Fast minimum-weight double-tree shortcutting for metric TSP

Abstract

The Metric Traveling Salesman Problem (TSP) is a classical NP-hard optimization problem. The double-tree shortcutting method for Metric TSP yields an exponential-sized space of TSP tours, each of which is a 2-approximation to the exact solution. We consider the problem of minimum-weight double-tree shortcutting, for which Burkard et al. gave an algorithm running in time O(2dn3) and memory O(2dn2), where d is the maximum node degree in the rooted minimum spanning tree (e.g. in the non-degenerate planar Euclidean case, d ≤ 4). We give an improved algorithm running in time O(4dn2) and memory O(4dn), which allows one to solve the problem on much larger instances. Our computational experiments suggest that the minimum-weight double-tree shortcutting method provides one of the best known tour-constructing heuristics. © Springer-Verlag Berlin Heidelberg 2007.