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For distributed graph processing on massive graphs, a graph is partitioned into multiple equally-sized parts which are distributed among machines in a compute cluster. In the last decade, many partitioning algorithms have been developed…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-04-12 Nikolai Merkel , Ruben Mayer , Tawkir Ahmed Fakir , Hans-Arno Jacobsen

We present a rectangle-based segmentation algorithm that sets up a graph and performs a graph cut to separate an object from the background. However, graph-based algorithms distribute the graph's nodes uniformly and equidistantly on the…

Computer Vision and Pattern Recognition · Computer Science 2012-03-14 Jan Egger , Tina Kapur , Thomas Dukatz , Malgorzata Kolodziej , Dzenan Zukic , Bernd Freisleben , Christopher Nimsky

In this paper we give fast distributed graph algorithms for detecting and listing small subgraphs, and for computing or approximating the girth. Our algorithms improve upon the state of the art by polynomial factors, and for girth, we…

Data Structures and Algorithms · Computer Science 2021-01-20 Keren Censor-Hillel , Orr Fischer , Tzlil Gonen , François Le Gall , Dean Leitersdorf , Rotem Oshman

We consider the problem of finding a local optimum for Max-Cut with FLIP-neighborhood, in which exactly one node changes the partition. Schaeffer and Yannakakis (SICOMP, 1991) showed PLS-completeness of this problem on graphs with unbounded…

Computational Complexity · Computer Science 2011-06-27 Robert Elsaesser , Tobias Tscheuschner

The problem of computing the vertex expansion of a graph is an NP-hard problem. The current best worst-case approximation guarantees for computing the vertex expansion of a graph are a $O(\sqrt{\log n})$-approximation algorithm due to…

Data Structures and Algorithms · Computer Science 2018-05-25 Anand Louis , Rakesh Venkat

In the maximum directed cut problem, the input is a directed graph $G=(V,E)$, and the goal is to pick a partition $V = S \cup (V \setminus S)$ of the vertices such that as many edges as possible go from $S$ to $V\setminus S$. Oblivious…

Data Structures and Algorithms · Computer Science 2024-11-21 Samuel Hwang , Noah G. Singer , Santhoshini Velusamy

Given an edge-weighted graph $G$ on $n$ nodes, the NP-hard Max-Cut problem asks for a node bipartition such that the sum of edge weights joining the different partitions is maximized. We propose a fixed-parameter tractable algorithm…

Data Structures and Algorithms · Computer Science 2020-07-23 Markus Chimani , Christine Dahn , Martina Juhnke-Kubitzke , Nils M. Kriege , Petra Mutzel , Alexander Nover

The Max-Cut problem is known to be NP-hard on general graphs, while it can be solved in polynomial time on planar graphs. In this paper, we present a fixed-parameter tractable algorithm for the problem on `almost' planar graphs: Given an…

Data Structures and Algorithms · Computer Science 2019-05-27 Yasuaki Kobayashi , Yusuke Kobayashi , Shuichi Miyazaki , Suguru Tamaki

The distance of a graph from being triangle-free is a fundamental graph parameter, counting the number of edges that need to be removed from a graph in order for it to become triangle-free. Its corresponding computational problem is the…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-02-22 Keren Censor-Hillel , Majd Khoury

The message complexity of a distributed algorithm is the total number of messages sent by all nodes over the course of the algorithm. This paper studies the message complexity of distributed algorithms for fundamental graph optimization…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-11-28 Fabien Dufoulon , Shreyas Pai , Gopal Pandurangan , Sriram V. Pemmaraju , Peter Robinson

The problem of finding the longest simple cycle in a directed graph is NP-hard, with critical applications in computational biology, scheduling, and network analysis. Existing approaches include exact algorithms with exponential runtimes,…

Data Structures and Algorithms · Computer Science 2026-01-13 Ali Dasdan

We develop a general deterministic distributed method for locally rounding fractional solutions of graph problems for which the analysis can be broken down into analyzing pairs of vertices. Roughly speaking, the method can transform…

Data Structures and Algorithms · Computer Science 2022-09-26 Salwa Faour , Mohsen Ghaffari , Christoph Grunau , Fabian Kuhn , Václav Rozhoň

Given a graph $G=(V,E)$ with two distinguished vertices $s,t\in V$ and an integer parameter $L>0$, an {\em $L$-bounded cut} is a subset $F$ of edges (vertices) such that the every path between $s$ and $t$ in $G\setminus F$ has length more…

Data Structures and Algorithms · Computer Science 2017-09-11 Petr Kolman

We design an algorithm for approximating the size of \emph{Max Cut} in dense graphs. Given a proximity parameter $\varepsilon \in (0,1)$, our algorithm approximates the size of \emph{Max Cut} of a graph $G$ with $n$ vertices, within an…

Data Structures and Algorithms · Computer Science 2021-12-21 Arijit Ghosh , Gopinath Mishra , Rahul Raychaudhury , Sayantan Sen

We consider the distributed optimization problem for the sum of convex functions where the underlying communications network connecting agents at each time is drawn at random from a collection of directed graphs. Building on an earlier work…

Optimization and Control · Mathematics 2020-09-16 Pouya Rezaeinia , Bahman Gharesifard

We consider the problem of estimating the size of a maximum cut (Max-Cut problem) in a random Erd\H{o}s-R\'{e}nyi graph on $n$ nodes and $\lfloor cn \rfloor$ edges. It is shown in Coppersmith et al. ~\cite{Coppersmith2004} that the size of…

Probability · Mathematics 2017-02-14 David Gamarnik , Quan Li

We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…

Numerous approaches study the vulnerability of networks against social contagion. Graph burning studies how fast a contagion, modeled as a set of fires, spreads in a graph. The burning process takes place in synchronous, discrete rounds. In…

Combinatorics · Mathematics 2019-04-08 Anthony Bonato , Shahin Kamali

We study polynomial-time approximation algorithms for the Quantum Max-Cut (QMC) problem. Given an edge-weighted graph $G$ on n vertices, the QMC problem is to determine the largest eigenvalue of a particular $2^n \times 2^n$ matrix that…

Quantum Physics · Physics 2025-04-16 Sander Gribling , Lennart Sinjorgo , Renata Sotirov

In the Matching Cut problem we ask whether a graph $G$ has a matching cut, that is, a matching which is also an edge cut of $G$. We consider the variants Perfect Matching Cut and Disconnected Perfect Matching where we ask whether there…

Combinatorics · Mathematics 2025-01-16 Felicia Lucke