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  • Computing $L(p,1)$-Labeling with Combined Parameters
    arXiv.cs.DS Pub Date : 2020-09-22
    Tesshu Hanaka; Kazuma Kawai; Hirotaka Ono

    Given a graph, an $L(p,1)$-labeling of the graph is an assignment $f$ from the vertex set to the set of nonnegative integers such that for any pair of vertices $(u,v),|f (u) - f (v)| \ge p$ if $u$ and $v$ are adjacent, and $f(u) \neq f(v)$ if $u$ and $v$ are at distance $2$. The \textsc{$L(p,1)$-labeling} problem is to minimize the span of $f$ (i.e.,$\max_{u\in V}(f(u)) - \min_{u\in V}(f(u))+1$). It

    更新日期:2020-09-23
  • A Faster Interior Point Method for Semidefinite Programming
    arXiv.cs.DS Pub Date : 2020-09-21
    Haotian Jiang; Tarun Kathuria; Yin Tat Lee; Swati Padmanabhan; Zhao Song

    Semidefinite programs (SDPs) are a fundamental class of optimization problems with important recent applications in approximation algorithms, quantum complexity, robust learning, algorithmic rounding, and adversarial deep learning. This paper presents a faster interior point method to solve generic SDPs with variable size $n \times n$ and $m$ constraints in time \begin{align*} \widetilde{O}(\sqrt{n}(

    更新日期:2020-09-23
  • On rooted $k$-connectivity problems in quasi-bipartite digraphs
    arXiv.cs.DS Pub Date : 2020-09-21
    Zeev Nutov

    We consider the directed Rooted Subset $k$-Edge-Connectivity problem: given a set $T \subseteq V$ of terminals in a digraph $G=(V+r,E)$ with edge costs and an integer $k$, find a min-cost subgraph of $G$ that contains $k$ edge disjoint $rt$-paths for all $t \in T$. The case when every edge of positive cost has head in $T$ admits a polynomial time algorithm due to Frank, and the case when all positive

    更新日期:2020-09-23
  • Fast Black-Box Quantum State Preparation
    arXiv.cs.DS Pub Date : 2020-09-22
    Johannes Bausch

    Quantum state preparation is an important ingredient for other higher-level quantum algorithms, such as Hamiltonian simulation, or for loading distributions into a quantum device to be used e.g. in the context of optimization tasks such as machine learning. Starting with a generic "black box" method devised by Grover in 2000, which employs amplitude amplification to load coefficients calculated by

    更新日期:2020-09-23
  • On the Mysteries of MAX NAE-SAT
    arXiv.cs.DS Pub Date : 2020-09-22
    Joshua Brakensiek; Neng Huang; Aaron Potechin; Uri Zwick

    MAX NAE-SAT is a natural optimization problem, closely related to its better-known relative MAX SAT. The approximability status of MAX NAE-SAT is almost completely understood if all clauses have the same size $k$, for some $k\ge 2$. We refer to this problem as MAX NAE-$\{k\}$-SAT. For $k=2$, it is essentially the celebrated MAX CUT problem. For $k=3$, it is related to the MAX CUT problem in graphs

    更新日期:2020-09-23
  • Control dynamics using quantum memory
    arXiv.cs.DS Pub Date : 2020-09-22
    Mathieu Roget; Basile Herzog; Giuseppe Di Molfetta

    We propose a new quantum numerical scheme to control the dynamics of a quantum walker in a two dimensional space-time grid. More specifically, we show how, introducing a quantum memory for each of the spatial grid, this result can be achieved simply by acting on the initial state of the whole system, and therefore can be exactly controlled once for all. As example we prove analytically how to encode

    更新日期:2020-09-23
  • A Low-Level Index for Distributed Logic Programming
    arXiv.cs.DS Pub Date : 2020-09-22
    Thomas ProkoschInstitute for Informatics, Ludwig-Maximilian University of Munich, Germany

    A distributed logic programming language with support for meta-programming and stream processing offers a variety of interesting research problems, such as: How can a versatile and stable data structure for the indexing of a large number of expressions be implemented with simple low-level data structures? Can low-level programming help to reduce the number of occur checks in Robinson's unification

    更新日期:2020-09-23
  • Space/time-efficient RDF stores based on circular suffix sorting
    arXiv.cs.DS Pub Date : 2020-09-21
    Nieves R. Brisaboa; Ana Cerdeira-Pena; Guillermo de Bernardo; Antonio Fariña; Gonzalo Navarro

    In recent years, RDF has gained popularity as a format for the standardized publication and exchange of information in the Web of Data. In this paper we introduce RDFCSA, a data structure that is able to self-index an RDF dataset in small space and supports efficient querying. RDFCSA regards the triples of the RDF store as short circular strings and applies suffix sorting on those strings, so that

    更新日期:2020-09-22
  • Efficiently Computing Maximum Flows in Scale-Free Networks
    arXiv.cs.DS Pub Date : 2020-09-21
    Thomas Bläsius; Tobias Friedrich; Christopher Weyand

    We study the maximum-flow/minimum-cut problem on scale-free networks, i.e., graphs whose degree distribution follows a power-law. We propose a simple algorithm that capitalizes on the fact that often only a small fraction of such a network is relevant for the flow. At its core, our algorithm augments Dinitz's algorithm with a balanced bidirectional search. Our experiments on a scale-free random network

    更新日期:2020-09-22
  • Length-Bounded Paths Interdiction in Continuous Domain for Network Performance Assessment
    arXiv.cs.DS Pub Date : 2020-09-18
    Lan N. Nguyen; My T. Thai

    Studying on networked systems, in which a communication between nodes is functional if their distance under a given metric is lower than a pre-defined threshold, has received significant attention recently. In this work, we propose a metric to measure network resilience on guaranteeing the pre-defined performance constraint. This metric is investigated under an optimization problem, namely \textbf{Length-bounded

    更新日期:2020-09-22
  • A Novel Method for Inference of Acyclic Chemical Compounds with Bounded Branch-height Based on Artificial Neural Networks and Integer Programming
    arXiv.cs.DS Pub Date : 2020-09-21
    Naveed Ahmed Azam; Jianshen Zhu; Yanming Sun; Yu Shi; Aleksandar Shurbevski; Liang Zhao; Hiroshi Nagamochi; Tatsuya Akutsu

    Analysis of chemical graphs is a major research topic in computational molecular biology due to its potential applications to drug design. One approach is inverse quantitative structure activity/property relationship (inverse QSAR/QSPR) analysis, which is to infer chemical structures from given chemical activities/properties. Recently, a framework has been proposed for inverse QSAR/QSPR using artificial

    更新日期:2020-09-22
  • The Complexity Landscape of Distributed Locally Checkable Problems on Trees
    arXiv.cs.DS Pub Date : 2020-09-21
    Yi-Jun Chang

    Recent research revealed the existence of gaps in the complexity landscape of locally checkable labeling (LCL) problems in the LOCAL model of distributed computing. For example, the deterministic round complexity of any LCL problem on bounded-degree graphs is either $O(\log^\ast n)$ or $\Omega(\log n)$ [Chang, Kopelowitz, and Pettie, FOCS 2016]. The complexity landscape of LCL problems is now quite

    更新日期:2020-09-22
  • Distributed Algorithms for Matching in Hypergraphs
    arXiv.cs.DS Pub Date : 2020-09-21
    Oussama Hanguir; Clifford Stein

    $ $We study the $d$-Uniform Hypergraph Matching ($d$-UHM) problem: given an $n$-vertex hypergraph $G$ where every hyperedge is of size $d$, find a maximum cardinality set of disjoint hyperedges. For $d\geq3$, the problem of finding the maximum matching is NP-complete, and was one of Karp's 21 $\mathcal{NP}$-complete problems. In this paper we are interested in the problem of finding matchings in hypergraphs

    更新日期:2020-09-22
  • TADOC: Text Analytics Directly on Compression
    arXiv.cs.DS Pub Date : 2020-09-20
    Feng Zhang; Jidong Zhai; Xipeng Shen; Dalin Wang; Zheng Chen; Onur Mutlu; Wenguang Chen; Xiaoyong Du

    This article provides a comprehensive description of Text Analytics Directly on Compression (TADOC), which enables direct document analytics on compressed textual data. The article explains the concept of TADOC and the challenges to its effective realizations. Additionally, a series of guidelines and technical solutions that effectively address those challenges, including the adoption of a hierarchical

    更新日期:2020-09-22
  • Improving on Best-of-Many-Christofides for $T$-tours
    arXiv.cs.DS Pub Date : 2020-09-21
    Vera Traub

    The $T$-tour problem is a natural generalization of TSP and Path TSP. Given a graph $G=(V,E)$, edge cost $c: E \to \mathbb{R}_{\ge 0}$, and an even cardinality set $T\subseteq V$, we want to compute a minimum-cost $T$-join connecting all vertices of $G$ (and possibly containing parallel edges). In this paper we give an $\frac{11}{7}$-approximation for the $T$-tour problem and show that the integrality

    更新日期:2020-09-22
  • On combinatorial optimization for dominating sets (literature survey, new models)
    arXiv.cs.DS Pub Date : 2020-09-19
    Mark Sh. Levin

    The paper focuses on some versions of connected dominating set problems: basic problems and multicriteria problems. A literature survey on basic problem formulations and solving approaches is presented. The basic connected dominating set problems are illustrated by simplifyed numerical examples. New integer programming formulations of dominating set problems (with multiset estimates) are suggested

    更新日期:2020-09-22
  • On Distributed Differential Privacy and Counting Distinct Elements
    arXiv.cs.DS Pub Date : 2020-09-21
    Lijie Chen; Badih Ghazi; Ravi Kumar; Pasin Manurangsi

    We study the setup where each of $n$ users holds an element from a discrete set, and the goal is to count the number of distinct elements across all users, under the constraint of $(\epsilon, \delta)$-differentially privacy: - In the non-interactive local setting, we prove that the additive error of any protocol is $\Omega(n)$ for any constant $\epsilon$ and for any $\delta$ inverse polynomial in $n$

    更新日期:2020-09-22
  • A General Framework for the Security Analysis of Blockchain Protocols
    arXiv.cs.DS Pub Date : 2020-09-20
    Andrew Lewis-Pye; Tim Roughgarden

    Blockchain protocols differ in fundamental ways, including the mechanics of selecting users to produce blocks (e.g., proof-of-work vs. proof-of-stake) and the method to establish consensus (e.g., longest chain rules vs. Byzantine fault-tolerant (BFT) inspired protocols). These fundamental differences have hindered "apples-to-apples" comparisons between different categories of blockchain protocols and

    更新日期:2020-09-22
  • Delay Optimization of Combinational Logic by And-Or Path Restructuring
    arXiv.cs.DS Pub Date : 2020-09-18
    Ulrich Brenner; Anna Hermann

    We propose a dynamic programming algorithm that constructs delay-optimized circuits for alternating And-Or paths with prescribed input arrival times. Our algorithm fulfills best-known approximation guarantees and empirically outperforms earlier methods by exploring a significantly larger portion of the solution space. Our algorithm is the core of a new timing optimization framework that replaces critical

    更新日期:2020-09-21
  • Efficient Constant-Factor Approximate Enumeration of Minimal Subsets for Monotone Properties with Cardinality Constraints
    arXiv.cs.DS Pub Date : 2020-09-18
    Yasuaki Kobayashi; Kazuhiro Kurita; Kunihiro Wasa

    A property $\Pi$ on a finite set $U$ is \emph{monotone} if for every $X \subseteq U$ satisfying $\Pi$, every superset $Y \subseteq U$ of $X$ also satisfies $\Pi$. Many combinatorial properties can be seen as monotone properties, and the problem of finding a minimum subset of $U$ satisfying $\Pi$ is a central problem in combinatorial optimization. Although many approximate/exact algorithms have been

    更新日期:2020-09-21
  • Longest Common Subsequence in Sublinear Space
    arXiv.cs.DS Pub Date : 2020-09-18
    Masashi Kiyomi; Takashi Horiyama; Yota Otachi

    We present the first $\mathrm{o}(n)$-space polynomial-time algorithm for computing the length of a longest common subsequence. Given two strings of length $n$, the algorithm runs in $\mathrm{O}(n^{3})$ time with $\mathrm{O}\left(\frac{n \log^{1.5} n}{2^{\sqrt{\log n}}}\right)$ bits of space.

    更新日期:2020-09-21
  • Deterministic Algorithms for Decremental Shortest Paths via Layered Core Decomposition
    arXiv.cs.DS Pub Date : 2020-09-17
    Julia Chuzhoy; Thatchaphol Saranurak

    In the decremental single-source shortest paths (SSSP) problem, the input is an undirected graph $G=(V,E)$ with $n$ vertices and $m$ edges undergoing edge deletions, together with a fixed source vertex $s\in V$. The goal is to maintain a data structure that supports shortest-path queries: given a vertex $v\in V$, quickly return an (approximate) shortest path from $s$ to $v$. The decremental all-pairs

    更新日期:2020-09-21
  • Low-rank MDP Approximation via Moment Coupling
    arXiv.cs.DS Pub Date : 2020-09-18
    Amy B. Z. Zhang; Itai Gurvich

    We propose a novel method---based on local moment matching---to approximate the value function of a Markov Decision Process. The method is grounded in recent work by Braverman et al (2020) that relates the solution of the Bellman equation to that of a PDE where, in the spirit of the central limit theorem, the transition matrix is reduced to its local first and second moments. Solving the PDE is not

    更新日期:2020-09-21
  • Quantum Search with Prior Knowledge
    arXiv.cs.DS Pub Date : 2020-09-18
    Xiaoyu He; Jialin Zhang; Xiaoming Sun

    Search-base algorithms have widespread applications in different scenarios. Grover's quantum search algorithms and its generalization, amplitude amplification, provide a quadratic speedup over classical search algorithms for unstructured search. We consider the problem of searching with prior knowledge. More preciously, search for the solution among N items with a prior probability distribution. This

    更新日期:2020-09-21
  • Coordinate Methods for Matrix Games
    arXiv.cs.DS Pub Date : 2020-09-17
    Yair Carmon; Yujia Jin; Aaron Sidford; Kevin Tian

    We develop primal-dual coordinate methods for solving bilinear saddle-point problems of the form $\min_{x \in \mathcal{X}} \max_{y\in\mathcal{Y}} y^\top A x$ which contain linear programming, classification, and regression as special cases. Our methods push existing fully stochastic sublinear methods and variance-reduced methods towards their limits in terms of per-iteration complexity and sample complexity

    更新日期:2020-09-20
  • Near-Optimal Decremental Approximate Multi-Source Shortest Paths
    arXiv.cs.DS Pub Date : 2020-09-17
    Jakub Łącki; Yasamin Nazari

    We provide new algorithms for maintaining approximate distances in a weighted undirected graph $G = (V, E)$ subject to edge deletions. Our first result is an algorithm that maintains $(1+\epsilon)$-approximate distances from a set of $s$ sources in $\tilde{O}(sm)$ total update time, assuming that $s= n^{\Omega(1)}$, $\epsilon = \Omega(1)$ and $|E|= n^{1+\Omega(1)}$. This matches the best known static

    更新日期:2020-09-20
  • Metrical Service Systems with Transformations
    arXiv.cs.DS Pub Date : 2020-09-17
    Sébastien Bubeck; Niv Buchbinder; Christian Coester; Mark Sellke

    We consider a generalization of the fundamental online metrical service systems (MSS) problem where the feasible region can be transformed between requests. In this problem, which we call T-MSS, an algorithm maintains a point in a metric space and has to serve a sequence of requests. Each request is a map (transformation) $f_t\colon A_t\to B_t$ between subsets $A_t$ and $B_t$ of the metric space. To

    更新日期:2020-09-20
  • Algorithms and Complexity for Variants of Covariates Fine Balance
    arXiv.cs.DS Pub Date : 2020-09-17
    Dorit S. Hochbaum; Asaf Levin; Xu Rao

    We study here several variants of the covariates fine balance problem where we generalize some of these problems and introduce a number of others. We present here a comprehensive complexity study of the covariates problems providing polynomial time algorithms, or a proof of NP-hardness. The polynomial time algorithms described are mostly combinatorial and rely on network flow techniques. In addition

    更新日期:2020-09-20
  • p-Edge/Vertex-Connected Vertex Cover: Parameterized and Approximation Algorithms
    arXiv.cs.DS Pub Date : 2020-09-17
    Carl Einarson; Gregory Gutin; Bart M. P. Jansen; Diptapriyo Majumdar; Magnus Wahlstrom

    We introduce and study two natural generalizations of the Connected VertexCover (VC) problem: the $p$-Edge-Connected and $p$-Vertex-Connected VC problem (where $p \geq 2$ is a fixed integer). Like Connected VC, both new VC problems are FPT, but do not admit a polynomial kernel unless $NP \subseteq coNP/poly$, which is highly unlikely. We prove however that both problems admit time efficient polynomial

    更新日期:2020-09-20
  • The Limits of Pan Privacy and Shuffle Privacy for Learning and Estimation
    arXiv.cs.DS Pub Date : 2020-09-17
    Albert Cheu; Jonathan Ullman

    There has been a recent wave of interest in intermediate trust models for differential privacy that eliminate the need for a fully trusted central data collector, but overcome the limitations of local differential privacy. This interest has led to the introduction of the shuffle model (Cheu et al., EUROCRYPT 2019; Erlingsson et al., SODA 2019) and revisiting the pan-private model (Dwork et al., ITCS

    更新日期:2020-09-20
  • Binarized Johnson-Lindenstrauss embeddings
    arXiv.cs.DS Pub Date : 2020-09-17
    Sjoerd Dirksen; Alexander Stollenwerk

    We consider the problem of encoding a set of vectors into a minimal number of bits while preserving information on their Euclidean geometry. We show that this task can be accomplished by applying a Johnson-Lindenstrauss embedding and subsequently binarizing each vector by comparing each entry of the vector to a uniformly random threshold. Using this simple construction we produce two encodings of a

    更新日期:2020-09-20
  • Fast and robust quantum state tomography from few basis measurements
    arXiv.cs.DS Pub Date : 2020-09-17
    Fernando G. S. L. Brandão; Richard Kueng; Daniel Stilck França

    Quantum state tomography is a powerful, but resource-intensive, general solution for numerous quantum information processing tasks. This motivates the design of robust tomography procedures that use relevant resources as sparingly as possible. Important cost factors include the number of state copies and measurement settings, as well as classical postprocessing time and memory. In this work, we present

    更新日期:2020-09-20
  • Finding Subgraphs in Highly Dynamic Networks
    arXiv.cs.DS Pub Date : 2020-09-17
    Keren Censor-Hillel; Victor I. Kolobov; Gregory Schwartzman

    In this paper we consider the fundamental problem of finding subgraphs in highly dynamic distributed networks - networks which allow an arbitrary number of links to be inserted / deleted per round. We show that the problems of $k$-clique membership listing (for any $k\geq 3$), 4-cycle listing and 5-cycle listing can be deterministically solved in $O(1)$-amortized round complexity, even with limited

    更新日期:2020-09-20
  • Strongly refuting all semi-random Boolean CSPs
    arXiv.cs.DS Pub Date : 2020-09-17
    Jackson Abascal; Venkatesan Guruswami; Pravesh K. Kothari

    We give an efficient algorithm to strongly refute \emph{semi-random} instances of all Boolean constraint satisfaction problems. The number of constraints required by our algorithm matches (up to polylogarithmic factors) the best-known bounds for efficient refutation of fully random instances. Our main technical contribution is an algorithm to strongly refute semi-random instances of the Boolean $k$-XOR

    更新日期:2020-09-20
  • Competitive Ratios for Online Multi-capacity Ridesharing
    arXiv.cs.DS Pub Date : 2020-09-16
    Meghna Lowalekar; Pradeep Varakantham; Patrick Jaillet

    In multi-capacity ridesharing, multiple requests (e.g., customers, food items, parcels) with different origin and destination pairs travel in one resource. In recent years, online multi-capacity ridesharing services (i.e., where assignments are made online) like Uber-pool, foodpanda, and on-demand shuttles have become hugely popular in transportation, food delivery, logistics and other domains. This

    更新日期:2020-09-20
  • On Symmetric Rectilinear Matrix Partitioning
    arXiv.cs.DS Pub Date : 2020-09-16
    Abdurrahman Yaşar; Muhammed Fatih Balin; Xiaojing An; Kaan Sancak; Ümit V. Çatalyürek

    Even distribution of irregular workload to processing units is crucial for efficient parallelization in many applications. In this work, we are concerned with a spatial partitioning called rectilinear partitioning (also known as generalized block distribution) of sparse matrices. More specifically, in this work, we address the problem of symmetric rectilinear partitioning of a square matrix. By symmetric

    更新日期:2020-09-18
  • Nonlinear quantum search via coined quantum walks
    arXiv.cs.DS Pub Date : 2020-09-16
    Basile Herzog; Giuseppe Di Molfetta

    We provide first evidence that some families of nonlinear quantum systems, rephrased in terms of coined quantum walks with effective nonlinear phase, display a strong computational advantage for search algorithms, over graphs having sets of vertices of constant size, e.g. the infinite square grid. The numerical simulations show that the walker finds the marked vertex in $O(N^{1/4} \log^{3/4} N)$ steps

    更新日期:2020-09-18
  • Accelerating Domain Propagation: an Efficient GPU-Parallel Algorithm over Sparse Matrices
    arXiv.cs.DS Pub Date : 2020-09-16
    Boro Sofranac; Ambros Gleixner; Sebastian Pokutta

    Fast domain propagation of linear constraints has become a crucial component of today's best algorithms and solvers for mixed integer programming and pseudo-boolean optimization to achieve peak solving performance. Irregularities in the form of dynamic algorithmic behaviour, dependency structures, and sparsity patterns in the input data make efficient implementations of domain propagation on GPUs and

    更新日期:2020-09-18
  • Faster Property Testers in a Variation of the Bounded Degree Model
    arXiv.cs.DS Pub Date : 2020-09-16
    Isolde Adler; Polly Fahey

    Property testing algorithms are highly efficient algorithms, that come with probabilistic accuracy guarantees. For a property P, the goal is to distinguish inputs that have P from those that are far from having P with high probability correctly, by querying only a small number of local parts of the input. In property testing on graphs, the distance is measured by the number of edge modifications (additions

    更新日期:2020-09-18
  • Positivity-preserving extensions of sum-of-squares pseudomoments over the hypercube
    arXiv.cs.DS Pub Date : 2020-09-15
    Dmitriy Kunisky

    We introduce a new method for building higher-degree sum-of-squares lower bounds over the hypercube $\mathbf{x} \in \{\pm 1\}^N$ from a given degree 2 lower bound. Our method constructs pseudoexpectations that are positive semidefinite by design, lightening some of the technical challenges common to other approaches to SOS lower bounds, such as pseudocalibration. We give general "incoherence" conditions

    更新日期:2020-09-16
  • An improved quantum-inspired algorithm for linear regression
    arXiv.cs.DS Pub Date : 2020-09-15
    András Gilyén; Zhao Song; Ewin Tang

    We give a classical algorithm for linear regression analogous to the quantum matrix inversion algorithm [Harrow, Hassidim, and Lloyd, Physical Review Letters '09] for low-rank matrices [Chakraborty et al., ICALP'19], when the input matrix $A$ is stored in a data structure applicable for QRAM-based state preparation. Namely, if the input model supports efficient $\ell_2$-norm importance sampling, and

    更新日期:2020-09-16
  • Approximation Algorithms for The Generalized Incremental Knapsack Problem
    arXiv.cs.DS Pub Date : 2020-09-15
    Yuri Faenza; Danny Segev; Lingyi Zhang

    We introduce and study a discrete multi-period extension of the classical knapsack problem, dubbed generalized incremental knapsack. In this setting, we are given a set of $n$ items, each associated with a non-negative weight, and $T$ time periods with non-decreasing capacities $W_1 \leq \dots \leq W_T$. When item $i$ is inserted at time $t$, we gain a profit of $p_{it}$; however, this item remains

    更新日期:2020-09-16
  • Optimal Decision Trees for Nonlinear Metrics
    arXiv.cs.DS Pub Date : 2020-09-15
    Emir Demirović; Peter J. Stuckey

    Nonlinear metrics, such as the F1-score, Matthews correlation coefficient, and Fowlkes-Mallows index, are often used to evaluate the performance of machine learning models, in particular, when facing imbalanced datasets that contain more samples of one class than the other. Recent optimal decision tree algorithms have shown remarkable progress in producing trees that are optimal with respect to linear

    更新日期:2020-09-16
  • Spatio-Temporal Top-k Similarity Search for Trajectories in Graphs
    arXiv.cs.DS Pub Date : 2020-09-14
    Anne Driemel; Petra Mutzel; Lutz Oettershagen

    We study the problem of finding the $k$ most similar trajectories in a graph to a given query trajectory. Our work was inspired by the work of Grossi et al. [6] that considered trajectories as walks in a graph in which each visited vertex is accompanied by a time-interval. Grossi et al. define a similarity function which is able to capture both temporal and spatial aspects. We modify this similarity

    更新日期:2020-09-16
  • Learning Mixtures of Permutations: Groups of Pairwise Comparisons and Combinatorial Method of Moments
    arXiv.cs.DS Pub Date : 2020-09-14
    Cheng Mao; Yihong Wu

    In applications such as rank aggregation, mixture models for permutations are frequently used when the population exhibits heterogeneity. In this work, we study the widely used Mallows mixture model. In the high-dimensional setting, we propose a polynomial-time algorithm that learns a Mallows mixture of permutations on $n$ elements with the optimal sample complexity that is proportional to $\log n$

    更新日期:2020-09-16
  • Optimal Testing of Discrete Distributions with High Probability
    arXiv.cs.DS Pub Date : 2020-09-14
    Ilias Diakonikolas; Themis Gouleakis; Daniel M. Kane; John Peebles; Eric Price

    We study the problem of testing discrete distributions with a focus on the high probability regime. Specifically, given samples from one or more discrete distributions, a property $\mathcal{P}$, and parameters $0< \epsilon, \delta <1$, we want to distinguish {\em with probability at least $1-\delta$} whether these distributions satisfy $\mathcal{P}$ or are $\epsilon$-far from $\mathcal{P}$ in total

    更新日期:2020-09-15
  • Breaking the $n$-Pass Barrier: A Streaming Algorithm for Maximum Weight Bipartite Matching
    arXiv.cs.DS Pub Date : 2020-09-13
    S. Cliff Liu; Zhao Song; Hengjie Zhang

    Given a weighted bipartite graph with $n$ vertices and $m$ edges, the $\mathit{maximum~weight~bipartite~matching}$ problem is to find a set of vertex-disjoint edges with the maximum weight. This classic problem has been extensively studied for over a century. In this paper, we present a new streaming algorithm for the maximum weight bipartite matching problem that uses $\widetilde{O}(n)$ space and

    更新日期:2020-09-15
  • Cut-Equivalent Trees are Optimal for Min-Cut Queries
    arXiv.cs.DS Pub Date : 2020-09-13
    Amir Abboud; Robert Krauthgamer; Ohad Trabelsi

    Min-Cut queries are fundamental: Preprocess an undirected edge-weighted graph, to quickly report a minimum-weight cut that separates a query pair of nodes $s,t$. The best data structure known for this problem simply builds a cut-equivalent tree, discovered 60 years ago by Gomory and Hu, who also showed how to construct it using $n-1$ minimum $st$-cut computations. Using state-of-the-art algorithms

    更新日期:2020-09-15
  • On Fault Tolerant Feedback Vertex Set
    arXiv.cs.DS Pub Date : 2020-09-13
    Pranabendu Misra

    The study of fault-tolerant data structures for various network design problems is a prominent area of research in computer science. Likewise, the study of NP-Complete problems lies at the heart of computer science with numerous results in algorithms and complexity. In this paper we raise the question of computing fault tolerant solutions to NP-Complete problems; that is computing a solution that can

    更新日期:2020-09-15
  • Simple, Deterministic, Constant-Round Coloring in the Congested Clique
    arXiv.cs.DS Pub Date : 2020-09-13
    Artur Czumaj; Peter Davies; Merav Parter

    We settle the complexity of the $(\Delta+1)$-coloring and $(\Delta+1)$-list coloring problems in the CONGESTED CLIQUE model by presenting a simple deterministic algorithm for both problems running in a constant number of rounds. This matches the complexity of the recent breakthrough randomized constant-round $(\Delta+1)$-list coloring algorithm due to Chang et al. (PODC'19), and significantly improves

    更新日期:2020-09-15
  • Robust production planning with budgeted cumulative demand uncertainty
    arXiv.cs.DS Pub Date : 2020-09-12
    Romain Guillaume; Adam Kasperski; Pawel Zielinski

    This paper deals with a problem of production planning, which is a version of the capacitated single-item lot sizing problem with backordering under demand uncertainty, modeled by uncertain cumulative demands. The well-known interval budgeted uncertainty representation is assumed. Two of its variants are considered. The first one is the discrete budgeted uncertainty, in which at most a specified number

    更新日期:2020-09-15
  • Answering Multi-Dimensional Range Queries under Local Differential Privacy
    arXiv.cs.DS Pub Date : 2020-09-14
    Jianyu Yang; Tianhao Wang; Ninghui Li; Xiang Cheng; Sen Su

    In this paper, we tackle the problem of answering multi-dimensional range queries under local differential privacy. There are three key technical challenges: capturing the correlations among attributes, avoiding the curse of dimensionality, and dealing with the large domains of attributes. None of the existing approaches satisfactorily deals with all three challenges. Overcoming these three challenges

    更新日期:2020-09-15
  • Bounds and Code Constructions for Partially Defect Memory Cells
    arXiv.cs.DS Pub Date : 2020-09-14
    Haider Al Kim; Sven Puchinger; Antonia Wachter-Zeh

    This paper considers coding for so-called partially stuck memory cells. Such memory cells can only store partial information as some of their levels cannot be used due to, e.g., wear out. First, we present a new code construction for masking such partially stuck cells while additionally correcting errors. This construction (for cells with $q >2$ levels) is achieved by generalizing an existing masking-only

    更新日期:2020-09-15
  • Statistical Query Algorithms and Low-Degree Tests Are Almost Equivalent
    arXiv.cs.DS Pub Date : 2020-09-13
    Matthew Brennan; Guy Bresler; Samuel B. Hopkins; Jerry Li; Tselil Schramm

    Researchers currently use a number of approaches to predict and substantiate information-computation gaps in high-dimensional statistical estimation problems. A prominent approach is to characterize the limits of restricted models of computation, which on the one hand yields strong computational lower bounds for powerful classes of algorithms and on the other hand helps guide the development of efficient

    更新日期:2020-09-15
  • On Achieving Fairness and Stability in Many-to-One Matchings
    arXiv.cs.DS Pub Date : 2020-09-12
    Shivika Narang; Arpita Biswas; Y Narahari

    Matching algorithms have been classically studied with the goal of finding stable solutions. However, in many important societal problems, the degree of fairness in the matching assumes crucial importance, for instance when we have to match COVID-19 patients to care units. We study the problem of finding a stable many-to-one matching while satisfying fairness among all the agents with cardinal utilities

    更新日期:2020-09-15
  • Terminating cases of flooding
    arXiv.cs.DS Pub Date : 2020-09-12
    Walter Hussak; Amitabh Trehan

    Basic synchronous flooding proceeds in rounds. Given a finite undirected (network) graph $G$, a set of sources $I \subseteq G$ initiate flooding in the first round by every node in $I$ sending the same message to all of its neighbours. In each subsequent round, nodes send the message to all of their neighbours from which they did not receive the message in the previous round. Flooding terminates when

    更新日期:2020-09-15
  • Fault-Tolerant Edge-Disjoint Paths -- Beyond Uniform Faults
    arXiv.cs.DS Pub Date : 2020-09-10
    David Adjiashvili; Felix Hommelsheim; Moritz Mühlenthaler; Oliver Schaudt

    The overwhelming majority of survivable (fault-tolerant) network design models assume a uniform fault model. Such a model assumes that every subset of the network resources (edges or vertices) of a given cardinality $k$ may fail. While this approach yields problems with clean combinatorial structure and good algorithms, it often fails to capture the true nature of the scenario set coming from applications

    更新日期:2020-09-14
  • On Light Spanners, Low-treewidth Embeddings and Efficient Traversing in Minor-free Graphs
    arXiv.cs.DS Pub Date : 2020-09-10
    Vincent Cohen-Addad; Arnold Filtser; Philip N. Klein; Hung Le

    Understanding the structure of minor-free metrics, namely shortest path metrics obtained over a weighted graph excluding a fixed minor, has been an important research direction since the fundamental work of Robertson and Seymour. A fundamental idea that helps both to understand the structural properties of these metrics and lead to strong algorithmic results is to construct a "small-complexity" graph

    更新日期:2020-09-11
  • Near-linear Size Hypergraph Cut Sparsifiers
    arXiv.cs.DS Pub Date : 2020-09-10
    Yu Chen; Sanjeev Khanna; Ansh Nagda

    Cuts in graphs are a fundamental object of study, and play a central role in the study of graph algorithms. The problem of sparsifying a graph while approximately preserving its cut structure has been extensively studied and has many applications. In a seminal work, Bencz\'ur and Karger (1996) showed that given any $n$-vertex undirected weighted graph $G$ and a parameter $\varepsilon \in (0,1)$, there

    更新日期:2020-09-11
  • Quick Streaming Algorithms for Maximization of Monotone Submodular Functions in Linear Time
    arXiv.cs.DS Pub Date : 2020-09-10
    Alan Kuhnle

    We consider the problem of monotone, submodular maximization over a ground set of size $n$ subject to cardinality constraint $k$. For this problem, we introduce streaming algorithms with linearquery complexity and linear number of arithmetic operations; these algorithms are the first deterministic algorithms for submodular maximization that require a linear number of arithmetic operations. Specifically

    更新日期:2020-09-11
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