OpenRaiser/Intern-Atlas huggingface dataset:
Set It and Forget It: Approximating the Set Once Strip Cover Problem
Venue: arXiv cs.DS 2013
Year: 2013

We consider the Set Once Strip Cover problem, in which n wireless sensors are deployed over a one-dimensional region. Each sensor has a fixed battery that drains in inverse proportion to a radius that can be set just once, but activated at any time. The problem is to find an assignment of radii and activation times that maximizes the length of time during which the entire region is covered. We show that this problem is NP-hard. Second, we show that RoundRobin, the algorithm in which the sensors simply take turns covering the entire region, has a tight approximation guarantee of 3/2 in both Set Once Strip Cover and the more general Strip Cover problem, in which each radius may be set finitely-many times. Moreover, we show that the more general class of duty cycle algorithms, in which groups of sensors take turns covering the entire region, can do no better. Finally, we give an optimal O(n^2 log n)-time algorithm for the related Set Radius Strip Cover problem, in which all sensors must be activated immediately.
A Characterization Theorem and An Algorithm for A Convex Hull Problem
Venue: arXiv cs.CG 2013
Year: 2013

Given $S= \{v_1, \dots, v_n\} \subset \mathbb{R} ^m$ and $p \in \mathbb{R} ^m$, testing if $p \in conv(S)$, the convex hull of $S$, is a fundamental problem in computational geometry and linear programming. First, we prove a Euclidean {\it distance duality}, distinct from classical separation theorems such as Farkas Lemma: $p$ lies in $conv(S)$ if and only if for each $p' \in conv(S)$ there exists a {\it pivot}, $v_j \in S$ satisfying $d(p',v_j) \geq d(p,v_j)$. Equivalently, $p \not \in conv(S)$ if and only if there exists a {\it witness}, $p' \in conv(S)$ whose Voronoi cell relative to $p$ contains $S$. A witness separates $p$ from $conv(S)$ and approximate $d(p, conv(S))$ to within a factor of two. Next, we describe the {\it Triangle Algorithm}: given $ε\in (0,1)$, an {\it iterate}, $p' \in conv(S)$, and $v \in S$, if $d(p, p') < εd(p,v)$, it stops. Otherwise, if there exists a pivot $v_j$, it replace $v$ with $v_j$ and $p'$ with the projection of $p$ onto the line $p'v_j$. Repeating this process, the algorithm terminates in $O(mn \min \{ε^{-2}, c^{-1}\ln ε^{-1} \})$ arithmetic operations, where $c$ is the {\it visibility factor}, a constant satisfying $c \geq ε^2$ and $\sin (\angle pp'v_j) \leq 1/\sqrt{1+c}$, over all iterates $p'$. Additionally, (i) we prove a {\it strict distance duality} and a related minimax theorem, resulting in more effective pivots; (ii) describe $O(mn \ln ε^{-1})$-time algorithms that may compute a witness or a good approximate solution; (iii) prove {\it generalized distance duality} and describe a corresponding generalized Triangle Algorithm; (iv) prove a {\it sensitivity theorem} to analyze the complexity of solving LP feasibility via the Triangle Algorithm. The Triangle Algorithm is practical and competitive with the simplex method, sparse greedy approximation and first-order methods.
Parallel and sequential in-place permuting and perfect shuffling using involutions
Venue: arXiv cs.DS 2013
Year: 2013

We show that any permutation of ${1,2,...,N}$ can be written as the product of two involutions. As a consequence, any permutation of the elements of an array can be performed in-place in parallel in time O(1). In the case where the permutation is the $k$-way perfect shuffle we develop two methods for efficiently computing such a pair of involutions. The first method works whenever $N$ is a power of $k$; in this case the time is O(N) and space $O(\log^2 N)$. The second method applies to the general case where $N$ is a multiple of $k$; here the time is $O(N \log N)$ and the space is $O(\log^2 N)$. If $k=2$ the space usage of the first method can be reduced to $O(\log N)$ on a machine that has a SADD (population count) instruction.
Stanley-Reisner resolution of constant weight linear codes
Venue: arXiv cs.DM 2013
Year: 2013

Given a constant weight linear code, we investigate its weight hierarchy and the Stanley-Reisner resolution of its associated matroid regarded as a simplicial complex. We also exhibit conditions on the higher weights sufficient to conclude that the code is of constant weight
EigenGP: Sparse Gaussian process models with data-dependent eigenfunctions
Venue: arXiv cs.LG 2013
Year: 2013

Gaussian processes (GPs) provide a nonparametric representation of functions. However, classical GP inference suffers from high computational cost and it is difficult to design nonstationary GP priors in practice. In this paper, we propose a sparse Gaussian process model, EigenGP, based on the Karhunen-Loeve (KL) expansion of a GP prior. We use the Nystrom approximation to obtain data dependent eigenfunctions and select these eigenfunctions by evidence maximization. This selection reduces the number of eigenfunctions in our model and provides a nonstationary covariance function. To handle nonlinear likelihoods, we develop an efficient expectation propagation (EP) inference algorithm, and couple it with expectation maximization for eigenfunction selection. Because the eigenfunctions of a Gaussian kernel are associated with clusters of samples - including both the labeled and unlabeled - selecting relevant eigenfunctions enables EigenGP to conduct semi-supervised learning. Our experimental results demonstrate improved predictive performance of EigenGP over alternative state-of-the-art sparse GP and semisupervised learning methods for regression, classification, and semisupervised classification.
Optimal Capacity Relay Node Placement in a Multi-hop Wireless Network on a Line
Venue: arXiv cs.NI 2013
Year: 2013

We use information theoretic achievable rate formulas for the multi-relay channel to study the problem of optimal placement of relay nodes along the straight line joining a source node and a sink node. The achievable rate formulas that we use are for full-duplex radios at the relays and decode- and-forward relaying. For the single relay case, and individual power constraints at the source node and the relay node, we provide explicit formulas for the optimal relay location and the optimal power allocation to the source-relay channel, for the exponential and the power-law path-loss channel models. For the multiple relay case, we consider exponential path-loss and a total power constraint over the source and the relays, and derive an optimization problem, the solution of which provides the optimal relay locations. Numerical results suggest that at low attenuation the relays are mostly clustered close to the source in order to be able to cooperate among themselves, whereas at high attenuation they are uniformly placed and work as repeaters. The structure of the optimal power allocation for a given placement of the nodes, then motivates us to formulate the problem of impromptu ("as-you-go") placement of relays along a line of exponentially distributed length, with exponential path- loss, so as to minimize a cost function that is additive over hops. The hop cost trades off a capacity limiting term, motivated from the optimal power allocation solution, against the cost of adding a relay node. We formulate the problem as a total cost Markov decision process, for which we prove results for the value function, and provide insights into the placement policy via numerical exploration.
Branch Flow Model: Relaxations and Convexification (Parts I, II)
Venue: arXiv cs.SY 2013
Year: 2013

We propose a branch flow model for the anal- ysis and optimization of mesh as well as radial networks. The model leads to a new approach to solving optimal power flow (OPF) that consists of two relaxation steps. The first step eliminates the voltage and current angles and the second step approximates the resulting problem by a conic program that can be solved efficiently. For radial networks, we prove that both relaxation steps are always exact, provided there are no upper bounds on loads. For mesh networks, the conic relaxation is always exact but the angle relaxation may not be exact, and we provide a simple way to determine if a relaxed solution is globally optimal. We propose convexification of mesh networks using phase shifters so that OPF for the convexified network can always be solved efficiently for an optimal solution. We prove that convexification requires phase shifters only outside a spanning tree of the network and their placement depends only on network topology, not on power flows, generation, loads, or operating constraints. Part I introduces our branch flow model, explains the two relaxation steps, and proves the conditions for exact relaxation. Part II describes convexification of mesh networks, and presents simulation results.
A Survey of Multi-Tape Automata
Venue: arXiv cs.FL 2013
Year: 2013

This paper summarizes the fundamental expressiveness, closure, and decidability properties of various finite-state automata classes with multiple input tapes. It also includes an original algorithm for the intersection of one-way nondeterministic finite-state automata.
Order-preserving Renaming in Synchronous Message Passing Systems with Byzantine Faults
Venue: arXiv cs.DS 2013
Year: 2013

Renaming is a fundamental problem in distributed computing, which consists of a set of processes picking distinct names from a given namespace. The paper presents algorithms that solve order-preserving renaming in synchronous message passing systems with Byzantine processes. To the best of our knowledge, this work is the first to address order-preserving renaming in the given model. Although this problem can be solved by using consensus, it is known that renaming is "weaker" than consensus, therefore we are mainly concerned with the efficiency of performing renaming and make three contributions in this direction. We present an order-preserving renaming algorithm for $N > 3t$ with target namespace of size $N+t-1$ and logarithmic step complexity (where $N$ is the number of processes and $t$ is an upper bound on the number of faults). Similarly to the existing crash-tolerant solution, our algorithm employs the ideas from the approximate agreement problem. We show that our algorithm has constant step complexity if $N>t^2+2t$ and achieves tight namespace of size $N$. Finally, we present an algorithm that solves order-preserving renaming in just 2 communication steps, if $N > 2t^2 + t$.
LP-rounding Algorithms for the Fault-Tolerant Facility Placement Problem
Venue: arXiv cs.DS 2013
Year: 2013

The Fault-Tolerant Facility Placement problem (FTFP) is a generalization of the classic Uncapacitated Facility Location Problem (UFL). In FTFP we are given a set of facility sites and a set of clients. Opening a facility at site $i$ costs $f_i$ and connecting client $j$ to a facility at site $i$ costs $d_{ij}$. We assume that the connection costs (distances) $d_{ij}$ satisfy the triangle inequality. Multiple facilities can be opened at any site. Each client $j$ has a demand $r_j$, which means that it needs to be connected to $r_j$ different facilities (some of which could be located on the same site). The goal is to minimize the sum of facility opening cost and connection cost. The main result of this paper is a 1.575-approximation algorithm for FTFP, based on LP-rounding. The algorithm first reduces the demands to values polynomial in the number of sites. Then it uses a technique that we call adaptive partitioning, which partitions the instance by splitting clients into unit demands and creating a number of (not yet opened) facilities at each site. It also partitions the optimal fractional solution to produce a fractional solution for this new instance. The partitioned instance satisfies a number of properties that allow us to exploit existing LP-rounding methods for UFL to round our partitioned solution to an integral solution, preserving the approximation ratio. In particular, our 1.575-approximation algorithm is based on the ideas from the 1.575-approximation algorithm for UFL by Byrka et al., with changes necessary to satisfy the fault-tolerance requirement.
On the Feasibility of Indoor Broadband Secondary Access to 960-1215 MHz Aeronautical Spectrum
Venue: arXiv cs.NI 2013
Year: 2013

In this paper, we analyze the feasibility of indoor broadband service provisioning using secondary spectrum access to the 960-1215 MHz band, primarily allocated to the distance measuring equipment (DME) system for aeronautical navigation. We propose a practical secondary sharing scheme customized to the characteristics of the DME. Since the primary system performs a safety-of-life functionality, protection from harmful interference becomes extremely critical. The proposed scheme controls aggregate interference by imposing an individual interference threshold on the secondary users. We examine the feasibility of large scale secondary access in terms of the transmission probability of the secondary users that keeps the probability of harmful interference below a given limit. Uncertainties in the estimation of propagation loss and DME location affect the feasibility of the secondary access. Numerical results show that large number of secondary users are able to operate in adjacent DME channels without harming the primary system even with limited accuracy in the estimation of the propagation loss.
A New Approach Towards the Golomb-Welch Conjecture
Venue: arXiv cs.IT 2013
Year: 2013

The Golomb-Welch conjecture deals with the existence of perfect $e$% -error correcting Lee codes of word length $n,$ $PL(n,e)$ codes. Although there are many papers on the topic, the conjecture is still far from being solved. In this paper we initiate the study of an invariant connected to abelian groups that enables us to reformulate the conjecture, and then to prove the non-existence of linear PL(n,2) codes for $n\leq 12$. Using this new approach we also construct the first quasi-perfect Lee codes for dimension $n=3,$ and show that, for fixed $n$, there are only finitely many such codes over $Z^n$.
Linear Network Code for Erasure Broadcast Channel with Feedback: Complexity and Algorithms
Venue: arXiv cs.IT 2013
Year: 2013

This paper investigates the construction of linear network codes for broadcasting a set of data packets to a number of users. The links from the source to the users are modeled as independent erasure channels. Users are allowed to inform the source node whether a packet is received correctly via feedback channels. In order to minimize the number of packet transmissions until all users have received all packets successfully, it is necessary that a data packet, if successfully received by a user, can increase the dimension of the vector space spanned by the encoding vectors he or she has received by one. Such an encoding vector is called innovative. We prove that innovative linear network code is uniformly optimal in minimizing user download delay. When the finite field size is strictly smaller than the number of users, the problem of determining the existence of innovative vectors is proven to be NP-complete. When the field size is larger than or equal to the number of users, innovative vectors always exist and random linear network code (RLNC) is able to find an innovative vector with high probability. While RLNC is optimal in terms of completion time, it has high decoding complexity due to the need of solving a system of linear equations. To reduce decoding time, we propose the use of sparse linear network code, since the sparsity property of encoding vectors can be exploited when solving systems of linear equations. Generating a sparsest encoding vector with large finite field size, however, is shown to be NP-hard. An approximation algorithm that guarantee the Hamming weight of a generated encoding vector to be smaller than a certain factor of the optimal value is constructed. Our simulation results show that our proposed methods have excellent performance in completion time and outperforms RLNC in terms of decoding time.
Google+ or Google-?: Dissecting the Evolution of the New OSN in its First Year
Venue: arXiv cs.SI 2013
Year: 2013

In the era when Facebook and Twitter dominate the market for social media, Google has introduced Google+ (G+) and reported a significant growth in its size while others called it a ghost town. This begs the question that "whether G+ can really attract a significant number of connected and active users despite the dominance of Facebook and Twitter?". This paper tackles the above question by presenting a detailed characterization of G+ based on large scale measurements. We identify the main components of G+ structure, characterize the key features of their users and their evolution over time. We then conduct detailed analysis on the evolution of connectivity and activity among users in the largest connected component (LCC) of G+ structure, and compare their characteristics with other major OSNs. We show that despite the dramatic growth in the size of G+, the relative size of LCC has been decreasing and its connectivity has become less clustered. While the aggregate user activity has gradually increased, only a very small fraction of users exhibit any type of activity. To our knowledge, our study offers the most comprehensive characterization of G+ based on the largest collected data sets.
On (Subgame Perfect) Secure Equilibrium in Quantitative Reachability Games
Venue: arXiv cs.GT 2013
Year: 2013

We study turn-based quantitative multiplayer non zero-sum games played on finite graphs with reachability objectives. In such games, each player aims at reaching his own goal set of states as soon as possible. A previous work on this model showed that Nash equilibria (resp. secure equilibria) are guaranteed to exist in the multiplayer (resp. two-player) case. The existence of secure equilibria in the multiplayer case remained and is still an open problem. In this paper, we focus our study on the concept of subgame perfect equilibrium, a refinement of Nash equilibrium well-suited in the framework of games played on graphs. We also introduce the new concept of subgame perfect secure equilibrium. We prove the existence of subgame perfect equilibria (resp. subgame perfect secure equilibria) in multiplayer (resp. two-player) quantitative reachability games. Moreover, we provide an algorithm deciding the existence of secure equilibria in the multiplayer case.
Bounds for projective codes from semidefinite programming
Venue: arXiv cs.IT 2013
Year: 2013

We apply the semidefinite programming method to derive bounds for projective codes over a finite field.
Signal Enhancement as Minimization of Relevant Information Loss
Venue: arXiv cs.IT 2013
Year: 2013

We introduce the notion of relevant information loss for the purpose of casting the signal enhancement problem in information-theoretic terms. We show that many algorithms from machine learning can be reformulated using relevant information loss, which allows their application to the aforementioned problem. As a particular example we analyze principle component analysis for dimensionality reduction, discuss its optimality, and show that the relevant information loss can indeed vanish if the relevant information is concentrated on a lower-dimensional subspace of the input space.
Approximating Local Homology from Samples
Venue: arXiv cs.CG 2013
Year: 2013

Recently, multi-scale notions of local homology (a variant of persistent homology) have been used to study the local structure of spaces around a given point from a point cloud sample. Current reconstruction guarantees rely on constructing embedded complexes which become difficult in high dimensions. We show that the persistence diagrams used for estimating local homology, can be approximated using families of Vietoris-Rips complexes, whose simple constructions are robust in any dimension. To the best of our knowledge, our results, for the first time, make applications based on local homology, such as stratification learning, feasible in high dimensions.
Near-Linear-Time Deterministic Plane Steiner Spanners and TSP Approximation for Well-Spaced Point Sets
Venue: arXiv cs.CG 2013
Year: 2013

We describe an algorithm that takes as input n points in the plane and a parameter ε, and produces as output an embedded planar graph having the given points as a subset of its vertices in which the graph distances are a (1 + ε)-approximation to the geometric distances between the given points. For point sets in which the Delaunay triangulation has bounded sharpest angle, our algorithm's output has O(n) vertices, its weight is O(1) times the minimum spanning tree weight, and the algorithm's running time is bounded by O(n \sqrt{log log n}). We use this result in a similarly fast deterministic approximation scheme for the traveling salesperson problem.
Rewritable storage channels with hidden state
Venue: arXiv cs.IT 2013
Year: 2013

Many storage channels admit reading and rewriting of the content at a given cost. We consider rewritable channels with a hidden state which models the unknown characteristics of the memory cell. In addition to mitigating the effect of the write noise, rewrites can help the write controller obtain a better estimate of the hidden state. The paper has two contributions. The first is a lower bound on the capacity of a general rewritable channel with hidden state. The lower bound is obtained using a coding scheme that combines Gelfand-Pinsker coding with superposition coding. The rewritable AWGN channel is discussed as an example. The second contribution is a simple coding scheme for a rewritable channel where the write noise and hidden state are both uniformly distributed. It is shown that this scheme is asymptotically optimal as the number of rewrites gets large.
A Construction of Quantum LDPC Codes from Cayley Graphs
Venue: arXiv cs.IT 2013
Year: 2013

We study a construction of Quantum LDPC codes proposed by MacKay, Mitchison and Shokrollahi. It is based on the Cayley graph of Fn together with a set of generators regarded as the columns of the parity-check matrix of a classical code. We give a general lower bound on the minimum distance of the Quantum code in $\mathcal{O}(dn^2)$ where d is the minimum distance of the classical code. When the classical code is the $[n, 1, n]$ repetition code, we are able to compute the exact parameters of the associated Quantum code which are $[[2^n, 2^{\frac{n+1}{2}}, 2^{\frac{n-1}{2}}]]$.
Factoring bivariate lacunary polynomials without heights
Venue: arXiv cs.CC 2013
Year: 2013

We present an algorithm which computes the multilinear factors of bivariate lacunary polynomials. It is based on a new Gap Theorem which allows to test whether a polynomial of the form P(X,X+1) is identically zero in time polynomial in the number of terms of P(X,Y). The algorithm we obtain is more elementary than the one by Kaltofen and Koiran (ISSAC'05) since it relies on the valuation of polynomials of the previous form instead of the height of the coefficients. As a result, it can be used to find some linear factors of bivariate lacunary polynomials over a field of large finite characteristic in probabilistic polynomial time.
C to O-O Translation: Beyond the Easy Stuff
Venue: arXiv cs.PL 2013
Year: 2013

Can we reuse some of the huge code-base developed in C to take advantage of modern programming language features such as type safety, object-orientation, and contracts? This paper presents a source-to-source translation of C code into Eiffel, a modern object-oriented programming language, and the supporting tool C2Eif. The translation is completely automatic and supports the entire C language (ANSI, as well as many GNU C Compiler extensions, through CIL) as used in practice, including its usage of native system libraries and inlined assembly code. Our experiments show that C2Eif can handle C applications and libraries of significant size (such as vim and libgsl), as well as challenging benchmarks such as the GCC torture tests. The produced Eiffel code is functionally equivalent to the original C code, and takes advantage of some of Eiffel's object-oriented features to produce safe and easy-to-debug translations.