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Operations Research Transactions >

2021 , Vol. 25 >Issue 1: 107 - 113

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2021.01.010

Approximation algorithm for min-max cycle cover problem on a mixed graph

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  • 1. College of Information Technology, Shanghai Ocean University, Shanghai 201306, China
    2. Shanghai University of Electric Power, Shanghai 200090, China
    3. School of Science, East China University of Science and Technology, Shanghai 200237, China

Received date: 2020-01-02

  Online published: 2021-03-05

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Abstract

We consider a min-max cycle cover problem, in which we are given a positive integer k and a mixed weighted graph G=(V, E, A) with vertex set V, edge set E and arc set A. Each edge in E and each arc in A is associated a weight, respectively. The problem is to determine k tours such that the k tours pass through all the arcs in A. The objective is to minimize the weight of the maximum weight tour. The problem is an important combinatorial optimization problem in operations research and computer science. This problem and its variants are widely used in related industries such as express delivery, trash collection, snow removal, etc. For the problem, we propose the first constant-factor approximation algorithm with ratio 37/5 by using binary search and tour splitting techniques.

Key words： approximation algorithm; mixed graph; min-max; cycle cover; rural postman problem; Chinese postman problem; traveling salesman problem

Cite this article

Xiaoguang BAO, Chao LU, Dongmei HUANG, Wei YU . Approximation algorithm for min-max cycle cover problem on a mixed graph[J]. Operations Research Transactions, 2021 , 25(1) : 107 -113 . DOI: 10.15960/j.cnki.issn.1007-6093.2021.01.010

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