Approximating Graphic Min-Max and Minimum Cycle/Path/Tree Cover Problems

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2025-05-10 DOI:10.1016/j.dam.2025.05.002

Wei Yu, Zhaohui Liu

引用次数: 0

Abstract

In this work we consider the Graphic Min-Max Cycle/Path/Tree Cover Problem and the Graphic Minimum Cycle/Path/Tree Cover Problem, some of which generalize the famous Graphic TSP. For all six problems, we obtain approximation algorithms with better ratios than the corresponding problems defined on general metrics. For the Graphic Minimum Path Cover Problem, we even show a best possible approximation ratio of 2, assuming

P \neq N P

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逼近图形最小最大值和最小周期/路径/树木覆盖问题

在这项工作中，我们考虑了图形最小-最大周期/路径/树覆盖问题和图形最小周期/路径/树覆盖问题，其中一些问题推广了著名的图形TSP。对于这六个问题，我们得到了比在一般度量上定义的相应问题具有更好比率的近似算法。对于图形最小路径覆盖问题，我们甚至给出了假设P≠NP的最佳可能近似比为2。

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.