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  • Searching, Sorting, and Cake Cutting in Rounds
    arXiv.cs.DS Pub Date : 2020-12-01
    Simina Brânzei; Dimitris Paparas; Nicholas J. Recker

    We study sorting and searching in rounds, motivated by a cake cutting problem. The search problem we consider is: we are given an array $x = (x_1, \ldots, x_n)$ and an element $z$ promised to be in the array. We have access to an oracle that answers comparison queries: "How is $x_i$ compared to $x_j$?", where the answer can be "$<$", "$=$", or "$>$". The goal is to find the location of $z$ with success

    更新日期:2020-12-02
  • Best Fit Bin Packing with Random Order Revisited
    arXiv.cs.DS Pub Date : 2020-12-01
    Susanne Albers; Arindam Khan; Leon Ladewig

    Best Fit is a well known online algorithm for the bin packing problem, where a collection of one-dimensional items has to be packed into a minimum number of unit-sized bins. In a seminal work, Kenyon [SODA 1996] introduced the (asymptotic) random order ratio as an alternative performance measure for online algorithms. Here, an adversary specifies the items, but the order of arrival is drawn uniformly

    更新日期:2020-12-02
  • Improved Online Algorithms for Knapsack and GAP in the Random Order Model
    arXiv.cs.DS Pub Date : 2020-12-01
    Susanne Albers; Arindam Khan; Leon Ladewig

    The knapsack problem is one of the classical problems in combinatorial optimization: Given a set of items, each specified by its size and profit, the goal is to find a maximum profit packing into a knapsack of bounded capacity. In the online setting, items are revealed one by one and the decision, if the current item is packed or discarded forever, must be done immediately and irrevocably upon arrival

    更新日期:2020-12-02
  • New Results for the $k$-Secretary Problem
    arXiv.cs.DS Pub Date : 2020-12-01
    Susanne Albers; Leon Ladewig

    Suppose that $n$ items arrive online in random order and the goal is to select $k$ of them such that the expected sum of the selected items is maximized. The decision for any item is irrevocable and must be made on arrival without knowing future items. This problem is known as the $k$-secretary problem, which includes the classical secretary problem with the special case $k=1$. It is well-known that

    更新日期:2020-12-02
  • Better Fewer but Better: Community Search with Outliers
    arXiv.cs.DS Pub Date : 2020-12-01
    Francesco Bonchi; Lorenzo Severini; Mauro Sozio

    Given a set of vertices in a network, that we believe are of interest for the application under analysis, community search is the problem of producing a subgraph potentially explaining the relationships existing among the vertices of interest. In practice this means that the solution should add some vertices to the query ones, so to create a connected subgraph that exhibits some "cohesiveness" property

    更新日期:2020-12-02
  • Comb inequalities for typical Euclidean TSP instances
    arXiv.cs.DS Pub Date : 2020-12-01
    Wesley Pegden; Anish Sevekari

    We prove that even in average case, the Euclidean Traveling Salesman Problem exhibits an integrality gap of $(1+\epsilon)$ for $\epsilon>0$ when the Held-Karp Linear Programming relaxation is augmented by all comb inequalities of bounded size. This implies that large classes of branch-and-cut algorithms take exponential time for the Euclidean TSP, even on random inputs.

    更新日期:2020-12-02
  • The Variable-Processor Cup Game
    arXiv.cs.DS Pub Date : 2020-11-30
    William Kuszmaul; Alek Westover

    The problem of scheduling tasks on $p$ processors so that no task ever gets too far behind is often described as a game with cups and water. In the $p$-processor cup game on $n$ cups, there are two players, a filler and an emptier, that take turns adding and removing water from a set of $n$ cups. In each turn, the filler adds $p$ units of water to the cups, placing at most $1$ unit of water in each

    更新日期:2020-12-02
  • Bridging the Gap Between Tree and Connectivity Augmentation: Unified and Stronger Approaches
    arXiv.cs.DS Pub Date : 2020-11-30
    Federica Cecchetto; Vera Traub; Rico Zenklusen

    We consider the Connectivity Augmentation Problem (CAP), a classical problem in the area of Survivable Network Design. It is about increasing the edge-connectivity of a graph by one unit in the cheapest possible way. More precisely, given a $k$-edge-connected graph $G=(V,E)$ and a set of extra edges, the task is to find a minimum cardinality subset of extra edges whose addition to $G$ makes the graph

    更新日期:2020-12-02
  • Dynamic Weighted Matching with Heterogeneous Arrival and Departure Rates
    arXiv.cs.DS Pub Date : 2020-12-01
    Natalie Collina; Nicole Immorlica; Kevin Leyton-Brown; Brendan Lucier; Neil Newman

    We study a dynamic non-bipartite matching problem. There is a fixed set of agent types, and agents of a given type arrive and depart according to type-specific Poisson processes. The value of a match is determined by the types of the matched agents. We present an online algorithm that is (1/6)-competitive with respect to the value of the optimal-in-hindsight policy, for arbitrary weighted graphs. This

    更新日期:2020-12-02
  • Train Tracks with Gaps: Applying the Probabilistic Method to Trains
    arXiv.cs.DS Pub Date : 2020-12-01
    William Kuszmaul

    We identify a tradeoff curve between the number of wheels on a train car, and the amount of track that must be installed in order to ensure that the train car is supported by the track at all times. The goal is to build an elevated track that covers some large distance $\ell$, but that consists primarily of gaps, so that the total amount of feet of train track that is actually installed is only a small

    更新日期:2020-12-02
  • Integer Programming and Incidence Treedepth
    arXiv.cs.DS Pub Date : 2020-11-30
    Eduard Eiben; Robert Ganian; Dušan Knop; Sebastian Ordyniak; Michał Pilipczuk; Marcin Wrochna

    Recently a strong connection has been shown between the tractability of integer programming (IP) with bounded coefficients on the one side and the structure of its constraint matrix on the other side. To that end, integer linear programming is fixed-parameter tractable with respect to the primal (or dual) treedepth of the Gaifman graph of its constraint matrix and the largest coefficient (in absolute

    更新日期:2020-12-02
  • Vertex Sparsification for Edge Connectivity in Polynomial Time
    arXiv.cs.DS Pub Date : 2020-11-30
    Yang P. Liu

    An important open question in the area of vertex sparsification is whether $(1+\epsilon)$-approximate cut-preserving vertex sparsifiers with size close to the number of terminals exist. The work Chalermsook et al. (SODA 2021) introduced a relaxation called connectivity-$c$ mimicking networks, which asks to construct a vertex sparsifier which preserves connectivity among $k$ terminals exactly up to

    更新日期:2020-12-01
  • A 3-2/b(G)-approximation algorithm for the graph burning problem
    arXiv.cs.DS Pub Date : 2020-11-30
    Jesús García Díaz

    The graph burning problem is an NP-Hard optimization problem that models the sequential spread of information over a network. Due to its nature, this problem has been approached through approximation algorithms and heuristics. This paper introduces a new 3-2/b(G)-approximation algorithm for the graph burning problem over general graphs, where b(G) is the size of an optimal solution. This algorithm

    更新日期:2020-12-01
  • Parameterized algorithms for locating-dominating sets
    arXiv.cs.DS Pub Date : 2020-11-30
    Márcia R. Cappelle; Guilherme C. M. Gomes; Vinicius F. dos Santos

    A locating-dominating set $D$ of a graph $G$ is a dominating set of $G$ where each vertex not in $D$ has a unique neighborhood in $D$, and the Locating-Dominating Set problem asks if $G$ contains such a dominating set of bounded size. This problem is known to be $\mathsf{NP-hard}$ even on restricted graph classes, such as interval graphs, split graphs, and planar bipartite subcubic graphs. On the other

    更新日期:2020-12-01
  • Windowed Prophet Inequalities
    arXiv.cs.DS Pub Date : 2020-11-27
    William Marshall; Nolan Miranda; Albert Zuo

    The prophet inequalities problem has received significant study over the past decades and has several applications such as to online auctions. In this paper, we study two variants of the i.i.d. prophet inequalities problem, namely the windowed prophet inequalities problem and the batched prophet inequalities problem. For the windowed prophet inequalities problem, we show that for window size $o(n)$

    更新日期:2020-12-01
  • On structural parameterizations of the selective coloring problem
    arXiv.cs.DS Pub Date : 2020-11-30
    Guilherme C. M. Gomes; Vinicius F. dos Santos

    In the Selective Coloring problem, we are given an integer $k$, a graph $G$, and a partition of $V(G)$ into $p$ parts, and the goal is to decide whether or not we can pick exactly one vertex of each part and obtain a $k$-colorable induced subgraph of $G$. This generalization of Vertex Coloring has only recently begun to be studied by Demange et al. [Theoretical Computer Science, 2014], motivated by

    更新日期:2020-12-01
  • Isomorphism Testing for Graphs Excluding Small Topological Subgraphs
    arXiv.cs.DS Pub Date : 2020-11-30
    Daniel Neuen

    We give an isomorphism test that runs in time $n^{\operatorname{polylog}(h)}$ on all $n$-vertex graphs excluding some $h$-vertex vertex graph as a topological subgraph. Previous results state that isomorphism for such graphs can be tested in time $n^{\operatorname{polylog}(n)}$ (Babai, STOC 2016) and $n^{f(h)}$ for some function $f$ (Grohe and Marx, SIAM J. Comp., 2015). Our result also unifies and

    更新日期:2020-12-01
  • A Model for Ant Trail Formation and its Convergence Properties
    arXiv.cs.DS Pub Date : 2020-11-30
    Moses Charikar; Shivam Garg; Deborah M. Gordon; Kirankumar Shiragur

    We introduce a model for ant trail formation, building upon previous work on biologically feasible local algorithms that plausibly describe how ants maintain trail networks. The model is a variant of a reinforced random walk on a directed graph, where ants lay pheromone on edges as they traverse them and the next edge to traverse is chosen based on the pheromone level; this pheromone decays with time

    更新日期:2020-12-01
  • Batch Optimization for DNA Synthesis
    arXiv.cs.DS Pub Date : 2020-11-30
    Konstantin Makarychev; Miklos Z. Racz; Cyrus Rashtchian; Sergey Yekhanin

    Large pools of synthetic DNA molecules have been recently used to reliably store significant volumes of digital data. While DNA as a storage medium has enormous potential because of its high storage density, its practical use is currently severely limited because of the high cost and low throughput of available DNA synthesis technologies. We study the role of batch optimization in reducing the cost

    更新日期:2020-12-01
  • AWLCO: All-Window Length Co-Occurrence
    arXiv.cs.DS Pub Date : 2020-11-29
    Joshua Sobel; Noah Bertram; Chen Ding; Fatemeh Nargesian; Daniel Gildea

    Analyzing patterns in a sequence of events has applications in text analysis, computer programming, and genomics research. In this paper, we consider the all-window-length analysis model which analyzes a sequence of events with respect to windows of all lengths. We study the exact co-occurrence counting problem for the all-window-length analysis model. Our first algorithm is an offline algorithm that

    更新日期:2020-12-01
  • Approximation algorithms for hitting subgraphs
    arXiv.cs.DS Pub Date : 2020-11-29
    Noah Brüstle; Tal Elbaz; Hamed Hatami; Onur Kocer; Bingchan Ma

    Let $H$ be a fixed undirected graph on $k$ vertices. The $H$-hitting set problem asks for deleting a minimum number of vertices from a given graph $G$ in such a way that the resulting graph has no copies of $H$ as a subgraph. This problem is a special case of the hypergraph vertex cover problem on $k$-uniform hypergraphs, and thus admits an efficient $k$-factor approximation algorithm. The purpose

    更新日期:2020-12-01
  • Erasure-Resilient Sublinear-Time Graph Algorithms
    arXiv.cs.DS Pub Date : 2020-11-29
    Amit Levi; Ramesh Krishnan S. Pallavoor; Sofya Raskhodnikova; Nithin Varma

    We investigate sublinear-time algorithms that take partially erased graphs represented by adjacency lists as input. Our algorithms make degree and neighbor queries to the input graph and work with a specified fraction of adversarial erasures in adjacency entries. We focus on two computational tasks: testing if a graph is connected or $\varepsilon$-far from connected and estimating the average degree

    更新日期:2020-12-01
  • Online Search with Maximum Clearance
    arXiv.cs.DS Pub Date : 2020-11-28
    Spyros Angelopoulos; Malachi Voss

    We study the setting in which a mobile agent must locate a hidden target in a bounded or unbounded environment, with no information about the hider's position. In particular, we consider online search, in which the performance of the search strategy is evaluated by its worst case competitive ratio. We introduce a multi-criteria search problem in which the searcher has a budget on its allotted search

    更新日期:2020-12-01
  • On Parameterized Complexity of Liquid Democracy
    arXiv.cs.DS Pub Date : 2020-11-28
    Palash Dey; Arnab Maiti; Amatya Sharma

    In liquid democracy, each voter either votes herself or delegates her vote to some other voter. This gives rise to what is called a delegation graph. To decide the voters who eventually votes along with the subset of voters whose votes they give, we need to resolve the cycles in the delegation graph. This gives rise to the Resolve Delegation problem where we need to find an acyclic sub-graph of the

    更新日期:2020-12-01
  • Feedback Effects in Repeat-Use Criminal Risk Assessments
    arXiv.cs.DS Pub Date : 2020-11-28
    Benjamin Laufer

    In the criminal legal context, risk assessment algorithms are touted as data-driven, well-tested tools. Studies known as validation tests are typically cited by practitioners to show that a particular risk assessment algorithm has predictive accuracy, establishes legitimate differences between risk groups, and maintains some measure of group fairness in treatment. To establish these important goals

    更新日期:2020-12-01
  • Group-level Fairness Maximization in Online Bipartite Matching
    arXiv.cs.DS Pub Date : 2020-11-27
    Will Ma; Pan Xu

    In typical online matching problems, the goal is to maximize the number of matches. This paper studies online bipartite matching from the perspective of group-level fairness, and the goal is to balance the number of matches made across different groups of online nodes. We assume that an online node's group belongings are revealed upon arrival, and measure performance based on the group with the smallest

    更新日期:2020-12-01
  • Near-Optimal Algorithms for Reachability, Strongly-Connected Components and Shortest Paths in Partially Dynamic Digraphs
    arXiv.cs.DS Pub Date : 2020-11-27
    Maximilian Probst Gutenberg

    In this thesis, we present new techniques to deal with fundamental algorithmic graph problems where graphs are directed and partially dynamic, i.e. undergo either a sequence of edge insertions or deletions: - Single-Source Reachability (SSR), - Strongly-Connected Components (SCCs), and - Single-Source Shortest Paths (SSSP). These problems have recently received an extraordinary amount of attention

    更新日期:2020-12-01
  • Minmax Regret 1-Sink Location Problems on Dynamic Flow Path Networks with Parametric Weights
    arXiv.cs.DS Pub Date : 2020-11-27
    Tetsuya Fujie; Yuya Higashikawa; Naoki Katoh; Junichi Teruyama; Yuki Tokuni

    This paper addresses the minmax regret 1-sink location problem on dynamic flow path networks with parametric weights. We are given a dynamic flow network consisting of an undirected path with positive edge lengths, positive edge capacities, and nonnegative vertex weights. A path can be considered as a road, an edge length as the distance along the road and a vertex weight as the number of people at

    更新日期:2020-12-01
  • Tight Bound on Vertex Cut Sparsifiers in Directed Acyclic Graphs
    arXiv.cs.DS Pub Date : 2020-11-26
    Zhiyang He; Jason Li

    For an unweighted graph on $k$ terminals, Kratsch and Wahlstr\"om constructed a vertex sparsifier with $O(k^3)$ vertices via the theory of representative families on matroids. Since their breakthrough result in 2012, no improvement upon the $O(k^3)$ bound has been found. In this paper, we interpret Kratsch and Wahlstr\"om's result through the lens of Bollob\'as's Two-Families Theorem from extremal

    更新日期:2020-12-01
  • Faster Projective Clustering Approximation of Big Data
    arXiv.cs.DS Pub Date : 2020-11-26
    Adiel Statman; Liat Rozenberg; Dan Feldman

    In projective clustering we are given a set of n points in $R^d$ and wish to cluster them to a set $S$ of $k$ linear subspaces in $R^d$ according to some given distance function. An $\eps$-coreset for this problem is a weighted (scaled) subset of the input points such that for every such possible $S$ the sum of these distances is approximated up to a factor of $(1+\eps)$. We suggest to reduce the size

    更新日期:2020-12-01
  • Tight Hardness Results for Training Depth-2 ReLU Networks
    arXiv.cs.DS Pub Date : 2020-11-27
    Surbhi Goel; Adam Klivans; Pasin Manurangsi; Daniel Reichman

    We prove several hardness results for training depth-2 neural networks with the ReLU activation function; these networks are simply weighted sums (that may include negative coefficients) of ReLUs. Our goal is to output a depth-2 neural network that minimizes the square loss with respect to a given training set. We prove that this problem is NP-hard already for a network with a single ReLU. We also

    更新日期:2020-12-01
  • Disjoint Stable Matchings in Linear Time
    arXiv.cs.DS Pub Date : 2020-11-26
    Prajakta Nimbhorkar; Geevarghese Philip; Vishwa Prakash HV

    We show that given a SM instance G as input we can find a largest collection of pairwise edge-disjoint stable matchings of G in time linear in the input size. This extends two classical results: 1. The Gale-Shapley algorithm, which can find at most two ("extreme") pairwise edge-disjoint stable matchings of G in linear time, and 2. The polynomial-time algorithm for finding a largest collection of pairwise

    更新日期:2020-12-01
  • Outcome Indistinguishability
    arXiv.cs.DS Pub Date : 2020-11-26
    Cynthia Dwork; Michael P. Kim; Omer Reingold; Guy N. Rothblum; Gal Yona

    Prediction algorithms assign numbers to individuals that are popularly understood as individual "probabilities" -- what is the probability of 5-year survival after cancer diagnosis? -- and which increasingly form the basis for life-altering decisions. Drawing on an understanding of computational indistinguishability developed in complexity theory and cryptography, we introduce Outcome Indistinguishability

    更新日期:2020-12-01
  • Grammar Compression By Induced Suffix Sorting
    arXiv.cs.DS Pub Date : 2020-11-25
    Daniel S. N. Nunes; Felipe A. Louza; Simon Gog; Mauricio Ayala-Rincón; Gonzalo Navarro

    A grammar compression algorithm, called GCIS, is introduced in this work. GCIS is based on the induced suffix sorting algorithm SAIS, presented by Nong et al. in 2009. The proposed solution builds on the factorization performed by SAIS during suffix sorting. A context-free grammar is used to replace factors by non-terminals. The algorithm is then recursively applied on the shorter sequence of non-terminals

    更新日期:2020-11-27
  • Left Lyndon tree construction
    arXiv.cs.DS Pub Date : 2020-11-25
    Golnaz Badkobeh; Maxime Crochemore

    We extend the left-to-right Lyndon factorisation of a word to the left Lyndon tree construction of a Lyndon word. It yields an algorithm to sort the prefixes of a Lyndon word according to the infinite ordering defined by Dolce et al. (2019). A straightforward variant computes the left Lyndon forest of a word. All algorithms run in linear time on a general alphabet, that is, in the letter-comparison

    更新日期:2020-11-27
  • Solving the r-pseudoforest Deletion Problem in Time Independent of r
    arXiv.cs.DS Pub Date : 2020-11-25
    Bin Sheng

    The feedback vertex set problem is one of the most studied parameterized problems. Several generalizations of the problem have been studied where one is to delete vertices to obtain graphs close to acyclic. In this paper, we give an FPT algorithm for the problem of deleting at most $k$ vertices to get an $r$-pseudoforest. A graph is an $r$-pseudoforest if we can delete at most $r$ edges from each component

    更新日期:2020-11-27
  • Quantum algorithms for matrix scaling and matrix balancing
    arXiv.cs.DS Pub Date : 2020-11-25
    Joran van Apeldoorn; Sander Gribling; Yinan Li; Harold Nieuwboer; Michael Walter; Ronald de Wolf

    Matrix scaling and matrix balancing are two basic linear-algebraic problems with a wide variety of applications, such as approximating the permanent, and pre-conditioning linear systems to make them more numerically stable. We study the power and limitations of quantum algorithms for these problems. We provide quantum implementations of two classical (in both senses of the word) methods: Sinkhorn's

    更新日期:2020-11-27
  • An $O(\log^{3/2}n)$ Parallel Time Population Protocol for Majority with $O(\log n)$ States
    arXiv.cs.DS Pub Date : 2020-11-25
    Stav Ben-Nun; Tsvi Kopelowitz; Matan Kraus; Ely Porat

    In population protocols, the underlying distributed network consists of $n$ nodes (or agents), denoted by $V$, and a scheduler that continuously selects uniformly random pairs of nodes to interact. When two nodes interact, their states are updated by applying a state transition function that depends only on the states of the two nodes prior to the interaction. The efficiency of a population protocol

    更新日期:2020-11-27
  • The Geometry of Distributed Representations for Better Alignment, Attenuated Bias, and Improved Interpretability
    arXiv.cs.DS Pub Date : 2020-11-25
    Sunipa Dev

    High-dimensional representations for words, text, images, knowledge graphs and other structured data are commonly used in different paradigms of machine learning and data mining. These representations have different degrees of interpretability, with efficient distributed representations coming at the cost of the loss of feature to dimension mapping. This implies that there is obfuscation in the way

    更新日期:2020-11-27
  • Contract Scheduling With Predictions
    arXiv.cs.DS Pub Date : 2020-11-24
    Spyros Angelopoulos; Shahin Kamali

    Contract scheduling is a general technique that allows to design a system with interruptible capabilities, given an algorithm that is not necessarily interruptible. Previous work on this topic has largely assumed that the interruption is a worst-case deadline that is unknown to the scheduler. In this work, we study the setting in which there is a potentially erroneous prediction concerning the interruption

    更新日期:2020-11-27
  • Optimal Mean Estimation without a Variance
    arXiv.cs.DS Pub Date : 2020-11-24
    Yeshwanth Cherapanamjeri; Nilesh Tripuraneni; Peter L. Bartlett; Michael I. Jordan

    We study the problem of heavy-tailed mean estimation in settings where the variance of the data-generating distribution does not exist. Concretely, given a sample $\mathbf{X} = \{X_i\}_{i = 1}^n$ from a distribution $\mathcal{D}$ over $\mathbb{R}^d$ with mean $\mu$ which satisfies the following \emph{weak-moment} assumption for some ${\alpha \in [0, 1]}$: \begin{equation*} \forall \|v\| = 1: \mathbb{E}_{X

    更新日期:2020-11-27
  • Towards the sampling Lovász Local Lemma
    arXiv.cs.DS Pub Date : 2020-11-24
    Vishesh Jain; Huy Tuan Pham; Thuy Duong Vuong

    Let $\Phi = (V, \mathcal{C})$ be a constraint satisfaction problem on variables $v_1,\dots, v_n$ such that each constraint depends on at most $k$ variables and such that each variable assumes values in an alphabet of size at most $[q]$. Suppose that each constraint shares variables with at most $\Delta$ constraints and that each constraint is violated with probability at most $p$ (under the product

    更新日期:2020-11-25
  • Min-Sum Clustering (with Outliers)
    arXiv.cs.DS Pub Date : 2020-11-24
    Sandip Banerjee; Rafail Ostrovsky; Yuval Rabani

    We give a constant factor polynomial time pseudo-approximation algorithm for min-sum clustering with or without outliers. The algorithm is allowed to exclude an arbitrarily small constant fraction of the points. For instance, we show how to compute a solution that clusters 98\% of the input data points and pays no more than a constant factor times the optimal solution that clusters 99\% of the input

    更新日期:2020-11-25
  • Algorithms and Experiments Comparing Two Hierarchical Drawing Frameworks
    arXiv.cs.DS Pub Date : 2020-11-24
    Panagiotis Lionakis; Giorgos Kritikakis; Ioannis G. Tollis

    We present algorithms that extend the path-based hierarchical drawing framework and give experimental results. Our algorithms run in $O(km)$ time, where $k$ is the number of paths and $m$ is the number of edges of the graph, and provide better upper bounds than the original path based framework: e.g., the height of the resulting drawings is equal to the length of the longest path of $G$, instead of

    更新日期:2020-11-25
  • Selectable Heaps and Optimal Lazy Search Trees
    arXiv.cs.DS Pub Date : 2020-11-23
    Bryce Sandlund; Lingyi Zhang

    We show the $O(\log n)$ time extract minimum function of efficient priority queues can be generalized to the extraction of the $k$ smallest elements in $O(k \log(n/k))$ time, where we define $\log(x)$ as $\max(\log_2(x), 1)$. We first show heap-ordered tree selection (Kaplan et al., SOSA '19) can be applied on the heap-ordered trees of the classic Fibonacci heap to support the extraction in $O(k \log(n/k))$

    更新日期:2020-11-25
  • An Estimator for Matching Size in Low Arboricity Graphs with Two Applications
    arXiv.cs.DS Pub Date : 2020-11-23
    Hossein Jowhari

    In this paper, we present a new simple degree-based estimator for the size of maximum matching in bounded arboricity graphs. When the arboricity of the graph is bounded by $\alpha$, the estimator gives a $\alpha+2$ factor approximation of the matching size. For planar graphs, we show the estimator does better and returns a $3.5$ approximation of the matching size. Using this estimator, we get new results

    更新日期:2020-11-25
  • Applying the Quantum Alternating Operator Ansatz to the Graph Matching Problem
    arXiv.cs.DS Pub Date : 2020-11-24
    Sagnik Chatterjee; Debajyoti Bera

    The Quantum Alternating Operator Ansatz (QAOA+) framework has recently gained attention due to its ability to solve discrete optimization problems on noisy intermediate-scale quantum (NISQ) devices in a manner that is amenable to derivation of worst-case guarantees. We design a technique in this framework to tackle a few problems over maximal matchings in graphs. Even though maximum matching is polynomial-time

    更新日期:2020-11-25
  • InstaHide's Sample Complexity When Mixing Two Private Images
    arXiv.cs.DS Pub Date : 2020-11-24
    Baihe Huang; Zhao Song; Runzhou Tao; Ruizhe Zhang; Danyang Zhuo

    Inspired by InstaHide challenge [Huang, Song, Li and Arora'20], [Chen, Song and Zhuo'20] recently provides one mathematical formulation of InstaHide attack problem under Gaussian images distribution. They show that it suffices to use $O(n_{\mathsf{priv}}^{k_{\mathsf{priv}} - 2/(k_{\mathsf{priv}} + 1)})$ samples to recover one private image in $n_{\mathsf{priv}}^{O(k_{\mathsf{priv}})} + \mathrm{pol

    更新日期:2020-11-25
  • Learnable and Instance-Robust Predictions for Online Matching, Flows and Load Balancing
    arXiv.cs.DS Pub Date : 2020-11-23
    Thomas Lavastida; Benjamin Moseley; R. Ravi; Chenyang Xu

    This paper proposes a new model for augmenting algorithms with useful predictions that go beyond worst-case bounds on the algorithm performance. By refining existing models, our model ensures predictions are formally learnable and instance robust. Learnability guarantees that predictions can be efficiently constructed from past data. Instance robustness formally ensures a prediction is robust to modest

    更新日期:2020-11-25
  • Analysis of the Harmonic Function Used in Bin-Packing
    arXiv.cs.DS Pub Date : 2020-11-23
    Eklavya Sharma

    The harmonic function was first introduced by Lee and Lee (JACM 1985) for analyzing their online bin-packing algorithm. Subsequently, it has been used to obtain approximation algorithms for many different packing problems. Here we slightly generalize the harmonic function and give alternative proofs of its important properties.

    更新日期:2020-11-25
  • Speeding up decimal multiplication
    arXiv.cs.DS Pub Date : 2020-11-23
    Viktor Krapivensky

    Decimal multiplication is the task of multiplying two numbers in base $10^N.$ Specifically, we focus on the number-theoretic transform (NTT) family of algorithms. Using only portable techniques, we achieve a 3x---5x speedup over the mpdecimal library. In this paper we describe our implementation and discuss further possible optimizations. We also present a simple cache-efficient algorithm for in-place

    更新日期:2020-11-25
  • An Approximation Algorithm for Covering Linear Programs and its Application to Bin-Packing
    arXiv.cs.DS Pub Date : 2020-11-23
    Eklavya Sharma

    We give an $\alpha(1+\epsilon)$-approximation algorithm for solving covering LPs, assuming the presence of a $(1/\alpha)$-approximation algorithm for a certain optimization problem. Our algorithm is based on a simple modification of the Plotkin-Shmoys-Tardos algorithm (MOR 1995). We then apply our algorithm to $\alpha(1+\epsilon)$-approximately solve the configuration LP for a large class of bin-packing

    更新日期:2020-11-25
  • Searching and Sorting with O(n^2) processors in O(1) time
    arXiv.cs.DS Pub Date : 2020-11-23
    Taeyoung An; A. Yavuz Oruc

    The proliferation of number of processing elements (PEs) in parallel computer systems, along with the use of more extensive parallelization of algorithms causes the interprocessor communications dominate VLSI chip space. This paper proposes a new architecture to overcome this issue by using simple crosspoint switches to pair PEs instead of a complex interconnection network. Based on the cyclic permutation

    更新日期:2020-11-25
  • Making mean-estimation more efficient using an MCMC trace variance approach: DynaMITE
    arXiv.cs.DS Pub Date : 2020-11-22
    Cyrus Cousins; Shahrzad Haddadan; Eli Upfal

    The Markov-Chain Monte-Carlo (MCMC) method has been used widely in the literature for various applications, in particular estimating the expectation $\mathbb{E}_{\pi}[f]$ of a function $f:\Omega\to [a,b]$ over a distribution $\pi$ on $\Omega$ (a.k.a. mean-estimation), to within $\varepsilon$ additive error (w.h.p.). Letting $R \doteq b-a$, standard variance-agnostic MCMC mean-estimators run the chain

    更新日期:2020-11-25
  • The VLSAT-1 Benchmark Suite
    arXiv.cs.DS Pub Date : 2020-11-19
    Pierre BouvierCONVECS; Hubert GaravelCONVECS

    This report presents VLSAT-1 (an acronym for "Very Large Boolean SATisfiability problems"), the first part of a benchmark suite to be used in scientificexperiments and software competitions addressing SAT-solving issues.VLSAT-1 contains 100~benchmarks of increasing complexity, proposed in DIMACSCNF format under a permissive Creative Commons license. These benchmarks havebeen used by the 2020 International

    更新日期:2020-11-25
  • Algorithmic upper bounds for graph geodetic number
    arXiv.cs.DS Pub Date : 2020-11-22
    Ahmad T. Anaqreh; Boglarka G. -Toth; Tamas Vinko

    Graph theoretical problems based on shortest paths are at the core of research due to their theoretical importance and applicability. This paper deals with the geodetic number which is a global measure for simple connected graphs and it belongs to the path covering problems: what is the minimal-cardinality set of vertices, such that all shortest paths between its elements cover every vertex of the

    更新日期:2020-11-25
  • Online Maximum $k$-Interval Coverage Problem
    arXiv.cs.DS Pub Date : 2020-11-22
    Songhua Li; Minming Li; Lingjie Duan; Victor C. S. Lee

    We study the online maximum coverage problem on a line, in which, given an online sequence of sub-intervals (which may intersect among each other) of a target large interval and an integer $k$, we aim to select at most $k$ of the sub-intervals such that the total covered length of the target interval is maximized. The decision to accept or reject each sub-interval is made immediately and irrevocably

    更新日期:2020-11-25
  • Improved Dynamic Algorithms for Longest Increasing Subsequence
    arXiv.cs.DS Pub Date : 2020-11-21
    Tomasz Kociumaka; Saeed Seddighin

    We study dynamic algorithms for the longest increasing subsequence (\textsf{LIS}) problem. A dynamic \textsf{LIS} algorithm maintains a sequence subject to operations of the following form arriving one by one: (i) insert an element, (ii) delete an element, or (iii) substitute an element for another. After performing each operation, the algorithm must report the length of the longest increasing subsequence

    更新日期:2020-11-25
  • Erdös-Szekeres Partitioning Problem
    arXiv.cs.DS Pub Date : 2020-11-21
    Michael Mitzenmacher; Saeed Seddighin

    In this note, we present a substantial improvement on the computational complexity of the Erd\"{o}s-Szekeres partitioning problem and review recent works on dynamic \textsf{LIS}.

    更新日期:2020-11-25
  • Sparse sketches with small inversion bias
    arXiv.cs.DS Pub Date : 2020-11-21
    Michał Dereziński; Zhenyu Liao; Edgar Dobriban; Michael W. Mahoney

    For a tall $n\times d$ matrix $A$ and a random $m\times n$ sketching matrix $S$, the sketched estimate of the inverse covariance matrix $(A^\top A)^{-1}$ is typically biased: $E[(\tilde A^\top\tilde A)^{-1}]\ne(A^\top A)^{-1}$, where $\tilde A=SA$. This phenomenon, which we call inversion bias, arises, e.g., in statistics and distributed optimization, when averaging multiple independently constructed

    更新日期:2020-11-25
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