Traveling salesman path problems

• 成果类型: Article
• 署名作者: Lam, Fumei; Newman, Alantha
• 署名单位: Massachusetts Institute of Technology (MIT); Max Planck Society
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-006-0046-8
• 发表日期: 2008
• 页码: 39-59
• 关键词: graphical relaxation; performance; algorithms; polytope

摘要

In the traveling salesman path problem, we are given a set of cities, traveling costs between city pairs and fixed source and destination cities. The objective is to find a minimum cost path from the source to destination visiting all cities exactly once. In this paper, we study polyhedral and combinatorial properties of a variant we call the traveling salesman walk problem, in which the objective is to find a minimum cost walk from the source to destination visiting all cities at least once. We first characterize traveling salesman walk perfect graphs, graphs for which the convex hull of incidence vectors of traveling salesman walks can be described by linear inequalities. We show these graphs have a description by way of forbidden minors and also characterize them constructively. We also address the asymmetric traveling salesman path problem (ATSPP) and give a factor O(root n)-approximation algorithm for this problem.