Abstract
In this paper the first results on the Online Dial-A-Ride Problem with Time-Windows (ODARPTW for short) are presented. Requests for rides appearing over time consist of two points in a metric space, a source and a destination. Servers transport objects of requests from sources to destinations. Each request specifies a deadline. If a request is not be served by its deadline, it will be called off. The goal is to plan the motion of servers in an online way so that the maximum number of requests is met by their deadlines. We perform competitive analysis of two deterministic strategies for the problem with a single server in two cases separately, where the server has unit capacity and where the server has infinite capacity. The competitive ratios of the strategies are obtained. We also prove a lower bound on the competitive ratio of any deterministic algorithm of \(\frac{2-T}{2T}\) for a server with unit capacity and of \(\frac{2-T}{2T} \lceil \frac{1}{T} \rceil\) for a server with infinite capacity, where T denotes the diameter of the metric space.
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
Manasse, M.S., McGeoch, L.A., Sleator, D.D.: Competitive algorithms for server problems. Journal of Algorithms 11(2), 208–230 (1990)
David, S.B., Borodin, A.: A new measure for the study of the on-line algorithm. Algorithmica 11(1), 73–91 (1994)
Alon, N., Karp, R.M., Peleg, D., et al.: A graph-theoretic game and its application to the k- server problem. SIAM. J. Comput. 24(1), 78–100 (1995)
Feuerstein, E., Stougie, L.: On-line single server dial-a-ride problems. Theoretical Computer Science 268(1), 91–105 (2001)
Ascheuer N., Krumke S.O., and Rambau J.: Online dial-a-ride problems: Minimizing the completion time. Lecture Notes in Computer Science. (2000) 639–650
Xu, Y.F., Wang, K.L.: Scheduling for on-line taxi problem and competitive algorithms. Journal of Xi’an Jiao Tong University 31(1), 56–61 (1997)
Ausiello, G., Feuerstein, E., Leonardi, S., Stougie, L., Talamo, M.: Algorithms for the on-line traveling salesman. Algorithmica 29(4), 560–581 (2001)
Irani, S., Lu, X., Regan, A.: On-line algorithms for the dynamic traveling repair problem. In: Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 517–524 (2002)
Krumke, S.O., Megow, N., Vredeveld, T.: How to whack moles. In: Solis-Oba, R., Jansen, K. (eds.) WAOA 2003. LNCS, vol. 2909, pp. 192–205. Springer, Heidelberg (2004)
Ma, W.M., Xu, Y.F., Wang, K.L.: On-line k-truck problem and its competitive algorithm. Journal of Global Optimization 21(1), 15–25 (2001)
Hauptmeier, D., Krumke, S.O., Rambau, J.: The online dial-a-ride problem under reasonable load. In: LNCS, pp. 125–136 (2000)
Krumke, S.O., de Paepe, W.E., Poensgen, D., Stougie, L.: News from the online traveling repairman. Theoretical Computer Science 295, 279–294 (2003)
Krumke, S.O., Laura, L., Lipmann, M., Marchetti-Spaccamela, A., de Paepe, W.E., Poensgen, D., Stougie, L.: Non-abusiveness helps: An \(\mathcal O(1)\)-competitive algorithm for minimizing the maximum flow time in the online traveling salesman problem. In: Jansen, K., Leonardi, S., Vazirani, V.V. (eds.) APPROX 2002. LNCS, vol. 2462, pp. 200–214. Springer, Heidelberg (2002)
Lipmann, M., Lu, X., de Paepe, W.E., Sitters, R.A.: On-Line Dial-a-Ride Problems under a Restricted Information Model. In: Möhring, R.H., Raman, R. (eds.) ESA 2002. LNCS, vol. 2461, pp. 674–685. Springer, Heidelberg (2002)
Xu, Y.F., Wang, K.L., Zhu, B.: On the k-taxi problem. Journal of Information 2, 429–434 (1999)
Xu, Y.F., Wang, K.L., Ding, J.H.: On-line k-taxi scheduling on a constrained graph and its competitive algorithm. Journal of System Engineering(P.R. China) 4 (1999)
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
Yi, F., Tian, L. (2005). On the Online Dial-A-Ride Problem with Time-Windows. In: Megiddo, N., Xu, Y., Zhu, B. (eds) Algorithmic Applications in Management. AAIM 2005. Lecture Notes in Computer Science, vol 3521. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11496199_11
Download citation
DOI: https://doi.org/10.1007/11496199_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26224-4
Online ISBN: 978-3-540-32440-9
eBook Packages: Computer ScienceComputer Science (R0)