A 2-Approximation Algorithm for the Metric 2-Peripatetic Salesman Problem

Abstract

In the m-peripatetic traveling salesman problem (m-PSP), given an n-vertex complete undirected edge-weighted graph, it is required to find m edge disjoint Hamiltonian cycles of minimum total weight. The problem was introduced by Krarup (1974) and has network design and scheduling applications. It is known that 2-PSP is NP-hard even in the metric case and does not admit any constant-factor approximation in the general case. Baburin, Gimadi, and Korkishko (2004) designed a (9/4 + Ɛ)-approximation algorithm for the metric case of 2-PSP, based on solving the traveling salesman problem. In this paper we present an improved 2-approximation algorithm with running time O(n2 log n) for the metric 2-PSP. Our algorithm exploits the fact that the problem of finding two edge disjoint spanning trees of minimum total weight is polynomially solvable.