A polytime preprocess algorithm for the maximum independent set problem

IF 1.3 4区数学 Q2 MATHEMATICS, APPLIED

Optimization Letters Pub Date : 2023-11-24 DOI:10.1007/s11590-023-02076-8

Samuel Kroger, Hamidreza Validi, Illya V. Hicks

引用次数: 0

Abstract

The maximum independent set (MIS) seeks to find a subset of vertices with the maximum size such that no pair of its vertices are adjacent. This paper develops a recursive fixing procedure that generalizes the existing polytime algorithm to solve the maximum independent set problem on chordal graphs, which admit simplicial orderings. We prove that the generalized fixing procedure is safe; i.e., it does not remove all optimal solutions of the MIS problem from the solution space. Our computational results show that the proposed recursive fixing algorithm, along with the basic mixed integer programming (MIP) of the MIS, outperforms the pure MIP formulation of the problem. Our codes, data, and results are available on GitHub.

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最大独立集问题的多时间预处理算法

最大独立集(MIS)试图找到一个最大大小的顶点子集，使得它的顶点对不相邻。本文提出了一种递归固定方法，推广了现有的多时算法来求解简序弦图上的最大独立集问题。证明了广义固定过程是安全的;也就是说，它不会从解空间中移除MIS问题的所有最优解。我们的计算结果表明，所提出的递归固定算法，以及MIS的基本混合整数规划(MIP)，优于问题的纯MIP公式。我们的代码、数据和结果可以在GitHub上找到。

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

Optimization Letters 管理科学-应用数学

CiteScore

3.40

自引率

6.20%

发文量

116

审稿时长

9 months

期刊介绍： Optimization Letters is an international journal covering all aspects of optimization, including theory, algorithms, computational studies, and applications, and providing an outlet for rapid publication of short communications in the field. Originality, significance, quality and clarity are the essential criteria for choosing the material to be published. Optimization Letters has been expanding in all directions at an astonishing rate during the last few decades. New algorithmic and theoretical techniques have been developed, the diffusion into other disciplines has proceeded at a rapid pace, and our knowledge of all aspects of the field has grown even more profound. At the same time one of the most striking trends in optimization is the constantly increasing interdisciplinary nature of the field. Optimization Letters aims to communicate in a timely fashion all recent developments in optimization with concise short articles (limited to a total of ten journal pages). Such concise articles will be easily accessible by readers working in any aspects of optimization and wish to be informed of recent developments.