On convex body chasing
Purchase on Springer.com
$39.95 / €34.95 / £29.95*
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.
A player moving in the plane is given a sequence of instructions of the following type: at stepi a planar convex setF i is specified, and the player has to move to a point inF i. The player is charged for the distance traveled. We provide a strategy for the player which is competitive, i.e., for any sequenceF i the cost to the player is within a constant (multiplicative) factor of the “off-line” cost (i.e., the least possible cost when allF i are known in advance). We conjecture that similar strategies can be developed for this game in any Euclidean space and perhaps even in all metric spaces. The analogous statement where convex sets are replaced by more general families of sets in a metric space includes many on-line/off-line problems such as thek-server problem; we make some remarks on these more general problems.
- S. Ben-David, A. Borodin, R. M. Karp, G. Tardos, and A. Wigderson. On the Power of Randomization in On-line Algorithms. InProc. of the 22nd Ann. ACM Symp. on Theory of Computing, pages 379–386, May 1990.
- P. Berman, H. J. Karloff, and G. Tardos. A Competitive Three-Server Algorithm. InProc. of the 1st Ann. ACM-SIAM Symp. on Discrete Algorithms, pages 280–290, January 1990.
- A. Bordoin, N. Linial, and M. Saks. An Optimal On-Line Algorithm for Metrical Task Systems. InProc. of the 19th Ann. ACM Symp. on Theory of Computing, pages 373–382, May 1987. Final version to appear inJ. Assoc. Comput. Mach.
- M. Chrobak, H. J. Karloff, T. Payne, and S. Vishwanathan. New Results on Server Problems. InProc. of the 1st Ann. ACM-SIAM Symp. on Discrete Algorithms, pates 291–300, January 1990.
- D. Coppersmith, P. Doyle, P. Raghavan, and M. Snir. Random Walks on Weighted Graphs and Applications to On-line Algorithms. InProc. of the 22nd Ann. ACM Symp. on Theory of Computing, pages 369–378, May 1990.
- A. Fiat, D. P. Foster, H. Karloff, Y. Rabani, Y. Ravid, and S. Vishwanathan. Competitive Algorithms for Layered Graph Traversal. Manuscript, 1991.
- A. Fiat, Y. Rabani, and Y. Ravid. Competitivek-Server Algorithms. InProc. of the 31st Ann. IEEE Symp. on Foundations of Computer Science, pages 454–463, October 1990.
- E. Grove. The Harmonic Onlinek-Server Algorithm Is Competitive. Manuscript, 1990.
- M. S. Manasse, L. A. McGeoch, and D. D. Sleator. Competitive Algorithms for On-Line Problems. InProc. of the 20th Ann. ACM Symp. on Theory of Computing, pages 322–333, May 1988.
- C. H. Papadimitriou and M. Yannakakis. Shortest Paths Without a Map. InProc. 16th ICALP, pages 610–620, July 1989.
- D. D. Slator and R. E. Tarjan. Amortized Efficiency of List Update and Paging Rules.Comm. ACM, 28:202–208, 1985.
- On convex body chasing
Discrete & Computational Geometry
Volume 9, Issue 1 , pp 293-321
- Cover Date
- Print ISSN
- Online ISSN
- Additional Links
- Industry Sectors