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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…

Data Structures and Algorithms · Computer Science 2020-06-24 Xiaoyan Zhang , Donglei Du , Gregory Gutin , Qiaoxia Ming , Jian Sun

Partitioning the vertices of a graph into two roughly equal parts while minimizing the number of edges crossing the cut is a fundamental problem (called Balanced Separator) that arises in many settings. For this problem, and variants such…

Computational Complexity · Computer Science 2015-03-20 Venkatesan Guruswami , Ali Kemal Sinop , Yuan Zhou

We study a planted clique model introduced by Feige where a complete graph of size $c\cdot n$ is planted uniformly at random in an arbitrary $n$-vertex graph. We give a simple deterministic algorithm that, in almost linear time, recovers a…

Computational Complexity · Computer Science 2025-05-13 Francesco Agrimonti , Marco Bressan , Tommaso d'Orsi

We study the k-route cut problem: given an undirected edge-weighted graph G=(V,E), a collection {(s_1,t_1),(s_2,t_2),...,(s_r,t_r)} of source-sink pairs, and an integer connectivity requirement k, the goal is to find a minimum-weight subset…

Data Structures and Algorithms · Computer Science 2015-03-19 Julia Chuzhoy , Yury Makarychev , Aravindan Vijayaraghavan , Yuan Zhou

In this work we study statistical properties of graph-based clustering algorithms that rely on the optimization of balanced graph cuts, the main example being the optimization of Cheeger cuts. We consider proximity graphs built from data…

Spectral Theory · Mathematics 2022-03-14 Nicolas Garcia Trillos , Ryan Murray , Matthew Thorpe

Given a source of iid samples of edges of an input graph $G$ with $n$ vertices and $m$ edges, how many samples does one need to compute a constant factor approximation to the maximum matching size in $G$? Moreover, is it possible to obtain…

Data Structures and Algorithms · Computer Science 2019-07-15 Michael Kapralov , Slobodan Mitrović , Ashkan Norouzi-Fard , Jakab Tardos

We consider the problem of sampling an edge almost uniformly from an unknown graph, $G = (V, E)$. Access to the graph is provided via queries of the following types: (1) uniform vertex queries, (2) degree queries, and (3) neighbor queries.…

Computational Complexity · Computer Science 2017-06-30 Talya Eden , Will Rosenbaum

An NP-hard problem is considered of intersecting a given set of $n$ straight line segments on the plane with the smallest cardinality set of disks of fixed radii $r>0,$ where the set of segments forms a straight line drawing $G=(V,E)$ of a…

Computational Geometry · Computer Science 2020-10-05 Konstantin Kobylkin

We study the Ordered k-Median problem, in which the solution is evaluated by first sorting the client connection costs and then multiplying them with a predefined non-increasing weight vector (higher connection costs are taken with larger…

Data Structures and Algorithms · Computer Science 2018-03-01 Jarosław Byrka , Krzysztof Sornat , Joachim Spoerhase

This paper initiates the study of the classic balanced graph partitioning problem from an online perspective: Given an arbitrary sequence of pairwise communication requests between $n$ nodes, with patterns that may change over time, the…

Data Structures and Algorithms · Computer Science 2020-05-15 Chen Avin , Marcin Bienkowski , Andreas Loukas , Maciej Pacut , Stefan Schmid

We design new polynomial-time algorithms for recovering planted cliques in the semi-random graph model introduced by Feige and Kilian 2001. The previous best algorithms for this model succeed if the planted clique has size at least…

Data Structures and Algorithms · Computer Science 2023-06-07 Rares-Darius Buhai , Pravesh K. Kothari , David Steurer

We give the first constant-factor approximation algorithm for quasi-bipartite instances of Directed Steiner Tree on graphs that exclude fixed minors. In particular, for $K_r$-minor-free graphs our approximation guarantee is…

Data Structures and Algorithms · Computer Science 2022-11-08 Zachary Friggstad , Ramin Mousavi

The Correlation Clustering problem is one of the most extensively studied clustering formulations due to its wide applications in machine learning, data mining, computational biology and other areas. We consider the Correlation Clustering…

Data Structures and Algorithms · Computer Science 2025-03-04 Jianqi Zhou , Zhongyi Zhang , Jiong Guo

Suppose you are given a graph $G=(V,E)$ with a weight assignment $w:V\rightarrow\mathbb{Z}$ and that your objective is to modify $w$ using legal steps such that all vertices will have the same weight, where in each legal step you are…

Discrete Mathematics · Computer Science 2015-07-03 Friedrich Eisenbrand , Shay Moran , Rom Pinchasi , Martin Skutella

This paper deals with the problem of graph matching or network alignment for Erd\H{o}s--R\'enyi graphs, which can be viewed as a noisy average-case version of the graph isomorphism problem. Let $G$ and $G'$ be $G(n, p)$ Erd\H{o}s--R\'enyi…

Statistics Theory · Mathematics 2022-07-08 Cheng Mao , Mark Rudelson , Konstantin Tikhomirov

We describe a new sampling-based method to determine cuts in an undirected graph. For a graph (V, E), its cycle space is the family of all subsets of E that have even degree at each vertex. We prove that with high probability, sampling the…

Distributed, Parallel, and Cluster Computing · Computer Science 2010-07-22 David Pritchard , Ramakrishna Thurimella

We devise a constant-factor approximation algorithm for the maximization version of the edge-disjoint paths problem if the supply graph together with the demand edges form a planar graph. By planar duality this is equivalent to packing cuts…

Data Structures and Algorithms · Computer Science 2021-12-14 Chien-Chung Huang , Mathieu Mari , Claire Mathieu , Kevin Schewior , Jens Vygen

In this paper, we present a simple factor 6 algorithm for approximating the optimal multiplicative distortion of embedding a graph metric into a tree metric (thus improving and simplifying the factor 100 and 27 algorithms of B\v{a}doiu,…

Metric Geometry · Mathematics 2015-03-17 Victor Chepoi , Feodor Dragan , Ilan Newman , Yuri Rabinovich , Yann Vaxes

We study the problem of graph clustering under a broad class of objectives in which the quality of a cluster is defined based on the ratio between the number of edges in the cluster, and the total weight of vertices in the cluster. We show…

Data Structures and Algorithms · Computer Science 2023-01-02 Jakub Łącki , Vahab Mirrokni , Christian Sohler

This paper describes a graph clustering algorithm that aims to minimize the normalized cut criterion and has a model order selection procedure. The performance of the proposed algorithm is comparable to spectral approaches in terms of…

Artificial Intelligence · Computer Science 2011-05-06 Seyed Salim Tabatabaei , Mark Coates , Michael Rabbat