文献类型：期刊文献

英文题名：New LP relaxations for Minimum Cycle/Path/Tree Cover Problems

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：2020

卷号：803

起止页码：71

外文期刊名：THEORETICAL COMPUTER SCIENCE

收录：;EI(收录号：20193007220331);WOS:【SCI-EXPANDED(收录号:WOS:000510312300007)】；

基金：The authors are grateful to the anonymous referees for their valuable and constructive comments. This research is supported 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; Path cover; Approximation algorithm; Integrality gap

摘要：Given an undirected complete graph G = (V, E) with nonnegative edge weight function obeying. the triangle inequality, a set (C-1, C-2, C-k} of cycles is called a cycle cover if V subset of boolean OR(k)(i=1) V(C-i), where V(C-i) represents the set of vertices in C-i, and its cost is given by the maximum weight of the cycles. The Minimum Cycle Cover Problem (MCCP) aims to find a cycle cover of cost at most lambda with the minimum number of cycles. We propose new LP relaxations for MCCP as well as its variants, called the Minimum Path Cover Problem (MPCP) and the Minimum Tree Cover Problem, where the cycles are replaced by paths or trees. Moreover, we give new LP relaxations for a special case of the rooted version of MCCP/MPCP. We show that these LP relaxations have significantly better integrality gaps than the previous relaxations. (C) 2019 Elsevier B.V. All rights reserved.