Article ID: | iaor20105461 |
Volume: | 5 |
Issue: | 1 |
Start Page Number: | 13 |
End Page Number: | 20 |
Publication Date: | Jan 2010 |
Journal: | Algorithmic Operations Research |
Authors: | Croce Federico Della, Calvo Roberto Wolfler, Paschos Vangelis Th |
This paper deals with the 2-Peripatetic Salesman Problem for the case where costs respect the triangle inequality. The aim is to determine 2 edge disjoint Hamiltonian cycles of minimum total cost on a graph. We first present a straightforward 9/4 approximation algorithm based on the well known Christofides algorithm for the travelling salesman problem. Then we propose a 2(n-1)/n-approximation polynomial time algorithm based on the solution of the minimum cost two-edge-disjoint spanning trees problem. Finally, we show that by partially combining these two algorithms, a 15/8 approximation ratio can be reached if a 5/4 approximation algorithm can be found for the related problem of finding two edge disjoint subgraphs consisting in a spanning tree and an hamiltonian cycle of minimum total cost.