文献类型：期刊文献

英文题名：Approximation algorithms for some min-max postmen cover problems

作者：Yu, Wei[1];Liu, Zhaohui[1];Bao, Xiaoguang[2]

机构：[1]East China Univ Sci & Technol, Dept Math, 130 Meilong Rd, Shanghai 200237, Peoples R China;[2]Shanghai Ocean Univ, Coll Informat Technol, 999 Huchenghuan Rd, Shanghai 201306, Peoples R China

年份：2021

卷号：300

期号：1

起止页码：267

外文期刊名：ANNALS OF OPERATIONS RESEARCH

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000625747900002)】；

基金：We would like to thank the anonymous reviewers for their valuable suggestions and insightful comments that help us to significantly improve the paper. This research is supported by the National Natural Science Foundation of China under Grant Numbers 11671135, 11871213, 11701363, the Natural Science Foundation of Shanghai under Grant Number 19ZR1411800 and the Fundamental Research Fund for the Central Universities under Grant Number 22220184028.

语种：英文

外文关键词：Approximation algorithm; Traveling salesman problem; Rural postman problem; Chinese postman problem; Postmen cover

摘要：We investigate two min-max k-postmen cover problems. The first is the Min-Max Rural Postmen Cover Problem (RPC), in which we are given an undirected weighted graph and the objective is to find at most k closed walks, covering a required subset of edges, to minimize the weight of the maximum weight closed walk. The other is called the Min-Max Chinese Postmen Cover Problem, in which the goal is to find at most k closed walks, covering all the edges of an undirected weighted graph, to minimize the weight of the maximum weight closed walk. For both problems we propose the first constant-factor approximation algorithms with ratios 10 and 4, respectively. For the Metric RPC, a special case of the RPC with the edge weights obeying the triangle inequality, we obtain an improved 6-approximation algorithm by a matching-based approach. For the Min-Max Rural Postmen Walk Cover Problem (RPWC), a variant of the RPC with the closed walks replaced by (open) walks, we give a 5-approximation algorithm that improves on the previous 7-approximation algorithm. If k is fixed, we devise improved approximation algorithms for the Metric RPC and the RPWC with ratios 4+epsilon and 3+epsilon, respectively, where epsilon>0 is an arbitrary small constant. The latter result improves on the existing (4+epsilon)-approximation algorithm. Moreover, we develop a (3+epsilon)-approximation algorithm for a special case of the RPC with fixed k, improving on the previous (4+epsilon)-approximation algorithm.