OpenRaiser/Intern-Atlas huggingface dataset:
Linear Network Coding, Linear Index Coding and Representable Discrete Polymatroids
Venue: arXiv cs.IT 2016
Year: 2016

Discrete polymatroids are the multi-set analogue of matroids. In this paper, we explore the connections among linear network coding, linear index coding and representable discrete polymatroids. We consider vector linear solutions of networks over a field $\mathbb{F}_q,$ with possibly different message and edge vector dimensions, which are referred to as linear fractional solutions. We define a \textit{discrete polymatroidal} network and show that a linear fractional solution over a field $\mathbb{F}_q,$ exists for a network if and only if the network is discrete polymatroidal with respect to a discrete polymatroid representable over $\mathbb{F}_q.$ An algorithm to construct networks starting from certain class of discrete polymatroids is provided. Every representation over $\mathbb{F}_q$ for the discrete polymatroid, results in a linear fractional solution over $\mathbb{F}_q$ for the constructed network. Next, we consider the index coding problem and show that a linear solution to an index coding problem exists if and only if there exists a representable discrete polymatroid satisfying certain conditions which are determined by the index coding problem considered. El Rouayheb et. al. showed that the problem of finding a multi-linear representation for a matroid can be reduced to finding a \textit{perfect linear index coding solution} for an index coding problem obtained from that matroid. We generalize the result of El Rouayheb et. al. by showing that the problem of finding a representation for a discrete polymatroid can be reduced to finding a perfect linear index coding solution for an index coding problem obtained from that discrete polymatroid.
Computing the Fréchet Distance with a Retractable Leash
Venue: arXiv cs.CG 2016
Year: 2016

All known algorithms for the Fréchet distance between curves proceed in two steps: first, they construct an efficient oracle for the decision version; second, they use this oracle to find the optimum from a finite set of critical values. We present a novel approach that avoids the detour through the decision version. This gives the first quadratic time algorithm for the Fréchet distance between polygonal curves in $R^d$ under polyhedral distance functions (e.g., $L_1$ and $L_\infty$). We also get a $(1+\varepsilon)$-approximation of the Fréchet distance under the Euclidean metric, in quadratic time for any fixed $\varepsilon > 0$. For the exact Euclidean case, our framework currently yields an algorithm with running time $O(n^2 \log^2 n)$. However, we conjecture that it may eventually lead to a faster exact algorithm.
Measuring Distance between Reeb Graphs
Venue: arXiv cs.CG 2016
Year: 2016

One of the prevailing ideas in geometric and topological data analysis is to provide descriptors that encode useful information about hidden objects from observed data. The Reeb graph is one such descriptor for a given scalar function. The Reeb graph provides a simple yet meaningful abstraction of the input domain, and can also be computed efficiently. Given the popularity of the Reeb graph in applications, it is important to understand its stability and robustness with respect to changes in the input function, as well as to be able to compare the Reeb graphs resulting from different functions. In this paper, we propose a metric for Reeb graphs, called the functional distortion distance. Under this distance measure, the Reeb graph is stable against small changes of input functions. At the same time, it remains discriminative at differentiating input functions. In particular, the main result is that the functional distortion distance between two Reeb graphs is bounded from below by (and thus more discriminative than) the bottleneck distance between both the ordinary and extended persistence diagrams for appropriate dimensions. As an application of our results, we analyze a natural simplification scheme for Reeb graphs, and show that persistent features in Reeb graph remains persistent under simplification. Understanding the stability of important features of the Reeb graph under simplification is an interesting problem on its own right, and critical to the practical usage of Reeb graphs.
Spatial Fluid Limits for Stochastic Mobile Networks
Venue: arXiv cs.NI 2016
Year: 2016

We consider Markov models of large-scale networks where nodes are characterized by their local behavior and by a mobility model over a two-dimensional lattice. By assuming random walk, we prove convergence to a system of partial differential equations (PDEs) whose size depends neither on the lattice size nor on the population of nodes. This provides a macroscopic view of the model which approximates discrete stochastic movements with continuous deterministic diffusions. We illustrate the practical applicability of this result by modeling a network of mobile nodes with on/off behavior performing file transfers with connectivity to 802.11 access points. By means of an empirical validation against discrete-event simulation we show high quality of the PDE approximation even for low populations and coarse lattices. In addition, we confirm the computational advantage in using the PDE limit over a traditional ordinary differential equation limit where the lattice is modeled discretely, yielding speed-ups of up to two orders of magnitude.
A unified approach to the performance analysis of caching systems
Venue: arXiv cs.NI 2016
Year: 2016

We propose a unified methodology to analyse the performance of caches (both isolated and interconnected), by extending and generalizing a decoupling technique originally known as Che's approximation, which provides very accurate results at low computational cost. We consider several caching policies, taking into account the effects of temporal locality. In the case of interconnected caches, our approach allows us to do better than the Poisson approximation commonly adopted in prior work. Our results, validated against simulations and trace-driven experiments, provide interesting insights into the performance of caching systems.
A nearly optimal algorithm for deciding connectivity queries in smooth and bounded real algebraic sets
Venue: arXiv cs.SC 2016
Year: 2016

A roadmap for a semi-algebraic set $S$ is a curve which has a non-empty and connected intersection with all connected components of $S$. Hence, this kind of object, introduced by Canny, can be used to answer connectivity queries (with applications, for instance, to motion planning) but has also become of central importance in effective real algebraic geometry, since it is used in higher-level algorithms. In this paper, we provide a probabilistic algorithm which computes roadmaps for smooth and bounded real algebraic sets. Its output size and running time are polynomial in $(nD)^{n\log(d)}$, where $D$ is the maximum of the degrees of the input polynomials, $d$ is the dimension of the set under consideration and $n$ is the number of variables. More precisely, the running time of the algorithm is essentially subquadratic in the output size. Even under our assumptions, it is the first roadmap algorithm with output size and running time polynomial in $(nD)^{n\log(d)}$.
Classical-Quantum Arbitrarily Varying Wiretap Channel: Ahlswede dichotomy, Positivity, Resources, Super Activation
Venue: arXiv cs.IT 2016
Year: 2016

We establish Ahlswede dichotomy for arbitrarily varying classical-quantum wiretap channels. This means that either the deterministic secrecy capacity of an arbitrarily varying classical-quantum wiretap channel is zero or it equals its randomness-assisted secrecy capacity. We analyze the secrecy capacity of arbitrarily varying classical-quantum wiretap channels when the sender and the receiver use various resources. It turns out that having randomness, common randomness, and correlation as resources are very helpful for achieving a positive deterministic secrecy capacity of arbitrarily varying classical-quantum wiretap channels. We prove the phenomenon super-activation for arbitrarily varying classical-quantum wiretap channels, i.e., if we use two arbitrarily varying classical-quantum wiretap channels, both with zero deterministic secrecy capacity together, they allow perfect secure transmission.
A Game-Theoretic Approach to Distributed Coalition Formation in Energy-Aware Cloud Federations (Extended Version)
Venue: arXiv cs.DC 2016
Year: 2016

Federations among sets of Cloud Providers (CPs), whereby a set of CPs agree to mutually use their own resources to run the VMs of other CPs, are considered a promising solution to the problem of reducing the energy cost. In this paper, we address the problem of federation formation for a set of CPs, whose solution is necessary to exploit the potential of cloud federations for the reduction of the energy bill. We devise a distributed algorithm, based on cooperative game theory, that allows a set of CPs to cooperatively set up their federations in such a way that their individual profit is increased with respect to the case in which they work in isolation, and we show that, by using our algorithm and the proposed CPs' utility function, they are able to self-organize into Nash-stable federations and, by means of iterated executions, to adapt themselves to environmental changes. Numerical results are presented to demonstrate the effectiveness of the proposed algorithm.
A new hierarchical clustering algorithm to identify non-overlapping like-minded communities
Venue: arXiv cs.SI 2016
Year: 2016

A network has a non-overlapping community structure if the nodes of the network can be partitioned into disjoint sets such that each node in a set is densely connected to other nodes inside the set and sparsely connected to the nodes out- side it. There are many metrics to validate the efficacy of such a structure, such as clustering coefficient, betweenness, centrality, modularity and like-mindedness. Many methods have been proposed to optimize some of these metrics, but none of these works well on the recently introduced metric like-mindedness. To solve this problem, we propose a be- havioral property based algorithm to identify communities that optimize the like-mindedness metric and compare its performance on this metric with other behavioral data based methodologies as well as community detection methods that rely only on structural data. We execute these algorithms on real-life datasets of Filmtipset and Twitter and show that our algorithm performs better than the existing algorithms with respect to the like-mindedness metric.
GPU-Acceleration of Parallel Unconditionally Stable Group Explicit Finite Difference Method
Venue: arXiv cs.NA 2016
Year: 2016

Graphics Processing Units (GPUs) are high performance co-processors originally intended to improve the use and quality of computer graphics applications. Once, researchers and practitioners noticed the potential of using GPU for general purposes, GPUs applications have been extended from graphics applications to other fields. The main objective of this paper is to evaluate the impact of using GPU in solution of the transient diffusion type equation by parallel and stable group explicit finite difference method and encourage the researchers in this field to immigrate from implementing their algorithms in CPU to the GPU emerging world. For comparing them, we implemented the method in both GPU and CPU (multi-core) programming context. Moreover, we proposed an optimal synchronization arrangement for the implementation pseudo-code. Also, the interrelation of GPU parallel programming and initializing the algorithm variables were discussed, taking advantage of numerical experiences. The GPU-approach results are faster than those obtained from a much expensive parallel 8-thread CPU-based programming. The GPU used in this paper, is an ordinary old laptop GPU (GT 335M, launched at 2010) and is accessible for everyone and the newer generations of GPU (as discussed in paper) have even more performance priority over the similar-price GPUs. Then, the results are expected to encourage the entire research society to take advantage of GPUs and improve the time efficiency of their studies.
The Discrete and Semi-continuous Fréchet Distance with Shortcuts via Approximate Distance Counting and Selection Techniques
Venue: arXiv cs.CG 2016
Year: 2016

The \emph{Fréchet distance} is a well studied similarity measures between curves. The \emph{discrete Fréchet distance} is an analogous similarity measure, defined for a sequence $A$ of $m$ points and a sequence $B$ of $n$ points, where the points are usually sampled from input curves. In this paper we consider a variant, called the \emph{discrete Fréchet distance with shortcuts}, which captures the similarity between (sampled) curves in the presence of outliers. For the \emph{two-sided} case, where shortcuts are allowed in both curves, we give an $O((m^{2/3}n^{2/3}+m+n)\log^3 (m+n))$-time algorithm for computing this distance. When shortcuts are allowed only in one noise-containing curve, we give an even faster randomized algorithm that runs in $O((m+n)^{6/5+\varepsilon})$ expected time, for any $\varepsilon>0$. Our techniques are novel and may find further applications. One of the main new technical results is: Given two sets of points $A$ and $B$ and an interval $I$, we develop an algorithm that decides whether the number of pairs $(x,y)\in A\times B$ whose distance ${\rm dist}(x,y)$ is in $I$, is less than some given threshold $L$. The running time of this algorithm decreases as $L$ increases. In case there are more than $L$ pairs of points whose distance is in $I$, we can get a small sample of pairs that contains a pair at approximate median distance (i.e., we can approximately "bisect" $I$). We combine this procedure with additional ideas to search, with a small overhead, for the optimal one-sided Fréchet distance with shortcuts, using a very fast decision procedure. We also show how to apply this technique for approximating distance selection (with respect to rank), and for computing the semi-continuous Fréchet distance with one-sided shortcuts.
Mondshein Sequences (a.k.a. (2,1)-Orders)
Venue: arXiv cs.DS 2016
Year: 2016

Canonical orderings [STOC'88, FOCS'92] have been used as a key tool in graph drawing, graph encoding and visibility representations for the last decades. We study a far-reaching generalization of canonical orderings to non-planar graphs that was published by Lee Mondshein in a PhD-thesis at M.I.T. as early as 1971. Mondshein proposed to order the vertices of a graph in a sequence such that, for any i, the vertices from 1 to i induce essentially a 2-connected graph while the remaining vertices from i+1 to n induce a connected graph. Mondshein's sequence generalizes canonical orderings and became later and independently known under the name non-separating ear decomposition. Surprisingly, this fundamental link between canonical orderings and non-separating ear decomposition has not been established before. Currently, the fastest known algorithm for computing a Mondshein sequence achieves a running time of O(nm); the main open problem in Mondshein's and follow-up work is to improve this running time to subquadratic time. After putting Mondshein's work into context, we present an algorithm that computes a Mondshein sequence in optimal time and space O(m). This improves the previous best running time by a factor of n. We illustrate the impact of this result by deducing linear-time algorithms for five other problems, for four out of which the previous best running times have been quadratic. In particular, we show how to - compute three independent spanning trees of a 3-connected graph in time O(m), - improve the preprocessing time from O(n^2) to O(m) for a data structure reporting 3 internally disjoint paths between any given vertex pair, - derive a very simple O(n)-time planarity test once a Mondshein sequence has been computed, - compute a nested family of contractible subgraphs of 3-connected graphs in time O(m), - compute a 3-partition in time O(m).
Private Matchings and Allocations
Venue: arXiv cs.GT 2016
Year: 2016

We consider a private variant of the classical allocation problem: given k goods and n agents with individual, private valuation functions over bundles of goods, how can we partition the goods amongst the agents to maximize social welfare? An important special case is when each agent desires at most one good, and specifies her (private) value for each good: in this case, the problem is exactly the maximum-weight matching problem in a bipartite graph. Private matching and allocation problems have not been considered in the differential privacy literature, and for good reason: they are plainly impossible to solve under differential privacy. Informally, the allocation must match agents to their preferred goods in order to maximize social welfare, but this preference is exactly what agents wish to hide. Therefore, we consider the problem under the relaxed constraint of joint differential privacy: for any agent i, no coalition of agents excluding i should be able to learn about the valuation function of agent i. In this setting, the full allocation is no longer published---instead, each agent is told what good to get. We first show that with a small number of identical copies of each good, it is possible to efficiently and accurately solve the maximum weight matching problem while guaranteeing joint differential privacy. We then consider the more general allocation problem, when bidder valuations satisfy the gross substitutes condition. Finally, we prove that the allocation problem cannot be solved to non-trivial accuracy under joint differential privacy without requiring multiple copies of each type of good.
On the List Update Problem with Advice
Venue: arXiv cs.DS 2016
Year: 2016

We study the online list update problem under the advice model of computation. Under this model, an online algorithm receives partial information about the unknown parts of the input in the form of some bits of advice generated by a benevolent offline oracle. We show that advice of linear size is required and sufficient for a deterministic algorithm to achieve an optimal solution or even a competitive ratio better than $15/14$. On the other hand, we show that surprisingly two bits of advice are sufficient to break the lower bound of $2$ on the competitive ratio of deterministic online algorithms and achieve a deterministic algorithm with a competitive ratio of $5/3$. In this upper-bound argument, the bits of advice determine the algorithm with smaller cost among three classical online algorithms, TIMESTAMP and two members of the MTF2 family of algorithms. We also show that MTF2 algorithms are $2.5$-competitive.
Asymptotic MMSE Analysis Under Sparse Representation Modeling
Venue: arXiv cs.IT 2016
Year: 2016

Compressed sensing is a signal processing technique in which data is acquired directly in a compressed form. There are two modeling approaches that can be considered: the worst-case (Hamming) approach and a statistical mechanism, in which the signals are modeled as random processes rather than as individual sequences. In this paper, the second approach is studied. In particular, we consider a model of the form $\boldsymbol{Y} = \boldsymbol{H}\boldsymbol{X}+\boldsymbol{W}$, where each comportment of $\boldsymbol{X}$ is given by $X_i = S_iU_i$, where $\left\{U_i\right\}$ are i.i.d. Gaussian random variables, and $\left\{S_i\right\}$ are binary random variables independent of $\left\{U_i\right\}$, and not necessarily independent and identically distributed (i.i.d.), $\boldsymbol{H}\in\mathbb{R}^{k\times n}$ is a random matrix with i.i.d. entries, and $\boldsymbol{W}$ is white Gaussian noise. Using a direct relationship between optimum estimation and certain partition functions, and by invoking methods from statistical mechanics and from random matrix theory (RMT), we derive an asymptotic formula for the minimum mean-square error (MMSE) of estimating the input vector $\boldsymbol{X}$ given $\boldsymbol{Y}$ and $\boldsymbol{H}$, as $k,n\to\infty$, keeping the measurement rate, $R = k/n$, fixed. In contrast to previous derivations, which are based on the replica method, the analysis carried out in this paper is rigorous.
A Randomized Incremental Algorithm for the Hausdorff Voronoi Diagram of Non-crossing Clusters
Venue: arXiv cs.CG 2016
Year: 2016

In the Hausdorff Voronoi diagram of a family of \emph{clusters of points} in the plane, the distance between a point $t$ and a cluster $P$ is measured as the maximum distance between $t$ and any point in $P$, and the diagram is defined in a nearest-neighbor sense for the input clusters. In this paper we consider %El."non-crossing" \emph{non-crossing} clusters in the plane, for which the combinatorial complexity of the Hausdorff Voronoi diagram is linear in the total number of points, $n$, on the convex hulls of all clusters. We present a randomized incremental construction, based on point location, that computes this diagram in expected $O(n\log^2{n})$ time and expected $O(n)$ space. Our techniques efficiently handle non-standard characteristics of generalized Voronoi diagrams, such as sites of non-constant complexity, sites that are not enclosed in their Voronoi regions, and empty Voronoi regions. The diagram finds direct applications in VLSI computer-aided design.
Optimal Spread in Network Consensus Models
Venue: arXiv cs.DM 2016
Year: 2016

In a model of network communication based on a random walk in an undirected graph, what subset of nodes (subject to constraints on the set size), enable the fastest spread of information? The dynamics of spread is described by a process dual to the movement from informed to uninformed nodes. In this setting, an optimal set $A$ minimizes the sum of the expected first hitting times $F(A)$, of random walks that start at nodes outside the set. In this paper,the problem is reformulated so that the search for solutions is restricted to a class of optimal and "near" optimal subsets of the graph. We introduce a submodular, non-decreasing rank function $ρ$, that permits some comparison between the solution obtained by the classical greedy algorithm and one obtained by our methods. The supermodularity and non-increasing properties of $F$ are used to show that the rank of our solution is at least $(1-\frac{1}{e})$ times the rank of the optimal set. When the solution has a higher rank than the greedy solution this constant can be improved to $(1-\frac{1}{e})(1+χ)$ where $χ>0$ is determined a posteriori. The method requires the evaluation of $F$ for sets of some fixed cardinality $m$, where $m$ is much smaller than the cardinality of the optimal set. When $F$ has forward elemental curvature $κ$, we can provide a rough description of the trade-off between solution quality and computational effort $m$ in terms of $κ$.
Graph Cuts with Interacting Edge Costs - Examples, Approximations, and Algorithms
Venue: arXiv cs.DS 2016
Year: 2016

We study an extension of the classical graph cut problem, wherein we replace the modular (sum of edge weights) cost function by a submodular set function defined over graph edges. Special cases of this problem have appeared in different applications in signal processing, machine learning, and computer vision. In this paper, we connect these applications via the generic formulation of "cooperative graph cuts", for which we study complexity, algorithms, and connections to polymatroidal network flows. Finally, we compare the proposed algorithms empirically.