On cut polytopes and graph minors

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Discrete Optimization Pub Date : 2023-10-10 DOI:10.1016/j.disopt.2023.100807

Konstantinos Kaparis , Adam N. Letchford , Ioannis Mourtos

引用次数: 0

Abstract

The max-cut problem is a fundamental and much-studied $NP$ -hard combinatorial optimisation problem, with a wide range of applications. Several authors have shown that the max-cut problem can be solved in polynomial time if the underlying graph is free of certain minors. We give a polyhedral counterpart of these results. In particular, we show that, if a family of valid inequalities for the cut polytope satisfies certain conditions, then there is an associated minor-closed family of graphs on which the max-cut problem can be solved efficiently.

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论切多面体和图的次形

最大割问题是一个基本的、研究较多的NP难组合优化问题，具有广泛的应用。几位作者已经证明，如果底层图没有某些子图，则最大割问题可以在多项式时间内求解。我们给出了这些结果的多面体对应。特别地，我们证明了，如果割多面体的一个有效不等式族满足某些条件，则存在一个相关的小闭图族，在该图族上可以有效地求解最大割问题。

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 Optimization 管理科学-应用数学

CiteScore

2.10

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： Discrete Optimization publishes research papers on the mathematical, computational and applied aspects of all areas of integer programming and combinatorial optimization. In addition to reports on mathematical results pertinent to discrete optimization, the journal welcomes submissions on algorithmic developments, computational experiments, and novel applications (in particular, large-scale and real-time applications). The journal also publishes clearly labelled surveys, reviews, short notes, and open problems. Manuscripts submitted for possible publication to Discrete Optimization should report on original research, should not have been previously published, and should not be under consideration for publication by any other journal.