Traveling salesman path problems Open Access FULL LENGTH PAPER First Online: 01 November 2006 Received: 07 November 2005 Accepted: 15 August 2006 DOI :
10.1007/s10107-006-0046-8

Cite this article as: Lam, F. & Newman, A. Math. Program. (2008) 113: 39. doi:10.1007/s10107-006-0046-8
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Abstract 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 \(O(\sqrt{n})\) -approximation algorithm for this problem.

Mathematics Subject Classification (2000) 68Q25 68R10 90C05 90C27 Alantha Newman was supported in part by NSF grant CCR0307536.

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Authors and Affiliations 1. Department of Mathematics MIT Cambridge USA 2. Max Planck Institut für Informatik Saarbrucken Germany