An Approximation Algorithm for the Asymmetric Travelling Salesman Problem with Distances One and Two

Abstract We present an approximation algorithm, with a performance ratio of at most 17⧸12, for the asymmetric travelling salesman problem with distances one and two. This problem is equivalent (in a sense that we describe in the paper) to the problem of covering the vertices of a diagraph with a minimum number of vertex-disjoint paths.