A fast (2+2/7)-approximation algorithm for capacitated cycle covering

• 成果类型: Article
• 署名作者: Traub, Vera; Trobst, Thorben
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich; University of California System; University of California Irvine
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-021-01678-3
• 发表日期: 2022
• 页码: 497-518
• 关键词: heuristics; bounds

摘要

We consider the capacitated cycle covering problem: given an undirected, complete graph G with metric edge lengths and demands on the vertices, we want to cover the vertices with vertex-disjoint cycles, each serving a demand of at most one. The objective is to minimize a linear combination of the total length and the number of cycles. This problem is closely related to the capacitated vehicle routing problem (CVRP) and other cycle cover problems such as min-max cycle cover and bounded cycle cover. We show that a greedy algorithm followed by a post-processing step yields a (2 + 2/7)-approximation for this problem by comparing the solution to a polymatroid relaxation. We also show that the analysis of our algorithm is tight and provide a 2+ epsilon lower bound for the relaxation.