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Mining dense subgraphs where vertices connect closely with each other is a common task when analyzing graphs. A very popular notion in subgraph analysis is core decomposition. Recently, Esfahani et al. presented a probabilistic core…

Machine Learning · Statistics 2023-03-29 Yang Guo , Xuekui Zhang , Fatemeh Esfahani , Venkatesh Srinivasan , Alex Thomo , Li Xing

In this paper, we present an approximation of the matching coverage on large bipartite graphs, for {\em local} online matching algorithms based on the sole knowledge of the remaining degree of the nodes of the graph at hand. This…

Probability · Mathematics 2021-05-11 Mohamed Habib Aliou Diallo Aoudi , Pascal Moyal , Vincent Robin

We study frequency allocation in wireless networks. A wireless network is modeled by an undirected graph, with vertices corresponding to cells. In each vertex we have a certain number of requests, and each of those requests must be assigned…

Data Structures and Algorithms · Computer Science 2011-02-17 Marek Chrobak , Łukasz Jeż , Jiří Sgall

Estimating the number of triangles in a graph is one of the most fundamental problems in sublinear algorithms. In this work, we provide an algorithm that approximately counts the number of triangles in a graph using only polylogarithmic…

Data Structures and Algorithms · Computer Science 2020-08-04 Anup Bhattacharya , Arijit Bishnu , Arijit Ghosh , Gopinath Mishra

We consider the problem of approximating partition functions for Ising models. We make use of recent tools in combinatorial optimization: the Sherali-Adams and Lasserre convex programming hierarchies, in combination with variational methods…

Machine Learning · Computer Science 2016-07-13 Andrej Risteski

We study the algorithmic problem of finding large $\gamma$-balanced independent sets in dense random bipartite graphs; an independent set is $\gamma$-balanced if a $\gamma$ proportion of its vertices lie on one side of the bipartition. In…

Data Structures and Algorithms · Computer Science 2025-09-12 Abhishek Dhawan , Eren C. Kızıldağ , Neeladri Maitra

We study the statistical complexity of estimating partition functions given sample access to a proposal distribution and an unnormalized density ratio for a target distribution. While partition function estimation is a classical problem,…

Machine Learning · Statistics 2026-03-02 Adam Block , Abhishek Shetty

We study the problem of constructing explicit sparse graphs that exhibit strong vertex expansion. Our main result is the first two-sided construction of imbalanced unique-neighbor expanders, meaning bipartite graphs where small sets…

Combinatorics · Mathematics 2024-01-17 Jun-Ting Hsieh , Theo McKenzie , Sidhanth Mohanty , Pedro Paredes

Fair graph partition of social networks is a crucial step toward ensuring fair and non-discriminatory treatments in unsupervised user analysis. Current fair partition methods typically consider node balance, a notion pursuing a…

Social and Information Networks · Computer Science 2023-07-18 Tingwei Liu , Peizhao Li , Hongfu Liu

In this note, we describe a $\alpha_{GW} + \tilde{\Omega}(1/d^2)$-factor approximation algorithm for Max-Cut on weighted graphs of degree $\leq d$. Here, $\alpha_{GW}\approx 0.878$ is the worst-case approximation ratio of the…

Data Structures and Algorithms · Computer Science 2022-06-23 Jun-Ting Hsieh , Pravesh K. Kothari

In this paper, we propose and study a new semi-random model for graph partitioning problems. We believe that it captures many properties of real--world instances. The model is more flexible than the semi-random model of Feige and Kilian and…

Data Structures and Algorithms · Computer Science 2015-03-20 Konstantin Makarychev , Yury Makarychev , Aravindan Vijayaraghavan

We consider the following basic problem: given an $n$-variate degree-$d$ homogeneous polynomial $f$ with real coefficients, compute a unit vector $x \in \mathbb{R}^n$ that maximizes $|f(x)|$. Besides its fundamental nature, this problem…

Data Structures and Algorithms · Computer Science 2017-04-25 Vijay Bhattiprolu , Mrinalkanti Ghosh , Venkatesan Guruswami , Euiwoong Lee , Madhur Tulsiani

Absence of (complex) zeros property is at the heart of the interpolation method developed by Barvinok \cite{barvinok2017combinatorics} for designing deterministic approximation algorithms for various graph counting and computing partition…

Probability · Mathematics 2020-12-02 David Gamarnik

We study the set of all decompositions (clusterings) of a graph through its characterization as a set of lifted multicuts. This leads us to practically relevant insights related to the definition of a class of decompositions by must-join…

Discrete Mathematics · Computer Science 2017-06-09 Andrea Horňáková , Jan-Hendrik Lange , Bjoern Andres

This work is concerned with the prime factor decomposition (PFD) of strong product graphs. A new quasi-linear time algorithm for the PFD with respect to the strong product for arbitrary, finite, connected, undirected graphs is derived.…

Discrete Mathematics · Computer Science 2017-05-11 Marc Hellmuth

A remarkable connection has been established for antiferromagnetic 2-spin systems, including the Ising and hard-core models, showing that the computational complexity of approximating the partition function for graphs with maximum degree D…

Computational Complexity · Computer Science 2014-11-05 Andreas Galanis , Daniel Stefankovic , Eric Vigoda

The benefits of a recently proposed method to approximate hard optimization problems are demonstrated on the graph partitioning problem. The performance of this new method, called Extremal Optimization, is compared to Simulated Annealing in…

Statistical Mechanics · Physics 2009-10-31 S. Boettcher

We prove that the maximal graph-density of an independent set in a Penrose P3 tiling considered as a planar non-directed graph is equal to $(57 - 25 \sqrt{5})/2 \approx 0.54915$ despite the fact that the graph is bipartite. Accordingly, the…

Mathematical Physics · Physics 2026-04-24 A. Mazel , I. Stuhl , Y. Suhov

Processing large complex networks like social networks or web graphs has recently attracted considerable interest. In order to do this in parallel, we need to partition them into pieces of about equal size. Unfortunately, previous parallel…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-01-27 Henning Meyerhenke , Peter Sanders , Christian Schulz

In this work, we study the problem of partitioning a set of graphs into different groups such that the graphs in the same group are similar while the graphs in different groups are dissimilar. This problem was rarely studied previously,…

Machine Learning · Computer Science 2023-02-07 Jinyu Cai , Yi Han , Wenzhong Guo , Jicong Fan