文献类型：期刊文献

英文题名：New approximation algorithms for the minimum cycle cover problem

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

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

年份：2019

卷号：793

起止页码：44

外文期刊名：THEORETICAL COMPUTER SCIENCE

收录：;EI(收录号：20192307001496);WOS:【SCI-EXPANDED(收录号:WOS:000491216500005)】；

基金：The authors are grateful to the anonymous referees for their valuable comments that greatly improve the presentation of this paper. This research is supported in part by the National Natural Science Foundation of China under grants numbers 11671135, 11701363 and the Fundamental Research Fund for the Central Universities under grant number 22220184028.

语种：英文

外文关键词：Vehicle routing; Cycle cover; Traveling Salesman Problem; Approximation algorithm

摘要：Given an undirected weighted graph G = (V, E) with nonnegative weight function obeying the triangle inequality, a set {C1, C2, ..., C-k} of cycles is called a cycle cover if V subset of boolean OR(k)(i=1) V(C-i) and its cost is given by the maximum weight of the cycles. The Minimum Cycle Cover Problem aims to find a cycle cover of cost at most lambda with the minimum number of cycles. An O(n(2)) 24/5-approximation algorithm and an O(n(5)) 14/3-approximation algorithm are given by Yu and Liu (Improved approximation algorithms for some min-max cycle cover problems. Theoretical Computer Science 654 (2016) 45-58). However, the original proofs for approximation ratios are incomplete. In this paper we first present a corrected simplified analysis on the 24/5-approximation algorithm. Based on the simplified approach of analysis and some new observations, we present a new 14/3-approximation algorithm that runs in O(n(3)) and give an improved 32/7-approximation algorithm that runs in O (n(5)). (C) 2019 Elsevier B.V. All rights reserved.