting by Placement and Shift | 13 pages, 4 figures, Proceedings of SODA 2009 | null | null | null | math.CO cs.DM cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | In sorting situations where the final destination of each item is known, it
is natural to repeatedly choose items and place them where they belong,
allowing the intervening items to shift by one to make room. (In fact, a
special case of this algorithm is commonly used to hand-sort files.) However,
it is not obvious that this algorithm necessarily terminates.
We show that in fact the algorithm terminates after at most $2^{n-1}-1$ steps
in the worst case (confirming a conjecture of L. Larson), and that there are
super-exponentially many permutations for which this exact bound can be
achieved. The proof involves a curious symmetrical binary representation.
| [
{
"version": "v1",
"created": "Wed, 17 Sep 2008 16:29:38 GMT"
}
] | 2008-09-18T00:00:00 | [
[
"Elizalde",
"Sergi",
""
],
[
"Winkler",
"Peter",
""
]
] |
0809.2970 | Raphael Yuster | Raphael Yuster | Single source shortest paths in $H$-minor free graphs | null | null | null | null | cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We present an algorithm for the Single Source Shortest Paths (SSSP) problem
in \emph{$H$-minor free} graphs. For every fixed $H$, if $G$ is a graph with
$n$ vertices having integer edge lengths and $s$ is a designated source vertex
of $G$, the algorithm runs in $\tilde{O}(n^{\sqrt{11.5}-2} \log L) \le
O(n^{1.392} \log L)$ time, where $L$ is the absolute value of the smallest edge
length. The algorithm computes shortest paths and the distances from $s$ to all
vertices of the graph, or else provides a certificate that $G$ is not $H$-minor
free. Our result improves an earlier $O(n^{1.5} \log L)$ time algorithm for
this problem, which follows from a general SSSP algorithm of Goldberg.
| [
{
"version": "v1",
"created": "Wed, 17 Sep 2008 17:51:09 GMT"
}
] | 2008-09-18T00:00:00 | [
[
"Yuster",
"Raphael",
""
]
] |
0809.3232 | Daniel A. Spielman | Daniel A. Spielman, Shang-Hua Teng | A Local Clustering Algorithm for Massive Graphs and its Application to
Nearly-Linear Time Graph Partitioning | null | null | null | null | cs.DS cs.DM | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We study the design of local algorithms for massive graphs. A local algorithm
is one that finds a solution containing or near a given vertex without looking
at the whole graph. We present a local clustering algorithm. Our algorithm
finds a good cluster--a subset of vertices whose internal connections are
significantly richer than its external connections--near a given vertex. The
running time of our algorithm, when it finds a non-empty local cluster, is
nearly linear in the size of the cluster it outputs.
Our clustering algorithm could be a useful primitive for handling massive
graphs, such as social networks and web-graphs. As an application of this
clustering algorithm, we present a partitioning algorithm that finds an
approximate sparsest cut with nearly optimal balance. Our algorithm takes time
nearly linear in the number edges of the graph.
Using the partitioning algorithm of this paper, we have designed a
nearly-linear time algorithm for constructing spectral sparsifiers of graphs,
which we in turn use in a nearly-linear time algorithm for solving linear
systems in symmetric, diagonally-dominant matrices. The linear system solver
also leads to a nearly linear-time algorithm for approximating the
second-smallest eigenvalue and corresponding eigenvector of the Laplacian
matrix of a graph. These other results are presented in two companion papers.
| [
{
"version": "v1",
"created": "Thu, 18 Sep 2008 19:20:07 GMT"
}
] | 2008-09-19T00:00:00 | [
[
"Spielman",
"Daniel A.",
""
],
[
"Teng",
"Shang-Hua",
""
]
] |
0809.3527 | Mugurel Ionut Andreica | Mugurel Ionut Andreica, Angela Andreica, Romulus Andreica | Inferring Company Structure from Limited Available Information | Some of the algorithmic techniques presented in this paper were used
as part of the solutions for some of the tasks proposed in several
programming contests in which the first author participated (see the related
materials for several such tasks and their solutions) | International Symposium on Social Development and Economic
Performance, Satu Mare : Romania (2008) | null | null | cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | In this paper we present several algorithmic techniques for inferring the
structure of a company when only a limited amount of information is available.
We consider problems with two types of inputs: the number of pairs of employees
with a given property and restricted information about the hierarchical
structure of the company. We provide dynamic programming and greedy algorithms
for these problems.
| [
{
"version": "v1",
"created": "Sat, 20 Sep 2008 20:05:21 GMT"
},
{
"version": "v2",
"created": "Sun, 23 Dec 2012 06:56:16 GMT"
}
] | 2012-12-27T00:00:00 | [
[
"Andreica",
"Mugurel Ionut",
""
],
[
"Andreica",
"Angela",
""
],
[
"Andreica",
"Romulus",
""
]
] |
0809.3528 | Mugurel Ionut Andreica | Mugurel Ionut Andreica, Cristina Teodora Andreica, Madalina Ecaterina
Andreica | Locating Restricted Facilities on Binary Maps | The algorithmic techniques presented in this paper were used by the
first author in the implementation of solutions to various algorithmic
contest tasks (see the attached zip archive for some examples) | International Symposium on Social Development and Economic
Performance, Satu Mare : Romania (2008) | null | null | cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | In this paper we consider several facility location problems with
applications to cost and social welfare optimization, when the area map is
encoded as a binary (0,1) mxn matrix. We present algorithmic solutions for all
the problems. Some cases are too particular to be used in practical situations,
but they are at least a starting point for more generic solutions.
| [
{
"version": "v1",
"created": "Sat, 20 Sep 2008 20:06:34 GMT"
},
{
"version": "v2",
"created": "Wed, 30 Jan 2013 07:48:10 GMT"
}
] | 2013-01-31T00:00:00 | [
[
"Andreica",
"Mugurel Ionut",
""
],
[
"Andreica",
"Cristina Teodora",
""
],
[
"Andreica",
"Madalina Ecaterina",
""
]
] |
0809.3577 | Philippe Robert | Han\`ene Mohamed, Philippe Robert | Dynamic tree algorithms | Published in at http://dx.doi.org/10.1214/09-AAP617 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org) | Annals of Applied Probability 2010, Vol. 20, No. 1, 26-51 | 10.1214/09-AAP617 | IMS-AAP-AAP617 | math.PR cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | In this paper, a general tree algorithm processing a random flow of arrivals
is analyzed. Capetanakis--Tsybakov--Mikhailov's protocol in the context of
communication networks with random access is an example of such an algorithm.
In computer science, this corresponds to a trie structure with a dynamic input.
Mathematically, it is related to a stopped branching process with exogeneous
arrivals (immigration). Under quite general assumptions on the distribution of
the number of arrivals and on the branching procedure, it is shown that there
exists a positive constant $\lambda_c$ so that if the arrival rate is smaller
than $\lambda_c$, then the algorithm is stable under the flow of requests, that
is, that the total size of an associated tree is integrable. At the same time,
a gap in the earlier proofs of stability in the literature is fixed. When the
arrivals are Poisson, an explicit characterization of $\lambda_c$ is given.
Under the stability condition, the asymptotic behavior of the average size of a
tree starting with a large number of individuals is analyzed. The results are
obtained with the help of a probabilistic rewriting of the functional equations
describing the dynamics of the system. The proofs use extensively this
stochastic background throughout the paper. In this analysis, two basic limit
theorems play a key role: the renewal theorem and the convergence to
equilibrium of an auto-regressive process with a moving average.
| [
{
"version": "v1",
"created": "Sun, 21 Sep 2008 11:46:05 GMT"
},
{
"version": "v2",
"created": "Wed, 13 Jan 2010 13:51:20 GMT"
}
] | 2010-01-13T00:00:00 | [
[
"Mohamed",
"Hanène",
""
],
[
"Robert",
"Philippe",
""
]
] |
0809.3646 | Petr Golovach | Fedor V. Fomin, Petr A. Golovach and Dimitrios M. Thilikos | Approximating acyclicity parameters of sparse hypergraphs | null | null | null | null | cs.DS cs.CC | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | The notions of hypertree width and generalized hypertree width were
introduced by Gottlob, Leone, and Scarcello in order to extend the concept of
hypergraph acyclicity. These notions were further generalized by Grohe and
Marx, who introduced the fractional hypertree width of a hypergraph. All these
width parameters on hypergraphs are useful for extending tractability of many
problems in database theory and artificial intelligence. In this paper, we
study the approximability of (generalized, fractional) hyper treewidth of
sparse hypergraphs where the criterion of sparsity reflects the sparsity of
their incidence graphs. Our first step is to prove that the (generalized,
fractional) hypertree width of a hypergraph H is constant-factor sandwiched by
the treewidth of its incidence graph, when the incidence graph belongs to some
apex-minor-free graph class. This determines the combinatorial borderline above
which the notion of (generalized, fractional) hypertree width becomes
essentially more general than treewidth, justifying that way its functionality
as a hypergraph acyclicity measure. While for more general sparse families of
hypergraphs treewidth of incidence graphs and all hypertree width parameters
may differ arbitrarily, there are sparse families where a constant factor
approximation algorithm is possible. In particular, we give a constant factor
approximation polynomial time algorithm for (generalized, fractional) hypertree
width on hypergraphs whose incidence graphs belong to some H-minor-free graph
class.
| [
{
"version": "v1",
"created": "Mon, 22 Sep 2008 08:17:22 GMT"
}
] | 2008-09-23T00:00:00 | [
[
"Fomin",
"Fedor V.",
""
],
[
"Golovach",
"Petr A.",
""
],
[
"Thilikos",
"Dimitrios M.",
""
]
] |
0809.4398 | Philipp Schuetz | Philipp Schuetz, Amedeo Caflisch | Multistep greedy algorithm identifies community structure in real-world
and computer-generated networks | 17 pages, 2 figures | Phys. Rev. E 78, 026112 (2008) | 10.1103/PhysRevE.78.026112 | null | cs.DS cond-mat.dis-nn physics.soc-ph q-bio.MN q-bio.QM | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We have recently introduced a multistep extension of the greedy algorithm for
modularity optimization. The extension is based on the idea that merging l
pairs of communities (l>1) at each iteration prevents premature condensation
into few large communities. Here, an empirical formula is presented for the
choice of the step width l that generates partitions with (close to) optimal
modularity for 17 real-world and 1100 computer-generated networks. Furthermore,
an in-depth analysis of the communities of two real-world networks (the
metabolic network of the bacterium E. coli and the graph of coappearing words
in the titles of papers coauthored by Martin Karplus) provides evidence that
the partition obtained by the multistep greedy algorithm is superior to the one
generated by the original greedy algorithm not only with respect to modularity
but also according to objective criteria. In other words, the multistep
extension of the greedy algorithm reduces the danger of getting trapped in
local optima of modularity and generates more reasonable partitions.
| [
{
"version": "v1",
"created": "Thu, 25 Sep 2008 13:46:30 GMT"
}
] | 2008-09-26T00:00:00 | [
[
"Schuetz",
"Philipp",
""
],
[
"Caflisch",
"Amedeo",
""
]
] |
0809.4577 | Jiajin Yu | Mordecai Golin, Xiaoming Xu and Jiajin Yu | A Generic Top-Down Dynamic-Programming Approach to Prefix-Free Coding | null | null | null | null | cs.DS cs.IT math.IT | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Given a probability distribution over a set of n words to be transmitted, the
Huffman Coding problem is to find a minimal-cost prefix free code for
transmitting those words. The basic Huffman coding problem can be solved in O(n
log n) time but variations are more difficult. One of the standard techniques
for solving these variations utilizes a top-down dynamic programming approach.
In this paper we show that this approach is amenable to dynamic programming
speedup techniques, permitting a speedup of an order of magnitude for many
algorithms in the literature for such variations as mixed radix, reserved
length and one-ended coding. These speedups are immediate implications of a
general structural property that permits batching together the calculation of
many DP entries.
| [
{
"version": "v1",
"created": "Fri, 26 Sep 2008 09:42:04 GMT"
}
] | 2008-09-29T00:00:00 | [
[
"Golin",
"Mordecai",
""
],
[
"Xu",
"Xiaoming",
""
],
[
"Yu",
"Jiajin",
""
]
] |
0809.4743 | Boris Ryabko | Boris Ryabko | The Imaginary Sliding Window As a New Data Structure for Adaptive
Algorithms | Published in: Problems of information transmission,1996,v.32,#2 | null | null | null | cs.IT cs.DS math.IT | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | The scheme of the sliding window is known in Information Theory, Computer
Science, the problem of predicting and in stastistics. Let a source with
unknown statistics generate some word $... x_{-1}x_{0}x_{1}x_{2}...$ in some
alphabet $A$. For every moment $t, t=... $ $-1, 0, 1, ...$, one stores the word
("window") $ x_{t-w} x_{t-w+1}... x_{t-1}$ where $w$,$w \geq 1$, is called
"window length". In the theory of universal coding, the code of the $x_{t}$
depends on source ststistics estimated by the window, in the problem of
predicting, each letter $x_{t}$ is predicted using information of the window,
etc. After that the letter $x_{t}$ is included in the window on the right,
while $x_{t-w}$ is removed from the window. It is the sliding window scheme.
This scheme has two merits: it allows one i) to estimate the source statistics
quite precisely and ii) to adapt the code in case of a change in the source'
statistics. However this scheme has a defect, namely, the necessity to store
the window (i.e. the word $x_{t-w}... x_{t-1})$ which needs a large memory size
for large $w$. A new scheme named "the Imaginary Sliding Window (ISW)" is
constructed. The gist of this scheme is that not the last element $x_{t-w}$ but
rather a random one is removed from the window. This allows one to retain both
merits of the sliding window as well as the possibility of not storing the
window and thus significantly decreasing the memory size.
| [
{
"version": "v1",
"created": "Sat, 27 Sep 2008 07:42:44 GMT"
}
] | 2008-09-30T00:00:00 | [
[
"Ryabko",
"Boris",
""
]
] |
0809.4794 | Adam Smith | Adam Smith | Efficient, Differentially Private Point Estimators | 9 pages | null | null | null | cs.CR cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Differential privacy is a recent notion of privacy for statistical databases
that provides rigorous, meaningful confidentiality guarantees, even in the
presence of an attacker with access to arbitrary side information.
We show that for a large class of parametric probability models, one can
construct a differentially private estimator whose distribution converges to
that of the maximum likelihood estimator. In particular, it is efficient and
asymptotically unbiased. This result provides (further) compelling evidence
that rigorous notions of privacy in statistical databases can be consistent
with statistically valid inference.
| [
{
"version": "v1",
"created": "Sat, 27 Sep 2008 19:57:34 GMT"
}
] | 2008-09-30T00:00:00 | [
[
"Smith",
"Adam",
""
]
] |
0809.4882 | Aleksandrs Slivkins | Robert Kleinberg, Aleksandrs Slivkins and Eli Upfal | Multi-Armed Bandits in Metric Spaces | 16 pages, 0 figures | null | null | null | cs.DS cs.LG | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | In a multi-armed bandit problem, an online algorithm chooses from a set of
strategies in a sequence of trials so as to maximize the total payoff of the
chosen strategies. While the performance of bandit algorithms with a small
finite strategy set is quite well understood, bandit problems with large
strategy sets are still a topic of very active investigation, motivated by
practical applications such as online auctions and web advertisement. The goal
of such research is to identify broad and natural classes of strategy sets and
payoff functions which enable the design of efficient solutions. In this work
we study a very general setting for the multi-armed bandit problem in which the
strategies form a metric space, and the payoff function satisfies a Lipschitz
condition with respect to the metric. We refer to this problem as the
"Lipschitz MAB problem". We present a complete solution for the multi-armed
problem in this setting. That is, for every metric space (L,X) we define an
isometry invariant which bounds from below the performance of Lipschitz MAB
algorithms for X, and we present an algorithm which comes arbitrarily close to
meeting this bound. Furthermore, our technique gives even better results for
benign payoff functions.
| [
{
"version": "v1",
"created": "Mon, 29 Sep 2008 01:58:13 GMT"
}
] | 2008-09-30T00:00:00 | [
[
"Kleinberg",
"Robert",
""
],
[
"Slivkins",
"Aleksandrs",
""
],
[
"Upfal",
"Eli",
""
]
] |
0810.0052 | Martin Ziegler | Matthias Fischer, Matthias Hilbig, Claudius J\"ahn, Friedhelm Meyer
auf der Heide and Martin Ziegler | Planar Visibility Counting | added Section 4: Implementation and Empirical Evaluation | null | null | null | cs.CG cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | For a fixed virtual scene (=collection of simplices) S and given observer
position p, how many elements of S are weakly visible (i.e. not fully occluded
by others) from p? The present work explores the trade-off between query time
and preprocessing space for these quantities in 2D: exactly, in the approximate
deterministic, and in the probabilistic sense. We deduce the EXISTENCE of an
O(m^2/n^2) space data structure for S that, given p and time O(log n), allows
to approximate the ratio of occluded segments up to arbitrary constant absolute
error; here m denotes the size of the Visibility Graph--which may be quadratic,
but typically is just linear in the size n of the scene S. On the other hand,
we present a data structure CONSTRUCTIBLE in O(n*log(n)+m^2*polylog(n)/k)
preprocessing time and space with similar approximation properties and query
time O(k*polylog n), where k<n is an arbitrary parameter. We describe an
implementation of this approach and demonstrate the practical benefit of the
parameter k to trade memory for query time in an empirical evaluation on three
classes of benchmark scenes.
| [
{
"version": "v1",
"created": "Wed, 1 Oct 2008 01:53:52 GMT"
},
{
"version": "v2",
"created": "Thu, 9 Oct 2008 02:43:08 GMT"
},
{
"version": "v3",
"created": "Thu, 5 Feb 2009 09:51:22 GMT"
}
] | 2009-02-05T00:00:00 | [
[
"Fischer",
"Matthias",
""
],
[
"Hilbig",
"Matthias",
""
],
[
"Jähn",
"Claudius",
""
],
[
"der Heide",
"Friedhelm Meyer auf",
""
],
[
"Ziegler",
"Martin",
""
]
] |
0810.0075 | Alvaro Salas Humberto | Alvaro Salas (Universidad de Caldas, Universidad Nacional de Colombia,
sede Manizales) | Acerca del Algoritmo de Dijkstra | In spanish, the paper contains illustrations | null | null | null | cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | In this paper we prove the correctness of Dijkstra's algorithm. We also
discuss it and at the end we show an application.
| [
{
"version": "v1",
"created": "Wed, 1 Oct 2008 04:55:11 GMT"
}
] | 2008-10-02T00:00:00 | [
[
"Salas",
"Alvaro",
"",
"Universidad de Caldas, Universidad Nacional de Colombia,\n sede Manizales"
]
] |
0810.0264 | David Musser | David R. Musser, Gor V. Nishanov | A Fast Generic Sequence Matching Algorithm | null | null | null | null | cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | A string matching -- and more generally, sequence matching -- algorithm is
presented that has a linear worst-case computing time bound, a low worst-case
bound on the number of comparisons (2n), and sublinear average-case behavior
that is better than that of the fastest versions of the Boyer-Moore algorithm.
The algorithm retains its efficiency advantages in a wide variety of sequence
matching problems of practical interest, including traditional string matching;
large-alphabet problems (as in Unicode strings); and small-alphabet,
long-pattern problems (as in DNA searches). Since it is expressed as a generic
algorithm for searching in sequences over an arbitrary type T, it is well
suited for use in generic software libraries such as the C++ Standard Template
Library. The algorithm was obtained by adding to the Knuth-Morris-Pratt
algorithm one of the pattern-shifting techniques from the Boyer-Moore
algorithm, with provision for use of hashing in this technique. In situations
in which a hash function or random access to the sequences is not available,
the algorithm falls back to an optimized version of the Knuth-Morris-Pratt
algorithm.
| [
{
"version": "v1",
"created": "Wed, 1 Oct 2008 19:54:51 GMT"
}
] | 2008-10-02T00:00:00 | [
[
"Musser",
"David R.",
""
],
[
"Nishanov",
"Gor V.",
""
]
] |
0810.0558 | Ashish Goel | Ashish Goel, Sanjeev Khanna, Brad Null | The Ratio Index for Budgeted Learning, with Applications | This paper has a substantial bug that we are trying to fix. Many
thanks to Joe Halpern for pointing this bug out. Please do not cite in the
meantime. Please let us know if you would like to understand and/or try to
fix the bug | null | null | null | cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | In the budgeted learning problem, we are allowed to experiment on a set of
alternatives (given a fixed experimentation budget) with the goal of picking a
single alternative with the largest possible expected payoff. Approximation
algorithms for this problem were developed by Guha and Munagala by rounding a
linear program that couples the various alternatives together. In this paper we
present an index for this problem, which we call the ratio index, which also
guarantees a constant factor approximation. Index-based policies have the
advantage that a single number (i.e. the index) can be computed for each
alternative irrespective of all other alternatives, and the alternative with
the highest index is experimented upon. This is analogous to the famous Gittins
index for the discounted multi-armed bandit problem.
The ratio index has several interesting structural properties. First, we show
that it can be computed in strongly polynomial time. Second, we show that with
the appropriate discount factor, the Gittins index and our ratio index are
constant factor approximations of each other, and hence the Gittins index also
gives a constant factor approximation to the budgeted learning problem.
Finally, we show that the ratio index can be used to create an index-based
policy that achieves an O(1)-approximation for the finite horizon version of
the multi-armed bandit problem. Moreover, the policy does not require any
knowledge of the horizon (whereas we compare its performance against an optimal
strategy that is aware of the horizon). This yields the following surprising
result: there is an index-based policy that achieves an O(1)-approximation for
the multi-armed bandit problem, oblivious to the underlying discount factor.
| [
{
"version": "v1",
"created": "Fri, 3 Oct 2008 01:37:45 GMT"
},
{
"version": "v2",
"created": "Mon, 11 Apr 2016 18:47:16 GMT"
}
] | 2016-04-12T00:00:00 | [
[
"Goel",
"Ashish",
""
],
[
"Khanna",
"Sanjeev",
""
],
[
"Null",
"Brad",
""
]
] |
0810.0674 | Shuchi Chawla | Siddharth Barman and Shuchi Chawla | Packing multiway cuts in capacitated graphs | The conference version of this paper is to appear at SODA 2009. This
is the full version | null | null | null | cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We consider the following "multiway cut packing" problem in undirected
graphs: we are given a graph G=(V,E) and k commodities, each corresponding to a
set of terminals located at different vertices in the graph; our goal is to
produce a collection of cuts {E_1,...,E_k} such that E_i is a multiway cut for
commodity i and the maximum load on any edge is minimized. The load on an edge
is defined to be the number of cuts in the solution crossing the edge. In the
capacitated version of the problem the goal is to minimize the maximum relative
load on any edge--the ratio of the edge's load to its capacity. Multiway cut
packing arises in the context of graph labeling problems where we are given a
partial labeling of a set of items and a neighborhood structure over them, and,
informally, the goal is to complete the labeling in the most consistent way.
This problem was introduced by Rabani, Schulman, and Swamy (SODA'08), who
developed an O(log n/log log n) approximation for it in general graphs, as well
as an improved O(log^2 k) approximation in trees. Here n is the number of nodes
in the graph. We present the first constant factor approximation for this
problem in arbitrary undirected graphs. Our approach is based on the
observation that every instance of the problem admits a near-optimal laminar
solution (that is, one in which no pair of cuts cross each other).
| [
{
"version": "v1",
"created": "Fri, 3 Oct 2008 16:13:00 GMT"
}
] | 2008-10-06T00:00:00 | [
[
"Barman",
"Siddharth",
""
],
[
"Chawla",
"Shuchi",
""
]
] |
0810.0906 | Hirotaka Ono | Toru Hasunuma, Toshimasa Ishii, Hirotaka Ono, Yushi Uno | A linear time algorithm for L(2,1)-labeling of trees | 23 pages, 3 figures | null | null | null | cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | An L(2,1)-labeling of a graph $G$ is an assignment $f$ from the vertex set
$V(G)$ to the set of nonnegative integers such that $|f(x)-f(y)|\ge 2$ if $x$
and $y$ are adjacent and $|f(x)-f(y)|\ge 1$ if $x$ and $y$ are at distance 2,
for all $x$ and $y$ in $V(G)$. A $k$-L(2,1)-labeling is an assignment
$f:V(G)\to\{0,..., k\}$, and the L(2,1)-labeling problem asks the minimum $k$,
which we denote by $\lambda(G)$, among all possible assignments. It is known
that this problem is NP-hard even for graphs of treewidth 2, and tree is one of
a very few classes for which the problem is polynomially solvable. The running
time of the best known algorithm for trees had been $\mO(\Delta^{4.5} n)$ for
more than a decade, however, an $\mO(n^{1.75})$-time algorithm has been
proposed recently, which substantially improved the previous one, where
$\Delta$ is the maximum degree of $T$ and $n=|V(T)|$. In this paper, we finally
establish a linear time algorithm for L(2,1)-labeling of trees.
| [
{
"version": "v1",
"created": "Mon, 6 Oct 2008 08:21:17 GMT"
},
{
"version": "v2",
"created": "Wed, 24 Nov 2010 07:06:08 GMT"
}
] | 2010-11-25T00:00:00 | [
[
"Hasunuma",
"Toru",
""
],
[
"Ishii",
"Toshimasa",
""
],
[
"Ono",
"Hirotaka",
""
],
[
"Uno",
"Yushi",
""
]
] |
0810.1355 | Michael Mahoney | Jure Leskovec, Kevin J. Lang, Anirban Dasgupta, and Michael W. Mahoney | Community Structure in Large Networks: Natural Cluster Sizes and the
Absence of Large Well-Defined Clusters | 66 pages, a much expanded version of our WWW 2008 paper | null | null | null | cs.DS physics.data-an physics.soc-ph | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | A large body of work has been devoted to defining and identifying clusters or
communities in social and information networks. We explore from a novel
perspective several questions related to identifying meaningful communities in
large social and information networks, and we come to several striking
conclusions. We employ approximation algorithms for the graph partitioning
problem to characterize as a function of size the statistical and structural
properties of partitions of graphs that could plausibly be interpreted as
communities. In particular, we define the network community profile plot, which
characterizes the "best" possible community--according to the conductance
measure--over a wide range of size scales. We study over 100 large real-world
social and information networks. Our results suggest a significantly more
refined picture of community structure in large networks than has been
appreciated previously. In particular, we observe tight communities that are
barely connected to the rest of the network at very small size scales; and
communities of larger size scales gradually "blend into" the expander-like core
of the network and thus become less "community-like." This behavior is not
explained, even at a qualitative level, by any of the commonly-used network
generation models. Moreover, it is exactly the opposite of what one would
expect based on intuition from expander graphs, low-dimensional or
manifold-like graphs, and from small social networks that have served as
testbeds of community detection algorithms. We have found that a generative
graph model, in which new edges are added via an iterative "forest fire"
burning process, is able to produce graphs exhibiting a network community
profile plot similar to what we observe in our network datasets.
| [
{
"version": "v1",
"created": "Wed, 8 Oct 2008 05:42:43 GMT"
}
] | 2008-10-13T00:00:00 | [
[
"Leskovec",
"Jure",
""
],
[
"Lang",
"Kevin J.",
""
],
[
"Dasgupta",
"Anirban",
""
],
[
"Mahoney",
"Michael W.",
""
]
] |
0810.1499 | Lenka Zdeborova | Lenka Zdeborov\'a and Marc M\'ezard | Constraint satisfaction problems with isolated solutions are hard | 19 pages, 12 figures | J. Stat. Mech. (2008) P12004 | 10.1088/1742-5468/2008/12/P12004 | null | cond-mat.dis-nn cond-mat.stat-mech cs.CC cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We study the phase diagram and the algorithmic hardness of the random
`locked' constraint satisfaction problems, and compare them to the commonly
studied 'non-locked' problems like satisfiability of boolean formulas or graph
coloring. The special property of the locked problems is that clusters of
solutions are isolated points. This simplifies significantly the determination
of the phase diagram, which makes the locked problems particularly appealing
from the mathematical point of view. On the other hand we show empirically that
the clustered phase of these problems is extremely hard from the algorithmic
point of view: the best known algorithms all fail to find solutions. Our
results suggest that the easy/hard transition (for currently known algorithms)
in the locked problems coincides with the clustering transition. These should
thus be regarded as new benchmarks of really hard constraint satisfaction
problems.
| [
{
"version": "v1",
"created": "Wed, 8 Oct 2008 18:28:28 GMT"
},
{
"version": "v2",
"created": "Thu, 4 Dec 2008 07:53:25 GMT"
}
] | 2008-12-09T00:00:00 | [
[
"Zdeborová",
"Lenka",
""
],
[
"Mézard",
"Marc",
""
]
] |
0810.1639 | Gabriel Istrate | Gabriel Istrate | Identifying almost sorted permutations from TCP buffer dynamics | null | null | null | null | cs.DS cs.DM math.CO | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Associate to each sequence $A$ of integers (intending to represent packet
IDs) a sequence of positive integers of the same length ${\mathcal M}(A)$. The
$i$'th entry of ${\mathcal M}(A)$ is the size (at time $i$) of the smallest
buffer needed to hold out-of-order packets, where space is accounted for
unreceived packets as well. Call two sequences $A$, $B$ {\em equivalent}
(written $A\equiv_{FB} B$) if ${\mathcal M}(A)={\mathcal M}(B)$.
We prove the following result: any two permutations $A,B$ of the same length
with $SUS(A)$, $SUS(B)\leq 3$ (where SUS is the {\em shuffled-up-sequences}
reordering measure), and such that $A\equiv_{FB} B$ are identical.
The result (which is no longer valid if we replace the upper bound 3 by 4)
was motivated by RESTORED, a receiver-oriented model of network traffic we have
previously introduced.
| [
{
"version": "v1",
"created": "Thu, 9 Oct 2008 12:27:32 GMT"
}
] | 2008-11-04T00:00:00 | [
[
"Istrate",
"Gabriel",
""
]
] |
0810.1756 | Milan Bradonjic | Milan Bradonjic, Eddie Kohler, Rafail Ostrovsky | Near-Optimal Radio Use For Wireless Network Synchronization | 23 pages | null | 10.1016/j.tcs.2011.09.026 | null | cs.DS cs.DM | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We consider the model of communication where wireless devices can either
switch their radios off to save energy, or switch their radios on and engage in
communication. We distill a clean theoretical formulation of this problem of
minimizing radio use and present near-optimal solutions. Our base model ignores
issues of communication interference, although we also extend the model to
handle this requirement. We assume that nodes intend to communicate
periodically, or according to some time-based schedule. Clearly, perfectly
synchronized devices could switch their radios on for exactly the minimum
periods required by their joint schedules. The main challenge in the deployment
of wireless networks is to synchronize the devices' schedules, given that their
initial schedules may be offset relative to one another (even if their clocks
run at the same speed). We significantly improve previous results, and show
optimal use of the radio for two processors and near-optimal use of the radio
for synchronization of an arbitrary number of processors. In particular, for
two processors we prove deterministically matching $\Theta(\sqrt{n})$ upper and
lower bounds on the number of times the radio has to be on, where $n$ is the
discretized uncertainty period of the clock shift between the two processors.
(In contrast, all previous results for two processors are randomized.) For
$m=n^\beta$ processors (for any $\beta < 1$) we prove $\Omega(n^{(1-\beta)/2})$
is the lower bound on the number of times the radio has to be switched on (per
processor), and show a nearly matching (in terms of the radio use)
$\~{O}(n^{(1-\beta)/2})$ randomized upper bound per processor, with failure
probability exponentially close to 0. For $\beta \geq 1$ our algorithm runs
with at most $poly-log(n)$ radio invocations per processor. Our bounds also
hold in a radio-broadcast model where interference must be taken into account.
| [
{
"version": "v1",
"created": "Thu, 9 Oct 2008 20:41:23 GMT"
},
{
"version": "v2",
"created": "Mon, 13 Feb 2012 22:44:09 GMT"
}
] | 2012-02-15T00:00:00 | [
[
"Bradonjic",
"Milan",
""
],
[
"Kohler",
"Eddie",
""
],
[
"Ostrovsky",
"Rafail",
""
]
] |
0810.1823 | Christophe Paul | Emeric Gioan and Christophe Paul | Split decomposition and graph-labelled trees: characterizations and
fully-dynamic algorithms for totally decomposable graphs | extended abstract appeared in ISAAC 2007: Dynamic distance hereditary
graphs using split decompositon. In International Symposium on Algorithms and
Computation - ISAAC. Number 4835 in Lecture Notes, pages 41-51, 2007 | null | null | null | cs.DM cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | In this paper, we revisit the split decomposition of graphs and give new
combinatorial and algorithmic results for the class of totally decomposable
graphs, also known as the distance hereditary graphs, and for two non-trivial
subclasses, namely the cographs and the 3-leaf power graphs. Precisely, we give
strutural and incremental characterizations, leading to optimal fully-dynamic
recognition algorithms for vertex and edge modifications, for each of these
classes. These results rely on a new framework to represent the split
decomposition, namely the graph-labelled trees, which also captures the modular
decomposition of graphs and thereby unify these two decompositions techniques.
The point of the paper is to use bijections between these graph classes and
trees whose nodes are labelled by cliques and stars. Doing so, we are also able
to derive an intersection model for distance hereditary graphs, which answers
an open problem.
| [
{
"version": "v1",
"created": "Fri, 10 Oct 2008 07:49:30 GMT"
},
{
"version": "v2",
"created": "Mon, 18 Apr 2011 12:53:57 GMT"
}
] | 2011-04-19T00:00:00 | [
[
"Gioan",
"Emeric",
""
],
[
"Paul",
"Christophe",
""
]
] |
0810.1851 | Marek Karpinski | Piotr Berman, Marek Karpinski, Alex Zelikovsky | 1.25 Approximation Algorithm for the Steiner Tree Problem with Distances
One and Two | null | null | null | null | cs.CC cs.DM cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We give a 1.25 approximation algorithm for the Steiner Tree Problem with
distances one and two, improving on the best known bound for that problem.
| [
{
"version": "v1",
"created": "Fri, 10 Oct 2008 11:25:09 GMT"
}
] | 2008-10-13T00:00:00 | [
[
"Berman",
"Piotr",
""
],
[
"Karpinski",
"Marek",
""
],
[
"Zelikovsky",
"Alex",
""
]
] |
0810.2150 | Christine Task | Christine Task, Arun Chauhan | A Model for Communication in Clusters of Multi-core Machines | This paper has been withdrawn by the author because it was basically
a short-hand write-up of an incompletely formed idea from her Masters, and
she'd like to start using her ArXiv account for her formal PhD research | null | null | null | cs.DC cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | A common paradigm for scientific computing is distributed message-passing
systems, and a common approach to these systems is to implement them across
clusters of high-performance workstations. As multi-core architectures become
increasingly mainstream, these clusters are very likely to include multi-core
machines. However, the theoretical models which are currently used to develop
communication algorithms across these systems do not take into account the
unique properties of processes running on shared-memory architectures,
including shared external network connections and communication via shared
memory locations. Because of this, existing algorithms are far from optimal for
modern clusters. Additionally, recent attempts to adapt these algorithms to
multicore systems have proceeded without the introduction of a more accurate
formal model and have generally neglected to capitalize on the full power these
systems offer. We propose a new model which simply and effectively captures the
strengths of multi-core machines in collective communications patterns and
suggest how it could be used to properly optimize these patterns.
| [
{
"version": "v1",
"created": "Mon, 13 Oct 2008 04:04:42 GMT"
},
{
"version": "v2",
"created": "Mon, 30 Apr 2012 19:16:37 GMT"
}
] | 2012-05-01T00:00:00 | [
[
"Task",
"Christine",
""
],
[
"Chauhan",
"Arun",
""
]
] |
0810.2390 | Simone Faro | Simone Faro and Thierry Lecroq | Efficient Pattern Matching on Binary Strings | 12 pages | null | null | null | cs.DS cs.IR | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | The binary string matching problem consists in finding all the occurrences of
a pattern in a text where both strings are built on a binary alphabet. This is
an interesting problem in computer science, since binary data are omnipresent
in telecom and computer network applications. Moreover the problem finds
applications also in the field of image processing and in pattern matching on
compressed texts. Recently it has been shown that adaptations of classical
exact string matching algorithms are not very efficient on binary data. In this
paper we present two efficient algorithms for the problem adapted to completely
avoid any reference to bits allowing to process pattern and text byte by byte.
Experimental results show that the new algorithms outperform existing solutions
in most cases.
| [
{
"version": "v1",
"created": "Tue, 14 Oct 2008 08:44:27 GMT"
},
{
"version": "v2",
"created": "Wed, 15 Oct 2008 12:15:24 GMT"
}
] | 2008-10-15T00:00:00 | [
[
"Faro",
"Simone",
""
],
[
"Lecroq",
"Thierry",
""
]
] |
0810.3058 | Dimitrios Tsolis Dr | Dimitrios K. Tsolis, Spyros Sioutas and Theodore S. Papatheodorou | Watermarking Digital Images Based on a Content Based Image Retrieval
Technique | 18 pages, 4 figures, 4 tables, submitted to Multimedia Tools and
Applications Journal, Springer | null | null | null | cs.DS cs.CR | http://creativecommons.org/licenses/by/3.0/ | The current work is focusing on the implementation of a robust watermarking
algorithm for digital images, which is based on an innovative spread spectrum
analysis algorithm for watermark embedding and on a content-based image
retrieval technique for watermark detection. The highly robust watermark
algorithms are applying "detectable watermarks" for which a detection mechanism
checks if the watermark exists or no (a Boolean decision) based on a
watermarking key. The problem is that the detection of a watermark in a digital
image library containing thousands of images means that the watermark detection
algorithm is necessary to apply all the keys to the digital images. This
application is non-efficient for very large image databases. On the other hand
"readable" watermarks may prove weaker but easier to detect as only the
detection mechanism is required. The proposed watermarking algorithm combine's
the advantages of both "detectable" and "readable" watermarks. The result is a
fast and robust watermarking algorithm.
| [
{
"version": "v1",
"created": "Fri, 17 Oct 2008 04:22:01 GMT"
}
] | 2009-09-29T00:00:00 | [
[
"Tsolis",
"Dimitrios K.",
""
],
[
"Sioutas",
"Spyros",
""
],
[
"Papatheodorou",
"Theodore S.",
""
]
] |
0810.3203 | David Harvey | David Harvey | A cache-friendly truncated FFT | 14 pages, 11 figures, uses algorithm2e package | null | null | null | cs.SC cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We describe a cache-friendly version of van der Hoeven's truncated FFT and
inverse truncated FFT, focusing on the case of `large' coefficients, such as
those arising in the Schonhage--Strassen algorithm for multiplication in Z[x].
We describe two implementations and examine their performance.
| [
{
"version": "v1",
"created": "Fri, 17 Oct 2008 17:36:27 GMT"
}
] | 2008-10-20T00:00:00 | [
[
"Harvey",
"David",
""
]
] |
0810.3227 | Oliver Kennedy | Oliver Kennedy, Christoph Koch, Al Demers | Dynamic Approaches to In-Network Aggregation | null | null | null | null | cs.DC cs.DB cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Collaboration between small-scale wireless devices hinges on their ability to
infer properties shared across multiple nearby nodes. Wireless-enabled mobile
devices in particular create a highly dynamic environment not conducive to
distributed reasoning about such global properties. This paper addresses a
specific instance of this problem: distributed aggregation. We present
extensions to existing unstructured aggregation protocols that enable
estimation of count, sum, and average aggregates in highly dynamic
environments. With the modified protocols, devices with only limited
connectivity can maintain estimates of the aggregate, despite
\textit{unexpected} peer departures and arrivals. Our analysis of these
aggregate maintenance extensions demonstrates their effectiveness in
unstructured environments despite high levels of node mobility.
| [
{
"version": "v1",
"created": "Fri, 17 Oct 2008 19:48:38 GMT"
}
] | 2008-10-20T00:00:00 | [
[
"Kennedy",
"Oliver",
""
],
[
"Koch",
"Christoph",
""
],
[
"Demers",
"Al",
""
]
] |
0810.3438 | Amit Bhosle | Amit M Bhosle and Teofilo F Gonzalez | Efficient Algorithms and Routing Protocols for Handling Transient Single
Node Failures | 6 pages, 2 columns, 3 figures. To appear in: Proceedings of the 20th
IASTED International Conference on Parallel and Distributed Computing and
Systems (Nov 16-18, 2008, Orlando, FL, USA) | null | null | null | cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | Single node failures represent more than 85% of all node failures in the
today's large communication networks such as the Internet. Also, these node
failures are usually transient. Consequently, having the routing paths globally
recomputed does not pay off since the failed nodes recover fairly quickly, and
the recomputed routing paths need to be discarded. Instead, we develop
algorithms and protocols for dealing with such transient single node failures
by suppressing the failure (instead of advertising it across the network), and
routing messages to the destination via alternate paths that do not use the
failed node. We compare our solution to that of Ref. [11] wherein the authors
have presented a "Failure Insensitive Routing" protocol as a proactive recovery
scheme for handling transient node failures. We show that our algorithms are
faster by an order of magnitude while our paths are equally good. We show via
simulation results that our paths are usually within 15% of the optimal for
randomly generated graph with 100-1000 nodes.
| [
{
"version": "v1",
"created": "Sun, 19 Oct 2008 22:57:53 GMT"
}
] | 2008-10-21T00:00:00 | [
[
"Bhosle",
"Amit M",
""
],
[
"Gonzalez",
"Teofilo F",
""
]
] |
0810.4002 | Laetitia Omer | Julien Allali (LaBRI), Marie-France Sagot (ENS Lyon / Insa Lyon /
INRIA Grenoble Rh\^one-Alpes) | A new distance for high level RNA secondary structure comparison | null | IEEE/ACM Transactions on Computational Biology and Bioinformatics
2 (2005) 3--14 | null | null | cs.DS q-bio.QM | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We describe an algorithm for comparing two RNA secondary structures coded in
the form of trees that introduces two new operations, called node fusion and
edge fusion, besides the tree edit operations of deletion, insertion, and
relabeling classically used in the literature. This allows us to address some
serious limitations of the more traditional tree edit operations when the trees
represent RNAs and what is searched for is a common structural core of two
RNAs. Although the algorithm complexity has an exponential term, this term
depends only on the number of successive fusions that may be applied to a same
node, not on the total number of fusions. The algorithm remains therefore
efficient in practice and is used for illustrative purposes on ribosomal as
well as on other types of RNAs.
| [
{
"version": "v1",
"created": "Wed, 22 Oct 2008 08:24:53 GMT"
}
] | 2008-10-23T00:00:00 | [
[
"Allali",
"Julien",
"",
"LaBRI"
],
[
"Sagot",
"Marie-France",
"",
"ENS Lyon / Insa Lyon /\n INRIA Grenoble Rhône-Alpes"
]
] |
0810.4061 | Satu Elisa Schaeffer | Pekka Orponen, Satu Elisa Schaeffer, Vanesa Avalos Gayt\'an | Locally computable approximations for spectral clustering and absorption
times of random walks | 21 pages, 8 figures | null | null | null | cs.DM cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | We address the problem of determining a natural local neighbourhood or
"cluster" associated to a given seed vertex in an undirected graph. We
formulate the task in terms of absorption times of random walks from other
vertices to the vertex of interest, and observe that these times are well
approximated by the components of the principal eigenvector of the
corresponding fundamental matrix of the graph's adjacency matrix. We further
present a locally computable gradient-descent method to estimate this
Dirichlet-Fiedler vector, based on minimising the respective Rayleigh quotient.
Experimental evaluation shows that the approximations behave well and yield
well-defined local clusters.
| [
{
"version": "v1",
"created": "Wed, 22 Oct 2008 17:48:12 GMT"
}
] | 2008-10-23T00:00:00 | [
[
"Orponen",
"Pekka",
""
],
[
"Schaeffer",
"Satu Elisa",
""
],
[
"Gaytán",
"Vanesa Avalos",
""
]
] |
0810.4423 | Mugurel Ionut Andreica | Mugurel Ionut Andreica | Efficient Algorithmic Techniques for Several Multidimensional Geometric
Data Management and Analysis Problems | The algorithmic techniques presented in this paper were later used by
the author in developing solutions for algorithmic tasks in several contests
in which the author participated (see the attached zip archive for some
examples of task statements and solutions). Knowledge Management - Projects,
Systems and Technologies, Bucharest : Romania (2008) | null | null | null | cs.CG cs.DM cs.DS | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | In this paper I present several novel, efficient, algorithmic techniques for
solving some multidimensional geometric data management and analysis problems.
The techniques are based on several data structures from computational geometry
(e.g. segment tree and range tree) and on the well-known sweep-line method.
| [
{
"version": "v1",
"created": "Fri, 24 Oct 2008 09:44:03 GMT"
},
{
"version": "v2",
"created": "Tue, 1 Jan 2013 20:58:46 GMT"
}
] | 2013-01-03T00:00:00 | [
[
"Andreica",
"Mugurel Ionut",
""
]
] |
0810.4796 | Daniel Raible | Henning Fernau, Fedor V. Fomin, Daniel Lokshtanov, Daniel Raible,
Saket Saurabh, Yngve Villanger | Kernel(s) for Problems With no Kernel: On Out-Trees With Many Leaves | null | null | null | null | cs.DS cs.CC | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ | The {\sc $k$-Leaf Out-Branching} problem is to find an out-branching (i.e. a
rooted oriented spanning tree) with at least $k$ leaves in a given digraph. The
problem has recently received much attention from the viewpoint of
parameterized algorithms {alonLNCS4596,AlonFGKS07fsttcs,BoDo2,KnLaRo}. In this
paper we step aside and take a kernelization based approach to the {\sc
$k$-Leaf-Out-Branching} problem. We give the first polynomial kernel for {\sc
Rooted $k$-Leaf-Out-Branching}, a variant of {\sc $k$-Leaf-Out-Branching} where
the root of the tree searched for is also a part of the input. Our kernel has
cubic size and is obtained using extremal combinatorics.
For the {\sc $k$-Leaf-Out-Branching} problem we show that no polynomial
kernel is possible unless polynomial hierarchy collapses to third level
%$PH=\Sigma_p^3$ by applying a recent breakthrough result by Bodlaender et al.
{BDFH08} in a non-trivial fashion. However our positive results for {\sc Rooted
$k$-Leaf-Out-Branching} immediately imply that the seemingly intractable the
{\sc $k$-Leaf-Out-Branching} problem admits a data reduction to $n$ independent
$O(k^3)$ kernels. These two results, tractability and intractability side by
side, are the first separating {\it many-to-one kernelization} from {\it Turing
kernelization}. This answers affirmatively an open problem regarding "cheat
kernelization" raised in {IWPECOPEN08}.
| [
{
"version": "v1",
"created": "Mon, 27 Oct 2008 11:53:47 GMT"
},
{
"version": "v2",
"created": "Thu, 6 Nov 2008 09:17:43 GMT"
}
] | 2008-11-06T00:00:00 | [
[
"Fernau",
"Henning",
""
],
[
"Fomin",
"Fedor V.",
""
],
[
"Lokshtanov",
"Daniel",
""
],
[
"Raible",
"Daniel",
""
],
[
"Saurabh",
"Saket",
""
],
[
"Villanger",
"Yngve",
""
]
] |
Subsets and Splits