Abstract
We consider two on-line versions of the asymmetric traveling salesman problem with triangle inequality. For the homing version, in which the salesman is required to return in the city where it started from, we give a \(\frac{3\sqrt{5}}{2}\) -competitive algorithm and prove that this is best possible. For the nomadic version, the on-line analogue of the shortest asymmetric hamiltonian path problem, we show that the competitive ratio of any on-line algorithm has to depend on the amount of asymmetry of the space in which the salesman moves. We also give bounds on the competitive ratio of on-line algorithms that are zealous, that is, in which the salesman cannot stay idle when some city can be served.
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
Ascheuer, N., Krumke, S.O., Rambau, J.: Online dial-a-ride problems: Minimizing the completion time. In: Reichel, H., Tison, S. (eds.) STACS 2000. LNCS, vol. 1770, pp. 639–650. Springer, Heidelberg (2000)
Ausiello, G., Demange, M., Laura, L., Paschos, V.: Algorithms for the on-line quota traveling salesman problem. In: Chwa, K.-Y., Munro, J.I. (eds.) COCOON 2004. LNCS, vol. 3106, pp. 290–299. Springer, Heidelberg (2004)
Ausiello, G., Feuerstein, E., Leonardi, S., Stougie, L., Talamo, M.: Algorithms for the on-line travelling salesman. Algorithmica 29(4), 560–581 (2001)
Blom, M., Krumke, S.O., de Paepe, W.E., Stougie, L.: The online-TSP against fair adversaries. INFORMS Journal on Computing 13, 138–148 (2001)
Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, Cambridge (1998)
Feuerstein, E., Stougie, L.: On-line single-server dial-a-ride problems. Theoretical Computer Science 268, 91–105 (2001)
Fiat, A., Woeginger, G.J. (eds.): Online Algorithms: The State of the Art. Springer, Heidelberg (1998)
Frieze, A.M., Galbiati, G., Maffioli, F.: On the worst-case performance of some algorithms for the asymmetric traveling salesman problem. Networks 12(1), 23–39 (1982)
Gutin, G., Punnen, A.P. (eds.): The Traveling Salesman Problem and its Variations. Kluwer, Dordrecht (2002)
Jünger, M., Reinelt, G., Rinaldi, G.: The traveling salesman problem. In: Ball, M.O., Magnanti, T., Monma, C.L., Nemhauser, G. (eds.) Network Models, Handbook on Operations Research and Management Science, vol. 7, pp. 225–230. Elsevier, Amsterdam (1995)
Kaplan, H., Lewenstein, M., Shafrir, N., Sviridenko, M.: Approximation algorithms for asymmetric TSP by decomposing directed regular multigraphs. In: Proc. 44th Symp. Foundations of Computer Science, pp. 56–66 (2003)
Krumke, S.O.: Online optimization: Competitive analysis and beyond. Habilitation Thesis, Technical University of Berlin (2001)
Krumke, S.O., de Paepe, W.E., Poensgen, D., Stougie, L.: News from the online traveling repairman. In: Sgall, J., Pultr, A., Kolman, P. (eds.) MFCS 2001. LNCS, vol. 2136, pp. 487–499. Springer, Heidelberg (2001)
Lawler, E.L., Lenstra, J.K., Kan, A.R., Shmoys, D.B.: The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization. Wiley, Chichester (1985)
Lipmann, M.: On-Line Routing. PhD thesis, Technical University of Eindhoven (2003)
Papadimitriou, C.H., Yannakakis, M.: The traveling salesman problem with distances one and two. Mathematics of Operations Research 18(1), 1–11 (1993)
Sahni, S., Gonzalez, T.F.: P-complete approximation problems. Journal of the ACM 23(3), 555–565 (1976)
Sleator, D., Tarjan, R.E.: Amortized efficiency of list update and paging rules. Communications of the ACM 28(2), 202–208 (1985)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ausiello, G., Bonifaci, V., Laura, L. (2005). The On-line Asymmetric Traveling Salesman Problem. In: Dehne, F., López-Ortiz, A., Sack, JR. (eds) Algorithms and Data Structures. WADS 2005. Lecture Notes in Computer Science, vol 3608. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11534273_27
Download citation
DOI: https://doi.org/10.1007/11534273_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28101-6
Online ISBN: 978-3-540-31711-1
eBook Packages: Computer ScienceComputer Science (R0)