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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

In this paper, we introduce a novel model for random hypergraphs based on weighted random connection models. In accordance with the standard theory for hypergraphs, this model is constructed from a bipartite graph. In our stochastic model,…

Probability · Mathematics 2025-10-01 Morten Brun , Christian Hirsch , Peter Juhasz , Moritz Otto

We present deterministic distributed algorithms for computing approximate maximum cardinality matchings and approximate maximum weight matchings. Our algorithm for the unweighted case computes a matching whose size is at least $(1-\eps)$…

Distributed, Parallel, and Cluster Computing · Computer Science 2014-11-12 Guy Even , Moti Medina , Dana Ron

The mincut graph bisection problem involves partitioning the n vertices of a graph into disjoint subsets, each containing exactly n/2 vertices, while minimizing the number of "cut" edges with an endpoint in each subset. When considered over…

Statistical Mechanics · Physics 2010-04-27 Allon G. Percus , Gabriel Istrate , Bruno Goncalves , Robert Z. Sumi , Stefan Boettcher

We analyse the scaling limit of the sizes of the largest components of the Random Intersection Graph $G(n,m,p)$ close to the critical point $p=\frac{1}{\sqrt{nm}}$, when the numbers $n$ of individuals and $m$ of communities have different…

Probability · Mathematics 2019-10-30 Lorenzo Federico

The Max-Cut problem is a well known combinatorial optimization problem. In this paper we describe a fast approximation method. Given a graph G, we want to find a cut whose size is maximal among all possible cuts. A cut is a partition of the…

Analysis of PDEs · Mathematics 2019-07-11 Blaine Keetch , Yves van Gennip

We investigate the problem of sequentially predicting the binary labels on the nodes of an arbitrary weighted graph. We show that, under a suitable parametrization of the problem, the optimal number of prediction mistakes can be…

Machine Learning · Computer Science 2012-12-27 Nicolo' Cesa-Bianchi , Claudio Gentile , Fabio Vitale , Giovanni Zappella

A mixed dominating set of a graph $G = (V, E)$ is a mixed set $D$ of vertices and edges, such that for every edge or vertex, if it is not in $D$, then it is adjacent or incident to at least one vertex or edge in $D$. The mixed domination…

Data Structures and Algorithms · Computer Science 2019-06-27 Mingyu Xiao

We present a polynomial-time $(\alpha_{GW} + \varepsilon)$-approximation algorithm for the Maximum Cut problem on interval graphs and split graphs, where $\alpha_{GW} \approx 0.878$ is the approximation guarantee of the Goemans-Williamson…

Data Structures and Algorithms · Computer Science 2025-07-15 Jungho Ahn , Ian DeHaan , Eun Jung Kim , Euiwoong Lee

We study the maximum weight perfect $f$-factor problem on any general simple graph $G=(V,E,w)$ with positive integral edge weights $w$, and $n=|V|$, $m=|E|$. When we have a function $f:V\rightarrow \mathbb{N}_+$ on vertices, a perfect…

Data Structures and Algorithms · Computer Science 2020-03-18 Ran Duan , Haoqing He , Tianyi Zhang

We describe a new approximation algorithm for Max Cut. Our algorithm runs in $\tilde O(n^2)$ time, where $n$ is the number of vertices, and achieves an approximation ratio of $.531$. On instances in which an optimal solution cuts a…

Data Structures and Algorithms · Computer Science 2008-12-08 Luca Trevisan

We propose improved exact and heuristic algorithms for solving the maximum weight clique problem, a well-known problem in graph theory with many applications. Our algorithms interleave successful techniques from related work with novel data…

Data Structures and Algorithms · Computer Science 2023-02-02 Roman Erhardt , Kathrin Hanauer , Nils Kriege , Christian Schulz , Darren Strash

We consider the problem of query-efficient global max-cut on a weighted undirected graph in the value oracle model examined by [RSW18]. Graph algorithms in this cut query model and other query models have recently been studied for various…

Data Structures and Algorithms · Computer Science 2024-04-24 Orestis Plevrakis , Seyoon Ragavan , S. Matthew Weinberg

We propose a random bipartite graph with weights assigned to both parts of the vertex sets. Edges are formed independently with probabilities that depend on these weights. This bipartite graph naturally gives rise to a random intersection…

Probability · Mathematics 2025-06-10 Alastair Haig , Minmin Wang

We prove essentially tight lower bounds, conditionally to the Exponential Time Hypothesis, for two fundamental but seemingly very different cutting problems on surface-embedded graphs: the Shortest Cut Graph problem and the Multiway Cut…

Computational Complexity · Computer Science 2021-02-18 Vincent Cohen-Addad , Éric Colin de Verdière , Daniel Marx , Arnaud de Mesmay

In this paper, we study two examples of minimum weight random graphs with edge constraints. First we consider the complete graph on ${n}$ vertices equipped with uniformly heavy edge weights and use iteration methods to obtain deviation…

Probability · Mathematics 2023-01-13 Ghurumuruhan Ganesan

A {\em local graph partitioning algorithm} finds a set of vertices with small conductance (i.e. a sparse cut) by adaptively exploring part of a large graph $G$, starting from a specified vertex. For the algorithm to be local, its complexity…

Data Structures and Algorithms · Computer Science 2008-11-25 Reid Andersen , Yuval Peres

In this paper we study maximum size and minimum weight planar matchings of inhomogenous random bipartite graphs. Our motivation for this study comes from efficient usage of cross edges in relay networks for overall improvement in network…

Probability · Mathematics 2025-04-10 Ghurumuruhan Ganesan

We study the asymptotic growth rate of the label size of high-degree vertices in weighted recursive graphs (WRG) when the weights are i.i.d. almost surely bounded random variables, and as a result confirm a conjecture by Lodewijks and…

Probability · Mathematics 2026-01-14 Bas Lodewijks

We study the problem of edge partitioning, where the goal is to partition the edge set of a graph into several parts. The replication factor of a vertex $v$ is the number of parts that contain edges incident to $v$. The goal is to minimize…

Discrete Mathematics · Computer Science 2026-05-08 Alexander Yakunin , Andrey Kupavskii , Alexander Sushin , Stanislav Moiseev