A polyhedral study of the maximum-impact coloring problem on hypergraphs

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2025-06-12 DOI:10.1016/j.dam.2025.05.042

Jessica Singer , Javier Marenco

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引用次数: 0

Abstract

Given a graph

G = (V, E)

and a hypergraph

H = (V, F)

over the same set of vertices, and a finite color set

C

, the maximum-impact coloring problem on hypergraphs asks for a

C

-coloring of

G

maximizing the number of hyperedges of

H

whose vertices are assigned the same color. This problem arises in the context of classroom assignment to courses, in which we need to assign a classroom to each lecture and we wish to assign the same classroom to all lectures from the same course. Since imposing this last concern as a constraint may be too restrictive, we seek to maximize the number of courses such that all of its lectures are assigned to the same classroom. In this work we present an integer programming formulation for this NP-hard problem and we explore the associated polytope. We present three families of facet-inducing inequalities, and we report computational experiments suggesting that the dynamic addition of these inequalities within a branch and cut environment may be effective in practice.

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超图上最大冲击着色问题的多面体研究

给定一个图G=（V，E）和一个超图H=（V，F）在相同的顶点集上，以及一个有限的颜色集C上，超图上的最大影响着色问题要求对G进行C着色，使顶点被赋予相同颜色的H的超边的数量最大化。这个问题出现在课堂分配课程的背景下，我们需要为每个讲座分配一个教室，我们希望为同一课程的所有讲座分配同一个教室。由于将最后一个问题作为约束施加可能过于严格，因此我们寻求最大限度地增加课程数量，以便将所有课程分配到同一个教室。在这项工作中，我们提出了一个np困难问题的整数规划公式，并探讨了相关的多面体。我们提出了三类面诱导不等式，并报告了计算实验，表明在分支和切割环境中动态添加这些不等式在实践中可能是有效的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

9.10%

发文量

422

审稿时长

4.5 months

期刊介绍： The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal. Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.