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Despite there being significant work on developing spectral, and metric embedding based approximation algorithms for hypergraph generalizations of conductance, little is known regarding the approximability of hypergraph partitioning…

Data Structures and Algorithms · Computer Science 2023-07-27 Antares Chen , Lorenzo Orecchia , Erasmo Tani

Max-k-Cut and correlation clustering are fundamental graph partitioning problems. For a graph with G=(V,E) with n vertices, the methods with the best approximation guarantees for Max-k-Cut and the Max-Agree variant of correlation clustering…

Optimization and Control · Mathematics 2021-10-28 Nimita Shinde , Vishnu Narayanan , James Saunderson

We address the problem of enumerating all maximal clique-partitions of an undirected graph and present an algorithm based on the observation that every maximal clique-partition can be produced from the maximal clique-cover of the graph by…

Discrete Mathematics · Computer Science 2023-09-26 Mircea Marin , Temur Kutsia , Cleo Pau , Mikheil Rukhaia

Motivated by the increasing need to understand the algorithmic foundations of distributed large-scale graph computations, we study a number of fundamental graph problems in a message-passing model for distributed computing where $k \geq 2$…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-07-07 Gopal Pandurangan , Peter Robinson , Michele Scquizzato

Understanding spatial correlation is vital in many fields including epidemiology and social science. Lee, Meeks and Pettersson (Stat. Comput. 2021) recently demonstrated that improved inference for areal unit count data can be achieved by…

Data Structures and Algorithms · Computer Science 2026-02-10 Jessica Enright , Duncan Lee , Kitty Meeks , William Pettersson , John Sylvester

We present a factor $14D^2$ approximation algorithm for the minimum linear arrangement problem on series-parallel graphs, where $D$ is the maximum degree in the graph. Given a suitable decomposition of the graph, our algorithm runs in time…

Discrete Mathematics · Computer Science 2014-10-17 Martina Eikel , Christian Scheideler , Alexander Setzer

Although NP-Complete problems are the most difficult decisional problems, it is possible to discover in them polynomial (or easy) observables. We study the Graph Partitioning Problem showing that it is possible to recognize in it two…

Condensed Matter · Physics 2009-11-07 M. A. Marchisio

Large-scale parallel numerical simulations are essential for a wide range of engineering problems that involve complex, coupled physical processes interacting across a broad range of spatial and temporal scales. The data structures involved…

Mathematical Software · Computer Science 2018-10-11 Fande Kong , Roy H. Stogner , Derek R. Gaston , John W. Peterson , Cody J. Permann , Andrew E. Slaughter , Richard C. Martineau

We study a broad class of graph partitioning problems, where each problem is specified by a graph $G=(V,E)$, and parameters $k$ and $p$. We seek a subset $U\subseteq V$ of size $k$, such that $\alpha_1m_1 + \alpha_2m_2$ is at most (or at…

Data Structures and Algorithms · Computer Science 2014-03-04 Hadas Shachnai , Meirav Zehavi

We define a distance metric between partitions of a graph using machinery from optimal transport. Our metric is built from a linear assignment problem that matches partition components, with assignment cost proportional to transport…

Optimization and Control · Mathematics 2019-10-23 Tara Abrishami , Nestor Guillen , Parker Rule , Zachary Schutzman , Justin Solomon , Thomas Weighill , Si Wu

We introduce the partition function of edge-colored graph homomorphisms, of which the usual partition function of graph homomorphisms is a specialization, and present an efficient algorithm to approximate it in a certain domain. Corollaries…

Combinatorics · Mathematics 2015-05-05 Alexander Barvinok , Pablo Soberón

The graph partitioning problem is widely used and studied in many practical and theoretical applications. The multilevel strategies represent today one of the most effective and efficient generic frameworks for solving this problem on…

Data Structures and Algorithms · Computer Science 2012-04-04 Ilya Safro , Peter Sanders , Christian Schulz

In the number partitioning problem (NPP) one aims to partition a given set of $N$ real numbers into two subsets with approximately equal sum. The NPP is a well-studied optimization problem and is famous for possessing a…

Statistics Theory · Mathematics 2025-05-28 Rushil Mallarapu , Mark Sellke

Graph partitioning (GP) and vertex connectivity have traditionally been two distinct fields of study. This paper introduces the highly connected graph partitioning (HCGP) problem, which partitions a graph into compact, size balanced, and…

Discrete Mathematics · Computer Science 2024-06-13 Rahul Swamy , Douglas M. King , Sheldon H. Jacobson

Graphs may be used to represent many different problem domains -- a concrete example is that of detecting communities in social networks, which are represented as graphs. With big data and more sophisticated applications becoming widespread…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-04-03 Miguel E. Coimbra , Alexandre P. Francisco , Luis Veiga

In the recent years we have witnessed a rapid development of new algorithmic techniques for parameterized algorithms for graph separation problems. We present experimental evaluation of two cornerstone theoretical results in this area:…

Data Structures and Algorithms · Computer Science 2018-11-20 Marcin Pilipczuk , Michał Ziobro

Quantum optimization algorithms are inherently probabilistic, yet they are most often used to search for a single high-quality solution. In this paper, we instead study hypergraph partitioning problems in which the desired output is itself…

Quantum Physics · Physics 2026-05-12 Cameron Ibrahim , Bao G. Bach , Jad Salem , Reuben Tate , Kien X. Nguyen , Stephan Eidenbenz , Ilya Safro

Spectral graph bisections are a popular heuristic aimed at approximating the solution of the NP-complete graph bisection problem. This technique, however, does not always provide a robust tool for graph partitioning. Using a special class…

Numerical Analysis · Mathematics 2015-12-22 John C. Urschel , Ludmil T. Zikatanov

Graphical models represent multivariate and generally not normalized probability distributions. Computing the normalization factor, called the partition function, is the main inference challenge relevant to multiple statistical and…

Machine Learning · Computer Science 2020-09-01 Michael Chertkov , Vladimir Chernyak , Yury Maximov

Graph embedding aims at learning a vector-based representation of vertices that incorporates the structure of the graph. This representation then enables inference of graph properties. Existing graph embedding techniques, however, do not…