区间图和和弦图上最大独立集最小度贪婪算法的近似率

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2024-09-20 DOI:10.1016/j.dam.2024.09.009

Steven Chaplick, Martin Frohn, Steven Kelk, Johann Lottermoser, Matúš Mihalák

引用次数: 0

摘要

在这篇文章中，我们证明了最小度贪婪算法与对抗性平局打破是区间图上最大独立集问题的 (2/3)- 近似。我们证明，即使在最大度数为 3 的单位区间图上，这一算法也是严密的。我们还证明，在和弦图上，贪婪算法是 (1/2)- 近似算法，而且这一算法也是严密的。这些结果与已知的贪婪算法对最大度数为 Δ 的一般图的 3Δ+2 的（紧密）近似率形成了鲜明对比。

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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Approximation ratio of the min-degree greedy algorithm for Maximum Independent Set on interval and chordal graphs

In this article we prove that the minimum-degree greedy algorithm, with adversarial tie-breaking, is a $(2 / 3)$ -approximation for the Maximum Independent Set problem on interval graphs. We show that this is tight, even on unit interval graphs of maximum degree 3. We show that on chordal graphs, the greedy algorithm is a $(1 / 2)$ -approximation and that this is again tight. These results contrast with the known (tight) approximation ratio of $\frac{3}{Δ + 2}$ of the greedy algorithm for general graphs of maximum degree $Δ$ .

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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.