• arXiv.cs.DS Pub Date : 2020-06-30
Hsin-Hao Su; Nicole Wein

We study the problem of distributed task allocation in multi-agent systems. Suppose there is a collection of agents, a collection of tasks, and a demand vector, which specifies the number of agents required to perform each task. The goal of the agents is to cooperatively allocate themselves to the tasks to satisfy the demand vector. We study the dynamic version of the problem where the demand vector

更新日期：2020-07-01
• arXiv.cs.DS Pub Date : 2020-06-30
Christine Markarian; Abdul-Nasser Kassar; Manal Yunis

Facility Location problems ask to place facilities in a way that optimizes a given objective function so as to provide a service to all clients. These are one of the most well-studied optimization problems spanning many research areas such as operations research, computer science, and management science. Traditionally, these problems are solved with the assumption that clients need to be served by

更新日期：2020-07-01
• arXiv.cs.DS Pub Date : 2020-06-30
Noga Alon; Andrei Graur

We provide approximation algorithms for two problems, known as NECKLACE SPLITTING and $\epsilon$-CONSENSUS SPLITTING. In the problem $\epsilon$-CONSENSUS SPLITTING, there are $n$ non-atomic probability measures on the interval $[0, 1]$ and $k$ agents. The goal is to divide the interval, via at most $n (k-1)$ cuts, into pieces and distribute them to the $k$ agents in an approximately equitable way,

更新日期：2020-07-01
• arXiv.cs.DS Pub Date : 2020-06-30
Daniele Calandriello; Michał Dereziński; Michal Valko

Determinantal point processes (DPPs) are a useful probabilistic model for selecting a small diverse subset out of a large collection of items, with applications in summarization, stochastic optimization, active learning and more. Given a kernel function and a subset size $k$, our goal is to sample $k$ out of $n$ items with probability proportional to the determinant of the kernel matrix induced by

更新日期：2020-07-01
• arXiv.cs.DS Pub Date : 2020-06-30
András Gilyén; Seth Lloyd; Iman Marvian; Yihui Quek; Mark M. Wilde

The Petz recovery channel plays an important role in quantum information science as an operation that approximately reverses the effect of a quantum channel. The pretty good measurement is a special case of the Petz recovery channel, and it allows for near-optimal state discrimination. A hurdle to the experimental realization of these vaunted theoretical tools is the lack of a systematic and efficient

更新日期：2020-07-01
• arXiv.cs.DS Pub Date : 2020-06-30
Nicolas Bousquet; Alice Joffard; Paul Ouvrard

Given a graph $G$ and an integer $k$, a token addition and removal ({\sf TAR} for short) reconfiguration sequence between two dominating sets $D_{\sf s}$ and $D_{\sf t}$ of size at most $k$ is a sequence $S= \langle D_0 = D_{\sf s}, D_1 \ldots, D_\ell = D_{\sf t} \rangle$ of dominating sets of $G$ such that any two consecutive dominating sets differ by the addition or deletion of one vertex, and no

更新日期：2020-07-01
• arXiv.cs.DS Pub Date : 2020-06-30
Amit Deshpande; Rameshwar Pratap

The subspace approximation problem with outliers, for given $n$ points in $d$ dimensions $x_{1},\ldots, x_{n} \in R^{d}$, an integer $1 \leq k \leq d$, and an outlier parameter $0 \leq \alpha \leq 1$, is to find a $k$-dimensional linear subspace of $R^{d}$ that minimizes the sum of squared distances to its nearest $(1-\alpha)n$ points. More generally, the $\ell_{p}$ subspace approximation problem with

更新日期：2020-07-01
• arXiv.cs.DS Pub Date : 2020-06-29
Arya Mazumdar; Soumyabrata Pal

Mixture of linear regressions is a popular learning theoretic model that is used widely to represent heterogeneous data. In the simplest form, this model assumes that the labels are generated from either of two different linear models and mixed together. Recent works of Yin et al. and Krishnamurthy et al., 2019, focus on an experimental design setting of model recovery for this problem. It is assumed

更新日期：2020-07-01
• arXiv.cs.DS Pub Date : 2020-06-29
Yongli Zhu; Renchang Dai; Guangyi Liu

Parallel betweenness computation algorithms are proposed and implemented in a graph database for power system contingency selection. Principles of the graph database and graph computing are investigated for both node and edge betweenness computation. Experiments on the 118-bus system and a real power system show that speed-up can be achieved for both node and edge betweenness computation while the

更新日期：2020-07-01
• arXiv.cs.DS Pub Date : 2020-06-29
Xiaotian Hao; Zhaoqing Peng; Yi Ma; Guan Wang; Junqi Jin; Jianye Hao; Shan Chen; Rongquan Bai; Mingzhou Xie; Miao Xu; Zhenzhe Zheng; Chuan Yu; Han Li; Jian Xu; Kun Gai

In E-commerce, advertising is essential for merchants to reach their target users. The typical objective is to maximize the advertiser's cumulative revenue over a period of time under a budget constraint. In real applications, an advertisement (ad) usually needs to be exposed to the same user multiple times until the user finally contributes revenue (e.g., places an order). However, existing advertising

更新日期：2020-07-01
• arXiv.cs.DS Pub Date : 2020-06-29
Abraham Frandsen; Rong Ge

Tucker decomposition is a popular technique for many data analysis and machine learning applications. Finding a Tucker decomposition is a nonconvex optimization problem. As the scale of the problems increases, local search algorithms such as stochastic gradient descent have become popular in practice. In this paper, we characterize the optimization landscape of the Tucker decomposition problem. In

更新日期：2020-07-01
• arXiv.cs.DS Pub Date : 2020-06-29
Kazuhiro Kurita; Yasuaki Kobayashi

Let $G = (V, E)$ be an undirected graph and let $B \subseteq V \times V$ be a set of terminal pairs. A node/edge multicut is a subset of vertices/edges of $G$ whose removal destroys all the paths between every terminal pair in $B$. The problem of computing a {\em minimum} node/edge multicut is NP-hard and extensively studied from several viewpoints. In this paper, we study the problem of enumerating

更新日期：2020-06-30
• arXiv.cs.DS Pub Date : 2020-06-29
Panagiotis Charalampopoulos; Huiping Chen; Peter Christen; Grigorios Loukides; Nadia Pisanti; Solon P. Pissis; Jakub Radoszewski

In the Pattern Masking for Dictionary Matching (PMDM) problem, we are given a dictionary $\mathcal{D}$ of $d$ strings, each of length $\ell$, a query string $q$ of length $\ell$, and a positive integer $z$, and we are asked to compute a smallest set $K\subseteq\{1,\ldots,\ell\}$, so that if $q[i]$, for all $i\in K$, is replaced by a wildcard, then $q$ matches at least $z$ strings from $\mathcal{D}$

更新日期：2020-06-30
• arXiv.cs.DS Pub Date : 2020-06-29
Panagiotis Charalampopoulos; Jakub Radoszewski; Wojciech Rytter; Tomasz Waleń; Wiktor Zuba

The notions of periodicity and repetitions in strings, and hence these of runs and squares, naturally extend to two-dimensional strings. We consider two types of repetitions in 2D-strings: 2D-runs and quartics (quartics are a 2D-version of squares in standard strings). Amir et al. introduced 2D-runs, showed that there are $O(n^3)$ of them in an $n \times n$ 2D-string and presented a simple construction

更新日期：2020-06-30
• arXiv.cs.DS Pub Date : 2020-06-28
Akbar Rafiey; Yuichi Yoshida

The problem of maximizing nonnegative monotone submodular functions under a certain constraint has been intensively studied in the last decade, and a wide range of efficient approximation algorithms have been developed for this problem. Many machine learning problems, including data summarization and influence maximization, can be naturally modeled as the problem of maximizing monotone submodular functions

更新日期：2020-06-30
• arXiv.cs.DS Pub Date : 2020-06-28
Eduard Eiben; William Lochet

The line graph of a graph $G$ is the graph $L(G)$ whose vertex set is the edge set of $G$ and there is an edge between $e,f\in E(G)$ if $e$ and $f$ share an endpoint in $G$. A graph is called line graph if it is a line graph of some graph. We study the Line-Graph-Edge Deletion problem, which asks whether we can delete at most $k$ edges from the input graph $G$ such that the resulting graph is a line

更新日期：2020-06-30
• arXiv.cs.DS Pub Date : 2020-06-28
Philip Bille; Inge Li Gørtz

We consider compact representations of collections of similar strings that support random access queries. The collection of strings is given by a rooted tree where edges are labeled by an edit operation (inserting, deleting, or replacing a character) and a node represents the string obtained by applying the sequence of edit operations on the path from the root to the node. The goal is to compactly

更新日期：2020-06-30
• arXiv.cs.DS Pub Date : 2020-06-28
Jeffrey M. Dudek; Moshe Y. Vardi

A promising new algebraic approach to weighted model counting makes use of tensor networks, following a reduction from weighted model counting to tensor-network contraction. Prior work has focused on analyzing the single-core performance of this approach, and demonstrated that it is an effective addition to the current portfolio of weighted-model-counting algorithms. In this work, we explore the impact

更新日期：2020-06-30
• arXiv.cs.DS Pub Date : 2020-06-27
Sangram K. Jena; Ramesh K. Jallu; Gautam K. Das; Subhas C. Nandy

In this article, we study a generalized version of the maximum independent set and minimum dominating set problems, namely, the maximum $d$-distance independent set problem and the minimum $d$-distance dominating set problem on unit disk graphs for a positive integer $d>0$. We first show that the maximum $d$-distance independent set problem and the minimum $d$-distance dominating set problem belongs

更新日期：2020-06-30
• arXiv.cs.DS Pub Date : 2020-06-27
Ramtin Afshar; Michael T. Goodrich; Pedro Matias; Martha C. Osegueda

In this paper, we study the parallel query complexity of reconstructing biological and digital phylogenetic trees from simple queries involving their nodes. This is motivated from computational biology, data protection, and computer security settings, which can be abstracted in terms of two parties, a \emph{responder}, Alice, who must correctly answer queries of a given type regarding a degree-$d$

更新日期：2020-06-30
• arXiv.cs.DS Pub Date : 2020-06-29
Ilias Diakonikolas; Daniel M. Kane; Nikos Zarifis

We study the fundamental problems of agnostically learning halfspaces and ReLUs under Gaussian marginals. In the former problem, given labeled examples $(\mathbf{x}, y)$ from an unknown distribution on $\mathbb{R}^d \times \{ \pm 1\}$, whose marginal distribution on $\mathbf{x}$ is the standard Gaussian and the labels $y$ can be arbitrary, the goal is to output a hypothesis with 0-1 loss $\mathrm{OPT}+\epsilon$

更新日期：2020-06-30
• arXiv.cs.DS Pub Date : 2020-06-29
Surbhi Goel; Aravind Gollakota; Adam Klivans

We give the first statistical-query lower bounds for agnostically learning any non-polynomial activation with respect to Gaussian marginals (e.g., ReLU, sigmoid, sign). For the specific problem of ReLU regression (equivalently, agnostically learning a ReLU), we show that any statistical-query algorithm with tolerance $n^{-\Theta(\epsilon^{-1/2})}$ must use at least $2^{n^c} \epsilon$ queries for some

更新日期：2020-06-30
• arXiv.cs.DS Pub Date : 2020-06-28
Haris Aziz

The Hylland-Zeckhauser (HZ) rule is a well-known rule for probabilistic assignment of items. The complexity of the rule has received renewed interest recently with Vazirani and Yannakakis (2020) proposing a strongly polynomial-time algorithm for the rule under bi-valued utilities, and making several general insights. We study the rule under the case of agents having bi-valued utilities. We point out

更新日期：2020-06-30
• arXiv.cs.DS Pub Date : 2020-06-27
Michael Mitzenmacher

Motivated by recent work on scheduling with predicted job sizes, we consider the performance of scheduling algorithms with minimal advice, namely a single bit. Besides demonstrating the power of very limited advice, such schemes are quite natural. In the prediction setting, one bit of advice can be used to model a simple prediction as to whether a job is "large" or "small"; that is, whether a job is

更新日期：2020-06-30
• arXiv.cs.DS Pub Date : 2020-06-27
Rishabh Iyer; Ninad Khargoankar; Jeff Bilmes; Himanshu Asanani

Information-theoretic quantities like entropy and mutual information have found numerous uses in machine learning. It is well known that there is a strong connection between these entropic quantities and submodularity since entropy over a set of random variables is submodular. In this paper, we study combinatorial information measures that generalize independence, (conditional) entropy, (conditional)

更新日期：2020-06-30
• arXiv.cs.DS Pub Date : 2020-06-27
Aman Khalid

In this paper, we present an implementation of a cuckoo filter for membership testing, optimized for distributed data stores operating in high workloads. In large databases, querying becomes inefficient using traditional search methods. To achieve optimal performance it is necessary to use probabilistic data structures to test the membership of a given key, at the cost of getting false positives while

更新日期：2020-06-30
• arXiv.cs.DS Pub Date : 2020-06-26
Abishek Sankararaman; Soumya Basu; Karthik Abinav Sankararaman

We study regret minimization problems in a two-sided matching market where uniformly valued demand side agents (a.k.a. agents) continuously compete for getting matched with supply side agents (a.k.a. arms) with unknown and heterogeneous valuations. Such markets abstract online matching platforms (for e.g. UpWork, TaskRabbit) and falls within the purview of matching bandit models introduced in Liu et

更新日期：2020-06-30
• arXiv.cs.DS Pub Date : 2020-06-26
Massimo Cairo; Shahbaz Khan; Romeo Rizzi; Sebastian Schmidt; Alexandru I. Tomescu; Elia Zirondelli

Given a directed graph $G$ and a pair of nodes $s$ and $t$, an $s$-$t$ bridge of $G$ is an edge whose removal breaks all $s$-$t$ paths of $G$. Similarly, an $s$-$t$ articulation point of $G$ is a node whose removal breaks all $s$-$t$ paths of $G$. Computing the sequence of all $s$-$t$ bridges of $G$ (as well as the $s$-$t$ articulation points) is a basic graph problem, solvable in linear time using

更新日期：2020-06-29
• arXiv.cs.DS Pub Date : 2020-06-26
Aleksander Figiel; Anne-Sophie Himmel; André Nichterlein; Rolf Niedermeier

Editing a graph into a disjoint union of clusters is a standard optimization task in graph-based data clustering. Here, complementing classic work where the clusters shall be cliques, we focus on clusters that shall be 2-clubs, that is, subgraphs of diameter two. This naturally leads to the two NP-hard problems 2-Club Cluster Editing (the allowed editing operations are edge insertion and edge deletion)

更新日期：2020-06-29
• arXiv.cs.DS Pub Date : 2020-06-26
Esther M. Arkin; Rathish Das; Jie Gao; Mayank Goswami; Joseph S. B. Mitchell; Valentin Polishchuk; Csaba D. Toth

Motivated by indoor localization by tripwire lasers, we study the problem of cutting a polygon into small-size pieces, using the chords of the polygon. Several versions are considered, depending on the definition of the "size" of a piece. In particular, we consider the area, the diameter, and the radius of the largest inscribed circle as a measure of the size of a piece. We also consider different

更新日期：2020-06-29
• arXiv.cs.DS Pub Date : 2020-06-25
Ojas Parekh; Cynthia A. Phillips; Conrad D. James; James B. Aimone

Boolean circuits of McCulloch-Pitts threshold gates are a classic model of neural computation studied heavily in the late 20th century as a model of general computation. Recent advances in large-scale neural computing hardware has made their practical implementation a near-term possibility. We describe a theoretical approach for multiplying two $N$ by $N$ matrices that integrates threshold gate logic

更新日期：2020-06-29
• arXiv.cs.DS Pub Date : 2020-06-26
Pjotr Buy; Andreas Galanis; Viresh Patel; Guus Regts

We study the computational complexity of approximating the partition function of the ferromagnetic Ising model in the Lee-Yang circle of zeros given by $|\lambda|=1$, where $\lambda$ is the external field of the model. Complex-valued parameters for the Ising model are relevant for quantum circuit computations and phase transitions in statistical physics, but have also been key in the recent deterministic

更新日期：2020-06-29
• arXiv.cs.DS Pub Date : 2020-06-25
Debajyoti Mondal; N. Parthiabn; V. Kavitha; Indra Rajasingh

Consider an information diffusion process on a graph $G$ that starts with $k>0$ burnt vertices, and at each subsequent step, burns the neighbors of the currently burnt vertices, as well as $k$ other unburnt vertices. The \emph{$k$-burning number} of $G$ is the minimum number of steps $b_k(G)$ such that all the vertices can be burned within $b_k(G)$ steps. Note that the last step may have smaller than

更新日期：2020-06-29
• arXiv.cs.DS Pub Date : 2020-06-25
Giulio Ermanno Pibiri; Rossano Venturini

Given an integer array A, the prefix-sum problem is to answer sum(i) queries that return the sum of the elements in A[0..i], knowing that the integers in A can be changed. It is a classic problem in data structure design with a wide range of applications in computing from coding to databases. In this work, we propose and compare several and practical solutions to this problem, showing that new trade-offs

更新日期：2020-06-26
• arXiv.cs.DS Pub Date : 2020-06-25
Bogdan-Adrian Manghiuc; Pan Peng; He Sun

For any undirected graph $G=(V,E)$ and a set $E_W$ of candidate edges with $E\cap E_W=\emptyset$, the $(k,\gamma)$-spectral augmentability problem is to find a set $F$ of $k$ edges from $E_W$ with appropriate weighting, such that the algebraic connectivity of the resulting graph $H=(V,E\cup F)$ is least $\gamma$. Because of a tight connection between the algebraic connectivity and many other graph

更新日期：2020-06-26
• arXiv.cs.DS Pub Date : 2020-06-25
Shichuan Deng; Jian Li; Yuval Rabani

In many classic clustering problems, we seek to sketch a massive data set of $n$ points in a metric space, by segmenting them into $k$ categories or clusters, each cluster represented concisely by a single point in the metric space. Two notable examples are the $k$-center/$k$-supplier problem and the $k$-median problem. In practical applications of clustering, the data set may evolve over time, reflecting

更新日期：2020-06-26
• arXiv.cs.DS Pub Date : 2020-06-25
Richard Santiago

We consider the following class of submodular k-multiway partitioning problems: (Sub-$k$-MP) $\min \sum_{i=1}^k f(S_i): S_1 \uplus S_2 \uplus \cdots \uplus S_k = V \mbox{ and } S_i \neq \emptyset \mbox{ for all }i\in [k]$. Here $f$ is a non-negative submodular function, and $\uplus$ denotes the union of disjoint sets. Hence the goal is to partition $V$ into $k$ non-empty sets $S_1,S_2,\ldots,S_k$ such

更新日期：2020-06-26
• arXiv.cs.DS Pub Date : 2020-06-25
Nicolas Bousquet; Takehiro Ito; Yusuke Kobayashi; Haruka Mizuta; Paul Ouvrard; Akira Suzuki; Kunihiro Wasa

Let $G$ be a graph and $T_1,T_2$ be two spanning trees of $G$. We say that $T_1$ can be transformed into $T_2$ via an edge flip if there exist two edges $e \in T_1$ and $f$ in $T_2$ such that $T_2= (T_1 \setminus e) \cup f$. Since spanning trees form a matroid, one can indeed transform a spanning tree into any other via a sequence of edge flips, as observed by Ito et al. We investigate the problem

更新日期：2020-06-26
• arXiv.cs.DS Pub Date : 2020-06-24
Haitao Wang; Yiming Zhao

Let $P$ be a path graph of $n$ vertices embedded in a metric space. We consider the problem of adding a new edge to $P$ so that the radius of the resulting graph is minimized, where any center is constrained to be one of the vertices of $P$. Previously, the "continuous" version of the problem where a center may be a point in the interior of an edge of the graph was studied and a linear-time algorithm

更新日期：2020-06-26
• arXiv.cs.DS Pub Date : 2020-06-24
Luís M. S. Russo; Alexandre P. Francisco

We consider the problem of identifying tandem scattered subsequences within a string. Our algorithm identifies a longest subsequence which occurs twice without overlap in a string. This algorithm is based on the Hunt-Szymanski algorithm, therefore its performance improves if the string is not self similar. This occurs naturally on strings over large alphabets. Our algorithm relies on new results for

更新日期：2020-06-26
• arXiv.cs.DS Pub Date : 2020-06-24
Cyrus Rashtchian; David P. Woodruff; Hanlin Zhu

We consider the general problem of learning about a matrix through vector-matrix-vector queries. These queries provide the value of $\boldsymbol{u}^{\mathrm{T}}\boldsymbol{M}\boldsymbol{v}$ over a fixed field $\mathbb{F}$ for a specified pair of vectors $\boldsymbol{u},\boldsymbol{v} \in \mathbb{F}^n$. To motivate these queries, we observe that they generalize many previously studied models, such as

更新日期：2020-06-26
• arXiv.cs.DS Pub Date : 2020-06-24
Ryan Alweiss; Yang P. Liu; Mehtaab Sawhney

We study discrepancy minimization for vectors in $\mathbb{R}^n$ under various settings. The main result is the analysis of a new simple random process in multiple dimensions through a comparison argument. As corollaries, we obtain bounds which are tight up to logarithmic factors for several problems in online vector balancing posed by Bansal, Jiang, Singla, and Sinha (STOC 2020), as well as linear

更新日期：2020-06-26
• arXiv.cs.DS Pub Date : 2020-06-25
Kyriakos Axiotis; Maxim Sviridenko

The goal of Sparse Convex Optimization is to optimize a convex function $f$ under a sparsity constraint $s\leq s^*\gamma$, where $s^*$ is the target number of non-zero entries in a feasible solution (sparsity) and $\gamma\geq 1$ is an approximation factor. There has been a lot of work to analyze the sparsity guarantees of various algorithms (LASSO, Orthogonal Matching Pursuit (OMP), Iterative Hard

更新日期：2020-06-26
• arXiv.cs.DS Pub Date : 2020-06-24
Frank Gurski; Dominique Komander; Carolin Rehs

An acyclic r-coloring of a directed graph G=(V,E) is a partition of the vertex set V into r acyclic sets. The dichromatic number of a directed graph G is the smallest r such that G allows an acyclic r-coloring. For symmetric digraphs the dichromatic number equals the well-known chromatic number of the underlying undirected graph. This allows us to carry over the W[1]-hardness and lower bounds for running

更新日期：2020-06-25
• arXiv.cs.DS Pub Date : 2020-06-23

Submodular function maximization has found a wealth of new applications in machine learning models during the past years. The related supermodular maximization models (submodular minimization) also offer an abundance of applications, but they appeared to be highly intractable even under simple cardinality constraints. Hence, while there are well-developed tools for maximizing a submodular function

更新日期：2020-06-25
• arXiv.cs.DS Pub Date : 2020-06-24
Ilaria Bordino; Francesco Gullo; Giacomo Legnaro

Receivable financing is the process whereby cash is advanced to firms against receivables their customers have yet to pay: a receivable can be sold to a funder, which immediately gives the firm cash in return for a small percentage of the receivable amount as a fee. Receivable financing has been traditionally handled in a centralized way, where every request is processed by the funder individually

更新日期：2020-06-25
• arXiv.cs.DS Pub Date : 2020-06-24
Fedor V. Fomin; Petr A. Golovach

A fundamental theorem of Whitney from 1933 asserts that 2-connected graphs G and H are 2-isomorphic, or equivalently, their cycle matroids are isomorphic, if and only if G can be transformed into H by a series of operations called Whitney switches. In this paper we consider the quantitative question arising from Whitney's theorem: Given two 2-isomorphic graphs, can we transform one into another by

更新日期：2020-06-25
• arXiv.cs.DS Pub Date : 2020-06-24
Eugenio Angriman; Maria Predari; Alexander van der Grinten; Henning Meyerhenke

The ubiquity of massive graph data sets in numerous applications requires fast algorithms for extracting knowledge from these data. We are motivated here by three electrical measures for the analysis of large small-world graphs $G = (V, E)$ -- i.e., graphs with diameter in $O(\log |V|)$, which are abundant in complex network analysis. From a computational point of view, the three measures have in common

更新日期：2020-06-25
• arXiv.cs.DS Pub Date : 2020-06-24
Shay Golan; Tomasz Kociumaka; Tsvi Kopelowitz; Ely Porat; Przemysław Uznański

The shift distance $\mathsf{sh}(S_1,S_2)$ between two strings $S_1$ and $S_2$ of the same length is defined as the minimum Hamming distance between $S_1$ and any rotation (cyclic shift) of $S_2$. We study the problem of sketching the shift distance, which is the following communication complexity problem: Strings $S_1$ and $S_2$ of length $n$ are given to two identical players (encoders), who independently

更新日期：2020-06-25
• arXiv.cs.DS Pub Date : 2020-06-24
M. R. C. da Silva; L. L. C. Pedrosa; R. C. S. Schouery

In the MAXSPACE problem, given a set of ads A, one wants to schedule a subset A' of A into K slots B_1, ..., B_K of size L. Each ad A_i in A has a size s_i and a frequency w_i. A schedule is feasible if the total size of ads in any slot is at most L, and each ad A_i in A' appears in exactly w_i slots. The goal is to find a feasible schedule that maximizes the sum of the space occupied by all slots

更新日期：2020-06-25
• arXiv.cs.DS Pub Date : 2020-06-24
Dezhou Shen

With the rapid development of social network applications, social network has become an important medium for people to interact. For the minimum distance computation of all pairs in networks, Alon N[4] proposed an algorithm with matrix multiplication, combining with distance product association law and block matrix multiplication, all pairs shortest path length algorithm on networks has time bound

更新日期：2020-06-25
• arXiv.cs.DS Pub Date : 2020-06-23
Jerry Li; Guanghao Ye

Robust covariance estimation is the following, well-studied problem in high dimensional statistics: given $N$ samples from a $d$-dimensional Gaussian $\mathcal{N}(\boldsymbol{0}, \Sigma)$, but where an $\varepsilon$-fraction of the samples have been arbitrarily corrupted, output $\widehat{\Sigma}$ minimizing the total variation distance between $\mathcal{N}(\boldsymbol{0}, \Sigma)$ and $\mathcal{N}(\boldsymbol{0} 更新日期：2020-06-25 • arXiv.cs.DS Pub Date : 2020-06-23 Jurek Czyzowicz; Konstantinos Georgiou; Ryan Killick; Evangelos Kranakis; Danny Krizanc; Lata Narayanan; Jaroslav Opatrny; Denis Pankratov Assume that$m \geq 1$autonomous mobile agents and$0 \leq b \leq m$single-agent transportation devices (called {\em bikes}) are initially placed at the left endpoint$0$of the unit interval$[0,1]$. The agents are identical in capability and can move at speed one. The bikes cannot move on their own, but any agent riding bike$i$can move at speed$v_i > 1$. An agent may ride at most one bike at 更新日期：2020-06-25 • arXiv.cs.DS Pub Date : 2020-06-24 Yuko Kuroki; Atsushi Miyauchi; Junya Honda; Masashi Sugiyama Dense subgraph discovery aims to find a dense component in edge-weighted graphs. This is a fundamental graph-mining task with a variety of applications and thus has received much attention recently. Although most existing methods assume that each individual edge weight is easily obtained, such an assumption is not necessarily valid in practice. In this paper, we introduce a novel learning problem for 更新日期：2020-06-25 • arXiv.cs.DS Pub Date : 2020-06-24 Shweta Jain; C. Seshadhri Clique and near-clique counts are important graph properties with applications in graph generation, graph modeling, graph analytics, community detection among others. They are the archetypal examples of dense subgraphs. While there are several different definitions of near-cliques, most of them share the attribute that they are cliques that are missing a small number of edges. Clique counting is itself 更新日期：2020-06-25 • arXiv.cs.DS Pub Date : 2020-06-06 Jie Shen; Chicheng Zhang This paper is concerned with computationally efficient learning of homogeneous sparse halfspaces in$\Rd$under noise. Though recent works have established attribute-efficient learning algorithms under various types of label noise (e.g. bounded noise), it remains an open question of when and how$s$-sparse halfspaces can be efficiently learned under the challenging {\em malicious noise} model, where 更新日期：2020-06-25 • arXiv.cs.DS Pub Date : 2020-06-23 Hao Wu; Junhao Gan; Rui Zhang Inspired by the great success of machine learning in the past decade, people have been thinking about the possibility of improving the theoretical results by exploring data distribution. In this paper, we revisit a fundamental problem called Distributed Tracking (DT) under an assumption that the data follows a certain (known or unknown) distribution, and propose a number data-dependent algorithms with 更新日期：2020-06-24 • arXiv.cs.DS Pub Date : 2020-06-23 Xiaoyan Zhang; Donglei Du; Gregory Gutin; Qiaoxia Ming; Jian Sun Graph routing problems have been investigated extensively in operations research, computer science and engineering due to their ubiquity and vast applications. In this paper, we study constant approximation algorithms for some variations of the general cluster routing problem. In this problem, we are given an edge-weighted complete undirected graph$G=(V,E,c),\$ whose vertex set is partitioned into

更新日期：2020-06-24
• arXiv.cs.DS Pub Date : 2020-06-23
Andreas Emil Feldmann; David Saulpic

We study clustering problems such as k-Median, k-Means, and Facility Location in graphs of low highway dimension, which is a graph parameter modeling transportation networks. It was previously shown that approximation schemes for these problems exist, which either run in quasi-polynomial time (assuming constant highway dimension) [Feldmann et al. SICOMP 2018] or run in FPT time (parameterized by the

更新日期：2020-06-24
• arXiv.cs.DS Pub Date : 2020-06-23
Agniva Chowdhury; Petros Drineas; David P. Woodruff; Samson Zhou

We present three provably accurate, polynomial time, approximation algorithms for the Sparse Principal Component Analysis (SPCA) problem, without imposing any restrictive assumptions on the input covariance matrix. The first algorithm is based on randomized matrix multiplication; the second algorithm is based on a novel deterministic thresholding scheme; and the third algorithm is based on a semidefinite

更新日期：2020-06-24
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