• 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

更新日期：2020-03-27
• 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

更新日期：2020-03-27
• 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

更新日期：2020-03-27
• 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

更新日期：2020-03-27
• 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

更新日期：2020-03-27
• 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

更新日期：2020-03-27
• arXiv.cs.DS Pub Date : 2019-03-08

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

更新日期：2020-03-27
• 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

更新日期：2020-03-27
• 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

更新日期：2020-03-27
• 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

更新日期：2020-03-27
• 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

更新日期：2020-03-26
• 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

更新日期：2020-03-26
• 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

更新日期：2020-03-26
• 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

更新日期：2020-03-26
• 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

更新日期：2020-03-26
• 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

更新日期：2020-03-26
• 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

更新日期：2020-03-26
• 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

更新日期：2020-03-26
• 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

更新日期：2020-03-26
• 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

更新日期：2020-03-24
• 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

更新日期：2020-03-24
• 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

更新日期：2020-03-24
• 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

更新日期：2020-03-24
• 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

更新日期：2020-03-24
• 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

更新日期：2020-03-24
• 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

更新日期：2020-03-24
• arXiv.cs.DS Pub Date : 2019-01-19
Tianyi Lin; Nhat Ho; Michael I. Jordan


更新日期：2020-03-18
• 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

更新日期：2020-03-18
• 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

更新日期：2020-03-18
• 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

更新日期：2020-03-18
• 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

更新日期：2020-03-18
• 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

更新日期：2020-03-16
• 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

更新日期：2020-03-16
• 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

更新日期：2020-03-16
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