Vol 5 No 1 (2010)
Articles

Approximating the metric 2-Peripatetic Salesman Problem

Federico Della Croce
DAI Politecnico di Torino, Italy
Vangelis Th. Paschos
LAMSADE - CNRS UMR 7024 and Université Paris Dauphine, France
Roberto Wolfler Calvo
LIPN - Université PARIS 13, France
Published April 14, 2010
Keywords
  • Peripatetic salesman,
  • approximation algorithm
How to Cite
Della Croce, F., Paschos, V. T., & Calvo, R. W. (2010). Approximating the metric 2-Peripatetic Salesman Problem. Algorithmic Operations Research, 5(1), Pages 13 - 20. Retrieved from https://journals.lib.unb.ca/index.php/AOR/article/view/11496

Abstract

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.