Abstract
We consider the following online dial-a-ride problem (OlDarp): Objects are to be transported between points in a metric space. Transportation requests arrive online, specifying the objects to be transported and the corresponding source and destination. These requests are to be handled by a server which starts its work at a designated origin and which picks up and drops objects at their sources and destinations. The server can move at constant unit speed. After the end of its service the server returns to its start in the origin. The goal of OlDarp is to come up with a transportation schedule for the server which finishes as early as possible, i.e., which minimizes the makespan.
We analyze several competitive algorithms for OlDarp and establish tight competitiveness results. The first two algorithms, REPLAN and IGNORE are very simple and natural: REPLAN completely discards its (preliminary) schedule and recomputes a new one when a new request arrives. IGNORE always runs a (locally optimal) schedule for a set of known requests and ignores all new requests until this schedule is completed. We show that both strategies, REPLAN and IGNORE, are 5/2-competitive.
We then present a somewhat less natural strategy SMARTSTART, which in contrast to the other two strategies may leave the server idle from time to time although unserved requests are known. The SMARTSTART-algorithm has an improved competitive ratio of 2, which matches our lower bound.
Research supported by the German Science Foundation (grant 883/5-2)
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
N. Ascheuer, M. Grötschel, S. O. Krumke, and J. Rambau. Combinatorial online optimization. In Proceedings of the International Conference of Operations Research, pages 21–37. Springer, 1998.
M. J. Atallah and S. R. Kosaraju. Efficient solutions to some transportation problems with applications to minimizing robot arm travel. SIAM Journal on Computing, 17(5):849–869, October 1988.
G. Ausiello, E. Feuerstein, S. Leonardi, L. Stougie, and M. Talamo. Serving request with on-line routing. In Proceedings of the 4th Scandinavian Workshop on Algorithm Theory, volume 824 of Lecture Notes in Computer Science, pages 37–48, July 1994.
G. Ausiello, E. Feuerstein, S. Leonardi, L. Stougie, and M. Talamo. Competitive algorithms for the traveling salesman. In Proceedings of the 4th Workshop on Algorithms and Data Structures, volume 955 of Lecture Notes in Computer Science, pages 206–217, August 1995.
G. Ausiello, E. Feuerstein, S. Leonardi, L. Stougie, and M. Talamo. Algorithms for the on-line traveling salesman. Algorithmica, 1999. To appear.
A. Borodin and R. El-Yaniv. Online Computation and Competitive Analysis. Cambridge University Press, 1998.
M. Charikar and B. Raghavachari. The finite capacity dial-A-ride problem. In Proceedings of the 39th Annual IEEE Symposium on the Foundations of Computer Science, 1998.
N. Christofides. Worst-case analysis of a new heuristic for the traveling salesman problem. Technical report, Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh, PA, 1976.
E. Feuerstein and L. Stougie. On-line single server dial-a-ride problems. Theoretical Computer Science, special issue on on-line algorithms, to appear.
G. N. Frederickson, M. S. Hecht, and C. E. Kim. Approximation algorithms for some routing problems. SIAM Journal on Computing, 7(2):178–193, May 1978.
D. Hauptmeier, S. O. Krumke, J. Rambau, and H.-C. Wirth. Euler is standing in line. In Proceedings of the 25th International Workshop on Graph-Theoretic Concepts in Computer Science, Ascona, Switzerland, volume 1665 of Lecture Notes in Computer Science, pages 42–54, June 1999.
D. B. Shmoys, J. Wein, and D. P. Williamson. Scheduling parallel machines on-line. SIAM Journal on Computing, 24(6):1313–1331, December 1995.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ascheuer, N., Krumke, S.O., Rambau, J. (2000). Online Dial-a-Ride Problems: Minimizing the Completion Time. In: Reichel, H., Tison, S. (eds) STACS 2000. STACS 2000. Lecture Notes in Computer Science, vol 1770. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46541-3_53
Download citation
DOI: https://doi.org/10.1007/3-540-46541-3_53
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67141-1
Online ISBN: 978-3-540-46541-6
eBook Packages: Springer Book Archive