当前期刊: arXiv - CS - Data Structures and Algorithms Go to current issue    加入关注   
显示样式:        排序: 导出
  • Further Results on Colored Range Searching
    arXiv.cs.DS Pub Date : 2020-03-25
    Timothy M. Chan; Qizheng He; Yakov Nekrich

    We present a number of new results about range searching for colored (or "categorical") data: 1. For a set of $n$ colored points in three dimensions, we describe randomized data structures with $O(n\mathop{\rm polylog}n)$ space that can report the distinct colors in any query orthogonal range (axis-aligned box) in $O(k\mathop{\rm polyloglog} n)$ expected time, where $k$ is the number of distinct colors

  • On Structural Parameterizations of Node Kayles
    arXiv.cs.DS Pub Date : 2020-03-26
    Yasuaki Kobayashi

    Node Kayles is a well-known two-player impartial game on graphs: Given an undirected graph, each player alternately chooses a vertex not adjacent to previously chosen vertices, and a player who cannot choose a new vertex loses the game. The problem of deciding if the first player has a winning strategy in this game is known to be PSPACE-complete. There are a few studies on algorithmic aspects of this

  • Succinct Dynamic Ordered Sets with Random Access
    arXiv.cs.DS Pub Date : 2020-03-26
    Giulio Ermanno Pibiri; Rossano Venturini

    The representation of a dynamic ordered set of $n$ integer keys drawn from a universe of size $m$ is a fundamental data structuring problem. Many solutions to this problem achieve optimal time but take polynomial space, therefore preserving time optimality in the \emph{compressed} space regime is the problem we address in this work. For a polynomial universe $m = n^{\Theta(1)}$, we give a solution

  • Geometric Pattern Matching Reduces to k-SUM
    arXiv.cs.DS Pub Date : 2020-03-26
    Boris Aronov; Jean Cardinal

    We prove that some exact geometric pattern matching problems reduce in linear time to $k$-SUM when the pattern has a fixed size $k$. This holds in the real RAM model for searching for a similar copy of a set of $k\geq 3$ points within a set of $n$ points in the plane, and for searching for an affine image of a set of $k\geq d+2$ points within a set of $n$ points in $d$-space. As corollaries, we obtain

  • A Blind Permutation Similarity Algorithm
    arXiv.cs.DS Pub Date : 2020-03-26
    Eric Barszcz

    This paper introduces a polynomial blind algorithm that determines when two square matrices, $A$ and $B$, are permutation similar. The shifted and translated matrices $(A+\beta I+\gamma J)$ and $(B+\beta I+\gamma J)$ are used to color the vertices of two square, edge weighted, rook's graphs. Then the orbits are found by repeated symbolic squaring of the vertex colored and edge weighted adjacency matrices

  • Taming Near Repeat Calculation for Crime Analysis via Cohesive Subgraph Computing
    arXiv.cs.DS Pub Date : 2017-05-18
    Zhaoming Yin; Xuan Shi

    Near repeat (NR) is a well known phenomenon in crime analysis assuming that crime events exhibit correlations within a given time and space frame. Traditional NR calculation generates 2 event pairs if 2 events happened within a given space and time limit. When the number of events is large, however, NR calculation is time consuming and how these pairs are organized are not yet explored. In this paper

  • Understanding Sparse JL for Feature Hashing
    arXiv.cs.DS Pub Date : 2019-03-08
    Meena Jagadeesan

    Feature hashing and other random projection schemes are commonly used to reduce the dimensionality of feature vectors. The goal is to efficiently project a high-dimensional feature vector living in $\mathbb{R}^n$ into a much lower-dimensional space $\mathbb{R}^m$, while approximately preserving Euclidean norm. These schemes can be constructed using sparse random projections, for example using a sparse

  • Data structures to represent sets of k-long DNA sequences
    arXiv.cs.DS Pub Date : 2019-03-29
    Rayan Chikhi; Jan Holub; Paul Medvedev

    The analysis of biological sequencing data has been one of the biggest applications of string algorithms. The approaches used in many such applications are based on the analysis of k-mers, which are short fixed-length strings present in a dataset. While these approaches are rather diverse, storing and querying k-mer sets has emerged as a shared underlying component. Sets of k-mers have unique features

  • Regular Partitions and Their Use in Structural Pattern Recognition
    arXiv.cs.DS Pub Date : 2019-09-16
    Marco Fiorucci

    Recent years are characterized by an unprecedented quantity of available network data which are produced at an astonishing rate by an heterogeneous variety of interconnected sensors and devices. This high-throughput generation calls for the development of new effective methods to store, retrieve, understand and process massive network data. In this thesis, we tackle this challenge by introducing a

  • Assignment and Pricing of Shared Rides in Ride-Sourcing using Combinatorial Double Auctions
    arXiv.cs.DS Pub Date : 2019-09-18
    Renos Karamanis; Eleftherios Anastasiadis; Panagiotis Angeloudis; Marc Stettler

    Transportation Network Companies employ dynamic pricing methods at periods of peak travel to incentivise driver participation and balance supply and demand for rides. Surge pricing multipliers are commonly used and are applied following demand and estimates of customer and driver trip valuations. Combinatorial double auctions have been identified as a suitable alternative, as they can achieve maximum

  • Efficient Algorithms for Multidimensional Segmented Regression
    arXiv.cs.DS Pub Date : 2020-03-24
    Ilias Diakonikolas; Jerry Li; Anastasia Voloshinov

    We study the fundamental problem of fixed design {\em multidimensional segmented regression}: Given noisy samples from a function $f$, promised to be piecewise linear on an unknown set of $k$ rectangles, we want to recover $f$ up to a desired accuracy in mean-squared error. We provide the first sample and computationally efficient algorithm for this problem in any fixed dimension. Our algorithm relies

  • Polynomial Kernels for Paw-free Edge Modification Problems
    arXiv.cs.DS Pub Date : 2020-03-25
    Yixin Cao; Yuping Ke; Hanchun Yuan

    Let $H$ be a fixed graph. Given a graph $G$ and an integer $k$, the $H$-free edge modification problem asks whether it is possible to modify at most $k$ edges in $G$ to make it $H$-free. Sandeep and Sivadasan (IPEC 2015) asks whether the paw-free completion problem and the paw-free edge deletion problem admit polynomial kernels. We answer both questions affirmatively by presenting, respectively, $O(k)$-vertex

  • Fair packing of independent sets
    arXiv.cs.DS Pub Date : 2020-03-25
    Nina Chiarelli; Matjaž Krnc; Martin Milanič; Ulrich Pferschy; Nevena Pivač; Joachim Schauer

    In this work we add a graph theoretical perspective to a classical problem of fairly allocating indivisible items to several agents. Agents have different profit valuations of items and we allow an incompatibility relation between pairs of items described in terms of a conflict graph. Hence, every feasible allocation of items to the agents corresponds to a partial coloring, that is, a collection of

  • Tight Algorithms for the Submodular Multiple Knapsack Problem
    arXiv.cs.DS Pub Date : 2020-03-25
    Xiaoming Sun; Jialin Zhang; Zhijie Zhang

    Submodular function maximization has been a central topic in the theoretical computer science community over the last decade. A plenty of well-performed approximation algorithms have been designed for the maximization of monotone/non-monotone submodular functions over a variety of constraints. In this paper, we consider the submodular multiple knapsack problem (SMKP), which is the submodular version

  • A Hybrid MPI+Threads Approach to Particle Group Finding Using Union-Find
    arXiv.cs.DS Pub Date : 2020-03-25
    James S. Willis; Matthieu Schaller; Pedro Gonnet; John C. Helly

    The Friends-of-Friends (FoF) algorithm is a standard technique used in cosmological $N$-body simulations to identify structures. Its goal is to find clusters of particles (called groups) that are separated by at most a cut-off radius. $N$-body simulations typically use most of the memory present on a node, leaving very little free for a FoF algorithm to run on-the-fly. We propose a new method that

  • The Exact Query Complexity of Yes-No Permutation Mastermind
    arXiv.cs.DS Pub Date : 2020-03-25
    Moura El Ouali; Volkmar Sauerland

    Mastermind is famous two-players game. The ?rst player (codemaker) chooses a secret code which the second player (codebreaker) is supposed to crack within a minimum number of code guesses (queries). Therefore, codemaker's duty is to help codebreaker by providing a well-de?ned error measure between the secret code and the guessed code after each query. We consider a variant, called Yes-No AB-Mastermind

  • Efficient Algorithms for Scheduling Moldable Tasks
    arXiv.cs.DS Pub Date : 2016-09-27
    Xiaohu Wu; Patrick Loiseau

    Moldable tasks allow schedulers to determine the number of processors assigned to each task, enabling efficient use of large-scale parallel processing systems. A common assumption is that every task is monotonic, i.e., its workload increases but its execution time decreases as the number of assigned processors increases. Motivated by many benchmark studies, we introduce a new speedup model: the speedup

  • Improved Budgeted Connected Domination and Budgeted Edge-Vertex Domination
    arXiv.cs.DS Pub Date : 2019-07-15
    Ioannis Lamprou; Ioannis Sigalas; Vassilis Zissimopoulos

    We consider the \emph{Budgeted} version of the classical \emph{Connected Dominating Set} problem (BCDS). Given a graph $G$ and a budget $k$, we seek a connected subset of at most $k$ vertices maximizing the number of dominated vertices in $G$. We improve over the previous $(1-1/e)/13$ approximation in [Khuller, Purohit, and Sarpatwar,\ \emph{SODA 2014}] by introducing a new method for performing tree

  • Weighted Maximum Independent Set of Geometric Objects in Turnstile Streams
    arXiv.cs.DS Pub Date : 2019-02-27
    Ainesh Bakshi; Nadiia Chepurko; David P. Woodruff

    We study the Maximum Independent Set problem for geometric objects given in the data stream model. A set of geometric objects is said to be independent if the objects are pairwise disjoint. We consider geometric objects in one and two dimensions, i.e., intervals and disks. Let $\alpha$ be the cardinality of the largest independent set. Our goal is to estimate $\alpha$ in a small amount of space, given

  • Efficient Oblivious Database Joins
    arXiv.cs.DS Pub Date : 2020-03-20
    Simeon Krastnikov; Florian Kerschbaum; Douglas Stebila

    A major algorithmic challenge in designing applications intended for secure remote execution is ensuring that they are oblivious to their inputs, in the sense that their memory access patterns do not leak sensitive information to the server. This problem is particularly relevant to cloud databases that wish to allow queries over the client's encrypted data. One of the major obstacles to such a goal

  • Hidden Words Statistics for Large Patterns
    arXiv.cs.DS Pub Date : 2020-03-21
    Svante Janson; Wojciech Szpankowski

    We study here the so called subsequence pattern matching also known as hidden pattern matching in which one searches for a given pattern $w$ of length $m$ as a subsequence in a random text of length $n$. The quantity of interest is the number of occurrences of $w$ as a subsequence (i.e., occurring in not necessarily consecutive text locations). This problem finds many applications from intrusion detection

  • Scaling up Kernel Ridge Regression via Locality Sensitive Hashing
    arXiv.cs.DS Pub Date : 2020-03-21
    Michael Kapralov; Navid Nouri; Ilya Razenshteyn; Ameya Velingker; Amir Zandieh

    Random binning features, introduced in the seminal paper of Rahimi and Recht (2007), are an efficient method for approximating a kernel matrix using locality sensitive hashing. Random binning features provide a very simple and efficient way of approximating the Laplace kernel but unfortunately do not apply to many important classes of kernels, notably ones that generate smooth Gaussian processes, such

  • Being Fast Means Being Chatty: The Local Information Cost of Graph Spanners
    arXiv.cs.DS Pub Date : 2020-03-22
    Peter Robinson

    We introduce a new measure for quantifying the amount of information that the nodes in a network need to learn to jointly solve a graph problem. We show that the local information cost presents a natural lower bound on the communication complexity of distributed algorithms. We demonstrate the application of local information cost by deriving a lower bound on the communication complexity of computing

  • Kac meets Johnson and Lindenstrauss: a memory-optimal, fast Johnson-Lindenstrauss transform
    arXiv.cs.DS Pub Date : 2020-03-23
    Vishesh Jain; Natesh S. Pillai; Aaron Smith

    Based on the Kac random walk on the orthogonal group, we present a fast Johnson-Lindenstrauss transform: given a set $X$ of $n$ point sets in $\mathbb{R}^{d}$ and an error parameter $\epsilon$, this is a linear transformation $\Psi: \mathbb{R}^{d} \to \mathbb{R}^{O(\epsilon^{-2}\log{n})}$ such that $\|\Psi x\|_{2} \in (1- \epsilon, 1+\epsilon)\cdot \|x\|_{2}$ for all $x\in X$, and such that for each

  • On the Expected Value of the Determinant of Random Sum of Rank-One Matrices
    arXiv.cs.DS Pub Date : 2017-02-27
    Kasra Khosoussi

    We present a simple, yet useful result about the expected value of the determinant of random sum of rank-one matrices. Computing such expectations in general may involve a sum over exponentially many terms. Nevertheless, we show that an interesting and useful class of such expectations that arise in, e.g., D-optimal estimation and random graphs can be computed efficiently via computing a single determinant

  • Polynomial-time algorithm for Maximum Weight Independent Set on $P_6$-free graphs
    arXiv.cs.DS Pub Date : 2017-07-18
    Andrzej Grzesik; Tereza Klimošová; Marcin Pilipczuk; Michał Pilipczuk

    In the classic Maximum Weight Independent Set problem we are given a graph $G$ with a nonnegative weight function on vertices, and the goal is to find an independent set in $G$ of maximum possible weight. While the problem is NP-hard in general, we give a polynomial-time algorithm working on any $P_6$-free graph, that is, a graph that has no path on $6$ vertices as an induced subgraph. This improves

  • On Efficient Optimal Transport: An Analysis of Greedy and Accelerated Mirror Descent Algorithms
    arXiv.cs.DS Pub Date : 2019-01-19
    Tianyi Lin; Nhat Ho; Michael I. Jordan

    We provide theoretical analyses for two algorithms that solve the regularized optimal transport (OT) problem between two discrete probability measures with at most $n$ atoms. We show that a greedy variant of the classical Sinkhorn algorithm, known as the \emph{Greenkhorn algorithm}, can be improved to $\widetilde{\mathcal{O}}(n^2\varepsilon^{-2})$, improving on the best known complexity bound of $

  • Oblivious Sketching of High-Degree Polynomial Kernels
    arXiv.cs.DS Pub Date : 2019-09-03
    Thomas D. Ahle; Michael Kapralov; Jakob B. T. Knudsen; Rasmus Pagh; Ameya Velingker; David Woodruff; Amir Zandieh

    Kernel methods are fundamental tools in machine learning that allow detection of non-linear dependencies between data without explicitly constructing feature vectors in high dimensional spaces. A major disadvantage of kernel methods is their poor scalability: primitives such as kernel PCA or kernel ridge regression generally take prohibitively large quadratic space and (at least) quadratic time, as

  • Practical Random Access to Large SLP-Compressed Texts
    arXiv.cs.DS Pub Date : 2019-10-16
    Travis Gagie; Tomohiro I; Giovanni Manzini; Gonzalo Navarro; Hiroshi Sakamoto; Louisa Seelbach Benkner; Yoshimasa Takabatake

    Grammar-based compression is a popular and powerful approach to compressing repetitive texts but until recently its relatively poor time-space trade-offs in real life made it impractical for truly massive datasets such as genomic databases. In a recent paper (SPIRE 2019) we showed how simple pre-processing can dramatically improve those trade-offs. Now that grammar-based compression itself is reasonably

  • Treewidth-Pliability and PTAS for Max-CSPs
    arXiv.cs.DS Pub Date : 2019-11-08
    Miguel Romero; Marcin Wrochna; Stanislav Živný

    We identify a sufficient condition, treewidth-pliability, that gives a polynomial-time approximation scheme (PTAS) for a large class of Max-2-CSPs parametrised by the class of allowed constraint graphs (with arbitrary constraints on an unbounded alphabet). Our result applies more generally to the maximum homomorphism problem between two rational-valued structures. The condition unifies the two main

  • Minimum Cut in $O(m\log^2 n)$ Time
    arXiv.cs.DS Pub Date : 2019-11-04
    Paweł Gawrychowski; Shay Mozes; Oren Weimann

    We give a randomized algorithm that finds a minimum cut in an undirected weighted $m$-edge $n$-vertex graph $G$ with high probability in $O(m \log^2 n)$ time. This is the first improvement to Karger's celebrated $O(m \log^3 n)$ time algorithm from 1996. Our main technical contribution is a deterministic $O(m \log n)$ time algorithm that, given a spanning tree $T$ of $G$, finds a minimum cut of $G$

  • Efficiency Guarantees for Parallel Incremental Algorithms under Relaxed Schedulers
    arXiv.cs.DS Pub Date : 2020-03-20
    Dan Alistarh; Nikita Koval; Giorgi Nadiradze

    Several classic problems in graph processing and computational geometry are solved via incremental algorithms, which split computation into a series of small tasks acting on shared state, which gets updated progressively. While the sequential variant of such algorithms usually specifies a fixed (but sometimes random) order in which the tasks should be performed, a standard approach to parallelizing

  • Optimal Algorithms for Ranked Enumeration of Answers to Full Conjunctive Queries
    arXiv.cs.DS Pub Date : 2019-11-13
    Nikolaos Tziavelis; Deepak Ajwani; Wolfgang Gatterbauer; Mirek Riedewald; Xiaofeng Yang

    We study ranked enumeration of join-query results according to very general orders defined by selective dioids. Our main contribution is a framework for ranked enumeration over a class of dynamic programming problems that generalizes seemingly different problems that had been studied in isolation. To this end, we extend classic algorithms that find the k-shortest paths in a weighted graph. For full

  • The Strahler number of a parity game
    arXiv.cs.DS Pub Date : 2020-03-19
    Laure Daviaud; Marcin Jurdziński; K. S. Thejaswini

    The Strahler number of a rooted tree is the largest height of a perfect binary tree that is its minor. The Strahler number of a parity game is proposed to be defined as the smallest Strahler number of the tree of any of its attractor decompositions. It is proved that parity games can be solved in quasi-linear space and in time that is polynomial in the number of vertices~$n$ and linear in $({d}/{2k})^k$

  • Faster Divergence Maximization for Faster Maximum Flow
    arXiv.cs.DS Pub Date : 2020-03-19
    Yang P. Liu; Aaron Sidford

    In this paper we provide an algorithm which given any $m$-edge $n$-vertex directed graph with integer capacities at most $U$ computes a maximum $s$-$t$ flow for any vertices $s$ and $t$ in $m^{4/3+o(1)}U^{1/3}$ time. This improves upon the previous best running times of $m^{11/8+o(1)}U^{1/4}$ (Liu Sidford 2019), $\tilde{O}(m \sqrt{n} \log U)$ (Lee Sidford 2014), and $O(mn)$ (Orlin 2013) when the graph

  • Computing Maximum Matchings in Temporal Graphs
    arXiv.cs.DS Pub Date : 2019-05-13
    George B. Mertzios; Hendrik Molter; Rolf Niedermeier; Viktor Zamaraev; Philipp Zschoche

    Temporal graphs are graphs whose topology is subject to discrete changes over time. Given a static underlying graph $G$, a temporal graph is represented by assigning a set of integer time-labels to every edge $e$ of $G$, indicating the discrete time steps at which $e$ is active. We introduce and study the complexity of a natural temporal extension of the classical graph problem Maximum Matching, taking

  • Hardness of Bounded Distance Decoding on Lattices in $\ell_p$ Norms
    arXiv.cs.DS Pub Date : 2020-03-17
    Huck Bennett; Chris Peikert

    $ \newcommand{\Z}{\mathbb{Z}} \newcommand{\eps}{\varepsilon} \newcommand{\cc}[1]{\mathsf{#1}} \newcommand{\NP}{\cc{NP}} \newcommand{\problem}[1]{\mathrm{#1}} \newcommand{\BDD}{\problem{BDD}} $Bounded Distance Decoding $\BDD_{p,\alpha}$ is the problem of decoding a lattice when the target point is promised to be within an $\alpha$ factor of the minimum distance of the lattice, in the $\ell_{p}$ norm

  • Speeding up Linear Programming using Randomized Linear Algebra
    arXiv.cs.DS Pub Date : 2020-03-18
    Agniva Chowdhury; Palma London; Haim Avron; Petros Drineas

    Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such as combinatorics. It is also used in many machine learning applications, such as $\ell_1$-regularized SVMs, basis pursuit, nonnegative matrix factorization, etc.

  • Acceleration with a Ball Optimization Oracle
    arXiv.cs.DS Pub Date : 2020-03-18
    Yair Carmon; Arun Jambulapati; Qijia Jiang; Yujia Jin; Yin Tat Lee; Aaron Sidford; Kevin Tian

    Consider an oracle which takes a point $x$ and returns the minimizer of a convex function $f$ in an $\ell_2$ ball of radius $r$ around $x$. It is straightforward to show that roughly $r^{-1}\log\frac{1}{\epsilon}$ calls to the oracle suffice to find an $\epsilon$-approximate minimizer of $f$ in an $\ell_2$ unit ball. Perhaps surprisingly, this is not optimal: we design an accelerated algorithm which

  • Grammar compression with probabilistic context-free grammar
    arXiv.cs.DS Pub Date : 2020-03-18
    Hiroaki Naganuma; Diptarama Hendrian; Ryo Yoshinaka; Ayumi Shinohara; Naoki Kobayashi

    We propose a new approach for universal lossless text compression, based on grammar compression. In the literature, a target string $T$ has been compressed as a context-free grammar $G$ in Chomsky normal form satisfying $L(G) = \{T\}$. Such a grammar is often called a \emph{straight-line program} (SLP). In this paper, we consider a probabilistic grammar $G$ that generates $T$, but not necessarily as

  • Enumeration of Unordered Forests
    arXiv.cs.DS Pub Date : 2020-03-18
    Florian Ingels; Romain Azaïs

    Reverse search is a convenient method for enumerating structured objects, that can be used both to address theoretical issues and to solve data mining problems. This method has already been successfully developed to handle unordered trees. If the literature proposes solutions to enumerate singletons of trees, we study in this article a more general, higher combinatorial problem, the enumeration of

  • A New Implementation of Manacher's Algorithm
    arXiv.cs.DS Pub Date : 2020-03-17
    Shoupu Wan

    Manacher's algorithm is optimal for the longest palindromic substring problem. The implementation of this algorithm traditionally requires in-memory construction of an augmented string that is twice as long as the original string. Although the string-augmentation preprocessing has found widespread use for the implementation Manacher's algorithm, this is neither economic nor necessary. In this article

  • Network disruption: maximizing disagreement and polarization in social networks
    arXiv.cs.DS Pub Date : 2020-03-18
    Mayee Chen; Miklos Z. Racz

    Recent years have seen a marked increase in the spread of misinformation, a phenomenon which has been accelerated and amplified by social media such as Facebook and Twitter. While some actors spread misinformation to push a specific agenda, it has also been widely documented that others aim to simply disrupt the network by increasing disagreement and polarization across the network and thereby destabilizing

  • Probabilistic Tools for the Analysis of Randomized Optimization Heuristics
    arXiv.cs.DS Pub Date : 2018-01-20
    Benjamin Doerr

    This chapter collects several probabilistic tools that proved to be useful in the analysis of randomized search heuristics. This includes classic material like Markov, Chebyshev and Chernoff inequalities, but also lesser known topics like stochastic domination and coupling or Chernoff bounds for geometrically distributed random variables and for negatively correlated random variables. Most of the results

  • Chain, Generalization of Covering Code, and Deterministic Algorithm for k-SAT
    arXiv.cs.DS Pub Date : 2018-04-21
    S. Cliff Liu

    We present the current fastest deterministic algorithm for $k$-SAT, improving the upper bound $(2-2/k)^{n + o(n)}$ dues to Moser and Scheder [STOC'11]. The algorithm combines a branching algorithm with the derandomized local search, whose analysis relies on a special sequence of clauses called chain, and a generalization of covering code based on linear programming. We also provide a more ingenious

  • Rapid mixing of path integral Monte Carlo for 1D stoquastic Hamiltonians
    arXiv.cs.DS Pub Date : 2018-12-05
    Elizabeth Crosson; Aram W. Harrow

    Path integral quantum Monte Carlo (PIMC) is a method for estimating thermal equilibrium properties of stoquastic quantum spin systems by sampling from a classical Gibbs distribution using Markov chain Monte Carlo. The PIMC method has been widely used to study the physics of materials and for simulated quantum annealing, but these successful applications are rarely accompanied by formal proofs that

  • Decentralized Deep Learning with Arbitrary Communication Compression
    arXiv.cs.DS Pub Date : 2019-07-22
    Anastasia Koloskova; Tao Lin; Sebastian U. Stich; Martin Jaggi

    Decentralized training of deep learning models is a key element for enabling data privacy and on-device learning over networks, as well as for efficient scaling to large compute clusters. As current approaches suffer from limited bandwidth of the network, we propose the use of communication compression in the decentralized training context. We show that Choco-SGD $-$ recently introduced and analyzed

  • Optimal Tree Decompositions Revisited: A Simpler Linear-Time FPT Algorithm
    arXiv.cs.DS Pub Date : 2019-12-19
    Ernst Althaus; Sarah Ziegler

    In 1996, Bodlaender showed the celebrated result that an optimal tree decomposition of a graph of bounded treewidth can be found in linear time. The algorithm is based on an algorithm of Bodlaender and Kloks that computes an optimal tree decomposition given a non-optimal tree decomposition of bounded width. Both algorithms, in particular the second, are hardly accessible. In our review, we present

  • A Spectral Approach to Network Design
    arXiv.cs.DS Pub Date : 2020-03-17
    Lap Chi Lau; Hong Zhou

    We present a spectral approach to design approximation algorithms for network design problems. We observe that the underlying mathematical questions are the spectral rounding problems, which were studied in spectral sparsification and in discrepancy theory. We extend these results to incorporate additional non-negative linear constraints, and show that they can be used to significantly extend the scope

  • Adapting Persistent Data Structures for Concurrency and Speculation
    arXiv.cs.DS Pub Date : 2020-03-16
    Thomas Dickerson

    This work unifies insights from the systems and functional programming communities, in order to enable compositional reasoning about software which is nonetheless efficiently realizable in hardware. It exploits a correspondence between design goals for efficient concurrent data structures and efficient immutable persistent data structures, to produce novel implementations of mutable concurrent trees

  • Beyond Alice and Bob: Improved Inapproximability for Maximum Independent Set in CONGEST
    arXiv.cs.DS Pub Date : 2020-03-16
    Yuval Efron; Ofer Grossman; Seri Khoury

    By far the most fruitful technique for showing lower bounds for the CONGEST model is reductions to two-party communication complexity. This technique has yielded nearly tight results for various fundamental problems such as distance computations, minimum spanning tree, minimum vertex cover, and more. In this work, we take this technique a step further, and we introduce a framework of reductions to

  • Efficient Two-Sided Markets with Limited Information
    arXiv.cs.DS Pub Date : 2020-03-17
    Paul Dütting; Federico Fusco; Philip Lazos; Stefano Leonardi; Rebecca Reiffenhäuser

    Many important practical markets inherently involve the interaction of strategic buyers with strategic sellers. A fundamental impossibility result for such two-sided markets due to Myerson and Satterthwaite establishes that even in the simplest such market, that of bilateral trade, it is impossible to design a mechanism that is individually rational, truthful, (weakly) budget balanced, and efficient

  • A Scaling Algorithm for Weighted $f$-Factors in General Graphs
    arXiv.cs.DS Pub Date : 2020-03-17
    Ran Duan; Haoqing He; Tianyi Zhang

    We study the maximum weight perfect $f$-factor problem on any general simple graph $G=(V,E,w)$ with positive integral edge weights $w$, and $n=|V|$, $m=|E|$. When we have a function $f:V\rightarrow \mathbb{N}_+$ on vertices, a perfect $f$-factor is a generalized matching so that every vertex $u$ is matched to $f(u)$ different edges. The previous best algorithms on this problem have running time $O(m

  • NP-completeness Results for Graph Burning on Geometric Graphs
    arXiv.cs.DS Pub Date : 2020-03-17
    Arya Tanmay Gupta; Swapnil Lokhande; Kaushik Mondal

    Graph burning runs on discrete time steps. The aim of the graph burning problem is to burn all the vertices in a given graph in the least amount of time steps. The least number of required time steps is known to be the burning number of the graph. The spread of social influence, an alarm, or a social contagion can be modeled using graph burning. The less the burning number, the quick the spread. Computationally

  • The Parameterized Complexity of Guarding Almost Convex Polygons
    arXiv.cs.DS Pub Date : 2020-03-17
    Akanksha Agrawal; Kristine V. K. Knudsen; Daniel Lokshtanov; Saket Saurabh; Meirav Zehavi

    Art Gallery is a fundamental visibility problem in Computational Geometry. The input consists of a simple polygon P, (possibly infinite) sets G and C of points within P, and an integer k; the task is to decide if at most k guards can be placed on points in G so that every point in C is visible to at least one guard. In the classic formulation of Art Gallery, G and C consist of all the points within

  • Hard to Solve Instances of the Euclidean Traveling Salesman Problem
    arXiv.cs.DS Pub Date : 2018-08-08
    Stefan Hougardy; Xianghui Zhong

    The well known $4/3$ conjecture states that the integrality ratio of the subtour LP is at most $4/3$ for metric Traveling Salesman instances. We present a family of Euclidean Traveling Salesman instances for which we prove that the integrality ratio of the subtour LP converges to $4/3$. These instances (using the rounded Euclidean norm) turn out to be hard to solve exactly with Concorde, the fastest

  • Lift & Project Systems Performing on the Partial-Vertex-Cover Polytope
    arXiv.cs.DS Pub Date : 2014-09-22
    Konstantinos Georgiou; Andy Jiang; Edward Lee; Astrid A. Olave; Ian Seong; Twesh Upadhyaya

    We study integrality gap (IG) lower bounds on strong LP and SDP relaxations derived by the Sherali-Adams (SA), Lovasz-Schrijver-SDP (LS+), and Sherali-Adams-SDP (SA+) lift-and-project (L&P) systems for the t-Partial-Vertex-Cover (t-PVC) problem, a variation of the classic Vertex-Cover problem in which only t edges need to be covered. t-PVC admits a 2-approximation using various algorithmic techniques

  • Joint Alignment From Pairwise Differences with a Noisy Oracle
    arXiv.cs.DS Pub Date : 2020-03-13
    Michael Mitzenmacher; Charalampos E. Tsourakakis

    In this work we consider the problem of recovering $n$ discrete random variables $x_i\in \{0,\ldots,k-1\}, 1 \leq i \leq n$ (where $k$ is constant) with the smallest possible number of queries to a noisy oracle that returns for a given query pair $(x_i,x_j)$ a noisy measurement of their modulo $k$ pairwise difference, i.e., $y_{ij} = (x_i-x_j) \mod k$. This is a joint discrete alignment problem with

  • Algorithms in Linear Algebraic Groups
    arXiv.cs.DS Pub Date : 2020-03-12
    Sushil Bhunia; Ayan Mahalanobis; Pralhad Shinde; Anupam Singh

    This paper presents some algorithms in linear algebraic groups. These algorithms solve the word problem and compute the spinor norm for orthogonal groups. This gives us an algorithmic definition of the spinor norm. We compute the double coset decomposition with respect to a Siegel maximal parabolic subgroup, which is important in computing infinite-dimensional representations for some algebraic groups

  • Binary Decision Diagrams: from Tree Compaction to Sampling
    arXiv.cs.DS Pub Date : 2019-07-15
    Julien Clément; Antoine Genitrini

    Any Boolean function corresponds with a complete full binary decision tree. This tree can in turn be represented in a maximally compact form as a direct acyclic graph where common subtrees are factored and shared, keeping only one copy of each unique subtree. This yields the celebrated and widely used structure called reduced ordered binary decision diagram (ROBDD). We propose to revisit the classical

Contents have been reproduced by permission of the publishers.
全球疫情及响应:BMC Medicine专题征稿