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 + ε)-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(n 2logn) 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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ageev, A.A., Baburin, A.E., Gimadi, E.K.: A polynomial algorithm with an accuracy estimate of 3/4 for finding two nonintersecting Hamiltonian cycles of maximum weight (in Russian). Diskretn. Anal. Issled. Oper. Ser. 13(2), 11–20 (2006)
Baburin, A.E., Gimadi, E.K., Korkishko, N.M.: Approximate algorithms for finding two edge-disjoint Hamiltonian cycles of minimal weight (in Russian), Diskretn. Anal. Issled. Oper. Ser. 2. 11(1), 11–25 (2004)
Christofides, N.: Worst-case analysis of a new heuristic for the traveling salesman problem, Technical Report CS-93-13, Carnegie Mellon University (1976)
De Brey, M.J.D., Volgenant, A.: Well-solved cases of the 2-peripatetic salesman problem. Optimization 39(3), 275–293 (1997)
Duchenne, E., Laporte, G., Semet, F.: Branch-and-cut algorithms for the undirected m-peripatetic salesman problem. European J. Oper. Res. 162(3), 700–712 (2005)
De Kort, J.B.J.M.: Lower bounds for symmetric K-peripatetic salesman problems. Optimization 22(1), 113–122 (1991)
De Kort, J.B.J.M.: Upper bounds for the symmetric 2-peripatetic salesman problem. Optimization 23(4), 357–367 (1992)
De Kort, J.B.J.M.: A branch and bound algorithm for symmetric 2-peripatetic salesman problems. European J. of Oper. Res. 70, 229–243 (1993)
Krarup, J.: The peripatetic salesman and some related unsolved problems, Combinatorial programming: methods and applications. In: Proc. NATO Advanced Study Inst., Versailles, 1974, pp. 173–178 (1975)
Roskind, J., Tarjan, R.E.: A note on finding minimum-cost edge-disjoint spanning trees. Math. Oper. Res. 10(4), 701–708 (1985)
Serdjukov, A.I.: Some extremal bypasses in graphs (in Russian). Upravlyaemye Sistemy 17(89), 76–79 (1978)
Wolfter, C.R., Cordone, R.: A Heuristic Approach to the Overnight Security Service Problem. Computers & Operations Research 30, 1269–1287 (2003)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ageev, A.A., Pyatkin, A.V. (2008). A 2-Approximation Algorithm for the Metric 2-Peripatetic Salesman Problem. In: Kaklamanis, C., Skutella, M. (eds) Approximation and Online Algorithms. WAOA 2007. Lecture Notes in Computer Science, vol 4927. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77918-6_9
Download citation
DOI: https://doi.org/10.1007/978-3-540-77918-6_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77917-9
Online ISBN: 978-3-540-77918-6
eBook Packages: Computer ScienceComputer Science (R0)