OpenRaiser/Intern-Atlas huggingface dataset:
Scaling Algorithms for Weighted Matching in General Graphs
Venue: arXiv cs.DS 2017
Year: 2017

We present a new scaling algorithm for maximum (or minimum) weight perfect matching on general, edge weighted graphs. Our algorithm runs in $O(m\sqrt{n}\log(nN))$ time, $O(m\sqrt{n})$ per scale, which matches the running time of the best cardinality matching algorithms on sparse graphs. Here $m,n,$ and $N$ bound the number of edges, vertices, and magnitude of any edge weight. Our result improves on a 25-year old algorithm of Gabow and Tarjan, which runs in $O(m\sqrt{n\log nα(m,n)} \log(nN))$ time.
Partitioning Well-Clustered Graphs: Spectral Clustering Works!
Venue: arXiv cs.DS 2017
Year: 2017

In this paper we study variants of the widely used spectral clustering that partitions a graph into k clusters by (1) embedding the vertices of a graph into a low-dimensional space using the bottom eigenvectors of the Laplacian matrix, and (2) grouping the embedded points into k clusters via k-means algorithms. We show that, for a wide class of graphs, spectral clustering gives a good approximation of the optimal clustering. While this approach was proposed in the early 1990s and has comprehensive applications, prior to our work similar results were known only for graphs generated from stochastic models. We also give a nearly-linear time algorithm for partitioning well-clustered graphs based on computing a matrix exponential and approximate nearest neighbor data structures.
Sketching and Embedding are Equivalent for Norms
Venue: arXiv cs.DS 2017
Year: 2017

An outstanding open question posed by Guha and Indyk in 2006 asks to characterize metric spaces in which distances can be estimated using efficient sketches. Specifically, we say that a sketching algorithm is efficient if it achieves constant approximation using constant sketch size. A well-known result of Indyk (J. ACM, 2006) implies that a metric that admits a constant-distortion embedding into $\ell_p$ for $p\in(0,2]$ also admits an efficient sketching scheme. But is the converse true, i.e., is embedding into $\ell_p$ the only way to achieve efficient sketching? We address these questions for the important special case of normed spaces, by providing an almost complete characterization of sketching in terms of embeddings. In particular, we prove that a finite-dimensional normed space allows efficient sketches if and only if it embeds (linearly) into $\ell_{1-\varepsilon}$ with constant distortion. We further prove that for norms that are closed under sum-product, efficient sketching is equivalent to embedding into $\ell_1$ with constant distortion. Examples of such norms include the Earth Mover's Distance (specifically its norm variant, called Kantorovich-Rubinstein norm), and the trace norm (a.k.a. Schatten $1$-norm or the nuclear norm). Using known non-embeddability theorems for these norms by Naor and Schechtman (SICOMP, 2007) and by Pisier (Compositio. Math., 1978), we then conclude that these spaces do not admit efficient sketches either, making progress towards answering another open question posed by Indyk in 2006. Finally, we observe that resolving whether "sketching is equivalent to embedding into $\ell_1$ for general norms" (i.e., without the above restriction) is equivalent to resolving a well-known open problem in Functional Analysis posed by Kwapien in 1969.
Congestion Games with Distance-Based Strict Uncertainty
Venue: arXiv cs.GT 2017
Year: 2017

We put forward a new model of congestion games where agents have uncertainty over the routes used by other agents. We take a non-probabilistic approach, assuming that each agent knows that the number of agents using an edge is within a certain range. Given this uncertainty, we model agents who either minimize their worst-case cost (WCC) or their worst-case regret (WCR), and study implications on equilibrium existence, convergence through adaptive play, and efficiency. Under the WCC behavior the game reduces to a modified congestion game, and welfare improves when agents have moderate uncertainty. Under WCR behavior the game is not, in general, a congestion game, but we show convergence and efficiency bounds for a simple class of games.
Subtyping in Java is a Fractal
Venue: arXiv cs.PL 2017
Year: 2017

While developing their software, professional object-oriented (OO) software developers keep in their minds an image of the subtyping relation between types in their software. The goal of this paper is to present an observation about the graph of the subtyping relation in Java, namely the observation that, after the addition of generics---and of wildcards, in particular---to Java, the graph of the subtyping relation is no longer a simple directed-acyclic graph (DAG), as in pre-generics Java, but is rather a fractal. Further, this observation equally applies to other mainstream nominally-typed OO languages (such as C#, C++ and Scala) where generics and wildcards (or some other form of 'variance annotations') are standard features. Accordingly, the shape of the subtyping relation in these OO languages is more complex than a tree or a simple DAG, and indeed is also a fractal. Given the popularity of fractals, the fractal observation may help OO software developers keep a useful and intuitive mental image of their software's subtyping relation, even if it is a little more frightening, and more amazing one than before. With proper support from IDEs, the fractal observation can help OO developers in resolving type errors they may find in their code in lesser time, and with more confidence.
Learning to Generate Chairs, Tables and Cars with Convolutional Networks
Venue: arXiv cs.CV 2017
Year: 2017

We train generative 'up-convolutional' neural networks which are able to generate images of objects given object style, viewpoint, and color. We train the networks on rendered 3D models of chairs, tables, and cars. Our experiments show that the networks do not merely learn all images by heart, but rather find a meaningful representation of 3D models allowing them to assess the similarity of different models, interpolate between given views to generate the missing ones, extrapolate views, and invent new objects not present in the training set by recombining training instances, or even two different object classes. Moreover, we show that such generative networks can be used to find correspondences between different objects from the dataset, outperforming existing approaches on this task.
Enhanced joint sparsity via Iterative Support Detection
Venue: arXiv cs.NA 2017
Year: 2017

Joint sparsity has attracted considerable attention in recent years in many fields including sparse signal recovery in compressed sensing (CS), statistics, and machine learning. Traditional convex models suffer from the suboptimal performance though enjoying tractable computation. In this paper, we propose a new non-convex joint sparsity model, and develop a corresponding multi-stage adaptive convex relaxation algorithm. This method extends the idea of iterative support detection (ISD) from the single vector estimation to the multi-vector estimation by considering the joint sparsity prior. We provide some preliminary theoretical analysis including convergence analysis and a sufficient recovery condition. Numerical experiments from both compressive sensing and feature learning show the better performance of the proposed method in comparison with several state-of-the-art alternatives. Moreover, we demonstrate that the extension of ISD from the single vector to multi-vector estimation is not trivial. In particular, while ISD does not work well for reconstructing the signal channel sparse Bernoulli signal, it does achieve significantly improved performance when recovering the multi-channel sparse Bernoulli signal thanks to its ability of natural incorporation of the joint sparsity structure.
Opportunistic Relaying without CSI: Optimizing Variable-Rate HARQ
Venue: arXiv cs.IT 2017
Year: 2017

We analyze the opportunistic relaying based on HARQ transmission over the block-fading channel with absence of channel state information (CSI) at the transmitter nodes. We assume that both the source and the relay are allowed to vary their transmission rate between the HARQ transmission rounds. We solve the problem of throughput maximization with respect to the transmission rates using double-recursive Dynamic Programming. Simplifications are also proposed to diminish the complexity of the optimization. The numerical results confirm that the variable-rate HARQ can increase the throughput significantly comparing to its fixed-rate counterpart.
Coordination in distributed networks via coded actions with application to power control
Venue: arXiv cs.IT 2017
Year: 2017

This paper investigates the problem of coordinating several agents through their actions. Although the methodology applies to general scenarios, the present work focuses on a situation with an asymmetric observation structure that only involves two agents. More precisely, one of the agents knows the past, present, and future realizations of a state (the system state) that affects the common payoff function of the agents; in contrast, the second agent is assumed either to know the past realizations of the system state or to have no knowledge of it. In both cases, the second agent has access to some strictly causal observations of the first agent's actions, which enables the two agents to coordinate. These scenarios are applied to the problem of distributed power control; the key idea is that a transmitter may embed information about the wireless channel state into its transmit power levels so that an observation of these levels, e.g. the signal-to-interference plus noise ratio, allows the other transmitter to coordinate its power levels. The main contributions of this paper are twofold. First, we provide a characterization of the set of feasible average payoffs when the agents repeatedly take long sequences of actions and the realizations of the system state are \acs{iid}. Second, we exploit these results in the context of distributed power control and introduce the concept of coded power control. We carry out an extensive numerical analysis of the benefits of coded power control over alternative power control policies, and highlight a simple yet non-trivial example of a power control code.
Network Analysis in the Legal Domain: A complex model for European Union legal sources
Venue: arXiv cs.SI 2017
Year: 2017

Legislators, designers of legal information systems, as well as citizens face often problems due to the interdependence of the laws and the growing number of references needed to interpret them. Quantifying this complexity is not an easy task. In this paper, we introduce the "Legislation Network" as a novel approach to address related problems. We have collected an extensive data set of a more than 60-year old legislation corpus, as published in the Official Journal of the European Union, and we further analysed it as a complex network, thus gaining insight into its topological structure. Among other issues, we have performed a temporal analysis of the evolution of the Legislation Network, as well as a robust resilience test to assess its vulnerability under specific cases that may lead to possible breakdowns. Results are quite promising, showing that our approach can lead towards an enhanced explanation in respect to the structure and evolution of legislation properties.
Capacity-achieving Sparse Superposition Codes via Approximate Message Passing Decoding
Venue: arXiv cs.IT 2017
Year: 2017

Sparse superposition codes were recently introduced by Barron and Joseph for reliable communication over the AWGN channel at rates approaching the channel capacity. The codebook is defined in terms of a Gaussian design matrix, and codewords are sparse linear combinations of columns of the matrix. In this paper, we propose an approximate message passing decoder for sparse superposition codes, whose decoding complexity scales linearly with the size of the design matrix. The performance of the decoder is rigorously analyzed and it is shown to asymptotically achieve the AWGN capacity with an appropriate power allocation. Simulation results are provided to demonstrate the performance of the decoder at finite blocklengths. We introduce a power allocation scheme to improve the empirical performance, and demonstrate how the decoding complexity can be significantly reduced by using Hadamard design matrices.
Models and termination of proof reduction in the $λ$$Π$-calculus modulo theory
Venue: arXiv cs.LO 2017
Year: 2017

We define a notion of model for the $λ$$Π$-calculus modulo theory and prove a soundness theorem. We then define a notion of super-consistency and prove that proof reduction terminates in the $λ$$Π$-calculus modulo any super-consistent theory. We prove this way the termination of proof reduction in several theories including Simple type theory and the Calculus of constructions .
Joint source-channel coding with feedback
Venue: arXiv cs.IT 2017
Year: 2017

This paper quantifies the fundamental limits of variable-length transmission of a general (possibly analog) source over a memoryless channel with noiseless feedback, under a distortion constraint. We consider excess distortion, average distortion and guaranteed distortion ($d$-semifaithful codes). In contrast to the asymptotic fundamental limit, a general conclusion is that allowing variable-length codes and feedback leads to a sizable improvement in the fundamental delay-distortion tradeoff. In addition, we investigate the minimum energy required to reproduce $k$ source samples with a given fidelity after transmission over a memoryless Gaussian channel, and we show that the required minimum energy is reduced with feedback and an average (rather than maximal) power constraint.
Efficiently Testing T-Interval Connectivity in Dynamic Graphs
Venue: arXiv cs.DS 2017
Year: 2017

Many types of dynamic networks are made up of durable entities whose links evolve over time. When considered from a {\em global} and {\em discrete} standpoint, these networks are often modelled as evolving graphs, i.e. a sequence of graphs ${\cal G}=(G_1,G_2,...,G_δ)$ such that $G_i=(V,E_i)$ represents the network topology at time step $i$. Such a sequence is said to be $T$-interval connected if for any $t\in [1, δ-T+1]$ all graphs in $\{G_t,G_{t+1},...,G_{t+T-1}\}$ share a common connected spanning subgraph. In this paper, we consider the problem of deciding whether a given sequence ${\cal G}$ is $T$-interval connected for a given $T$. We also consider the related problem of finding the largest $T$ for which a given ${\cal G}$ is $T$-interval connected. We assume that the changes between two consecutive graphs are arbitrary, and that two operations, {\em binary intersection} and {\em connectivity testing}, are available to solve the problems. We show that $Ω(δ)$ such operations are required to solve both problems, and we present optimal $O(δ)$ online algorithms for both problems. We extend our online algorithms to a dynamic setting in which connectivity is based on the recent evolution of the network.
Vivace: a collaborative live coding language and platform
Venue: arXiv cs.CY 2017
Year: 2017

Live coding is a performance and creative technique based on improvised and interactive coding. Many recent endeavors have focused in live coding both because of aesthetics and as a way to alleviate performance drawbacks when the musical instrument is a computer. This paper describes the principles and the design of Vivace, a live coding language and environment built with Web technologies to be executed on web browsers. The approach is compelling by 1) allowing many performers to code simultaneously, 2) the synthesis of audio and video, 3) a very simple syntax, 4) being a multiplatform software. We also strive to contextualize Vivace by means of historical and usage summaries including a live coding sub-genre.
Universal channel coding for general output alphabet
Venue: arXiv cs.IT 2017
Year: 2017

We propose two types of universal codes that are suited to two asymptotic regimes when the output alphabet is possibly continuous. The first class has the property that the error probability decays exponentially fast and we identify an explicit lower bound on the error exponent. The other class attains the epsilon-capacity the channel and we also identify the second-order term in the asymptotic expansion. The proposed encoder is essentially based on the packing lemma of the method of types. For the decoder, we first derive a Rényi-relative-entropy version of Clarke and Barron's formula the distance between the true distribution and the Bayesian mixture, which is of independent interest. The universal decoder is stated in terms of this formula and quantities used in the information spectrum method. The methods contained herein allow us to analyze universal codes for channels with continuous and discrete output alphabets in a unified manner, and to analyze their performances in terms of the exponential decay of the error probability and the second-order coding rate.
Efficient Algorithms for Envy-Free Stick Division With Fewest Cuts
Venue: arXiv cs.DS 2017
Year: 2017

Given a set of n sticks of various (not necessarily different) lengths, what is the largest length so that we can cut k equally long pieces of this length from the given set of sticks? We analyze the structure of this problem and show that it essentially reduces to a single call of a selection algorithm; we thus obtain an optimal linear-time algorithm. This algorithm also solves the related envy-free stick-division problem, which Segal-Halevi, Hassidim, and Aumann (AAMAS, 2015) recently used as their central primitive operation for the first discrete and bounded envy-free cake cutting protocol with a proportionality guarantee when pieces can be put to waste.
Trust Region Policy Optimization
Venue: arXiv cs.LG 2017
Year: 2017

We describe an iterative procedure for optimizing policies, with guaranteed monotonic improvement. By making several approximations to the theoretically-justified procedure, we develop a practical algorithm, called Trust Region Policy Optimization (TRPO). This algorithm is similar to natural policy gradient methods and is effective for optimizing large nonlinear policies such as neural networks. Our experiments demonstrate its robust performance on a wide variety of tasks: learning simulated robotic swimming, hopping, and walking gaits; and playing Atari games using images of the screen as input. Despite its approximations that deviate from the theory, TRPO tends to give monotonic improvement, with little tuning of hyperparameters.
A finite basis theorem for the description logic ${\cal ALC}$
Venue: arXiv cs.LO 2017
Year: 2017

The main result of this paper is to prove the existence of a finite basis in the description logic ${\cal ALC}$. We show that the set of General Concept Inclusions (GCIs) holding in a finite model has always a finite basis, i.e. these GCIs can be derived from finitely many of the GCIs. This result extends a previous result from Baader and Distel, which showed the existence of a finite basis for GCIs holding in a finite model but for the inexpressive description logics ${\cal EL}$ and ${\cal EL}_{gfp}$. We also provide an algorithm for computing this finite basis, and prove its correctness. As a byproduct, we extend our finite basis theorem to any finitely generated complete covariety (i.e. any class of models closed under morphism domain, coproduct and quotient, and generated from a finite set of finite models).
A Simple Spectral Algorithm for Recovering Planted Partitions
Venue: arXiv cs.DS 2017
Year: 2017

In this paper, we consider the planted partition model, in which $n = ks$ vertices of a random graph are partitioned into $k$ "clusters," each of size $s$. Edges between vertices in the same cluster and different clusters are included with constant probability $p$ and $q$, respectively (where $0 \le q < p \le 1$). We give an efficient algorithm that, with high probability, recovers the clusters as long as the cluster sizes are are least $Ω(\sqrt{n})$. Informally, our algorithm constructs the projection operator onto the dominant $k$-dimensional eigenspace of the graph's adjacency matrix and uses it to recover one cluster at a time. To our knowledge, our algorithm is the first purely spectral algorithm which runs in polynomial time and works even when $s = Θ(\sqrt n)$, though there have been several non-spectral algorithms which accomplish this. Our algorithm is also among the simplest of these spectral algorithms, and its proof of correctness illustrates the usefulness of the Cauchy integral formula in this domain.
EmptyHeaded: A Relational Engine for Graph Processing
Venue: arXiv cs.DB 2017
Year: 2017

There are two types of high-performance graph processing engines: low- and high-level engines. Low-level engines (Galois, PowerGraph, Snap) provide optimized data structures and computation models but require users to write low-level imperative code, hence ensuring that efficiency is the burden of the user. In high-level engines, users write in query languages like datalog (SociaLite) or SQL (Grail). High-level engines are easier to use but are orders of magnitude slower than the low-level graph engines. We present EmptyHeaded, a high-level engine that supports a rich datalog-like query language and achieves performance comparable to that of low-level engines. At the core of EmptyHeaded's design is a new class of join algorithms that satisfy strong theoretical guarantees but have thus far not achieved performance comparable to that of specialized graph processing engines. To achieve high performance, EmptyHeaded introduces a new join engine architecture, including a novel query optimizer and data layouts that leverage single-instruction multiple data (SIMD) parallelism. With this architecture, EmptyHeaded outperforms high-level approaches by up to three orders of magnitude on graph pattern queries, PageRank, and Single-Source Shortest Paths (SSSP) and is an order of magnitude faster than many low-level baselines. We validate that EmptyHeaded competes with the best-of-breed low-level engine (Galois), achieving comparable performance on PageRank and at most 3x worse performance on SSSP.
Random Coding Error Exponents for the Two-User Interference Channel
Venue: arXiv cs.IT 2017
Year: 2017

This paper is about deriving lower bounds on the error exponents for the two-user interference channel under the random coding regime for several ensembles. Specifically, we first analyze the standard random coding ensemble, where the codebooks are comprised of independently and identically distributed (i.i.d.) codewords. For this ensemble, we focus on optimum decoding, which is in contrast to other, suboptimal decoding rules that have been used in the literature (e.g., joint typicality decoding, treating interference as noise, etc.). The fact that the interfering signal is a codeword, rather than an i.i.d. noise process, complicates the application of conventional techniques of performance analysis of the optimum decoder. Also, unfortunately, these conventional techniques result in loose bounds. Using analytical tools rooted in statistical physics, as well as advanced union bounds, we derive single-letter formulas for the random coding error exponents. We compare our results with the best known lower bound on the error exponent, and show that our exponents can be strictly better. Then, in the second part of this paper, we consider more complicated coding ensembles, and find a lower bound on the error exponent associated with the celebrated Han-Kobayashi (HK) random coding ensemble, which is based on superposition coding.