Clairvoyant scheduling of random walks

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Clairvoyant scheduling of random walks

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Annual ACM Symposium on Theory of Computing archive
Proceedings of the thiry-fourth annual ACM symposium on Theory of computing table of contents

Montreal, Quebec, Canada

SESSION: Session 2B table of contents

Pages: 99 - 108

Year of Publication: 2002

ISBN:1-58113-495-9

Author

Peter Gács

Boston University, Boston, MA

Sponsor

SIGACT: ACM Special Interest Group on Algorithms and Computation Theory

Publisher

ACM New York, NY, USA

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ABSTRACT

Two infinite walks on the same finite graph are called compatible if it is possible to introduce delays into them in such a way that they never collide. About 10 years ago, Peter Winkler asked the question: for which graphs are two independent walks compatible with positive probability. Up to now, no such graphs were found. We show in this paper that large complete graphs have this property. The question is equivalent to a certain dependent percolation with a power-law behavior: the probability that the origin is blocked at distance n but not closer decreases only polynomially fast and not, as usual, exponentially.

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	P. Balister, B. Bollobas, and A. Stacey. Dependent percolation in two dimensions. Probab. Theory Relat. Fields, 117(4):495--513, 2000.
	2	Don Coppersmith , Prasad Tetali , Peter Winkler, Collisions among random walks on a graph, SIAM Journal on Discrete Mathematics, v.6 n.3, p.363-374, Aug. 1993 [doi>10.1137/0406029]
	3	Peter Gács, The Clairvoyant Demon Has a Hard Task, Combinatorics, Probability and Computing, v.9 n.5, p.421-424, September 2000 [doi>10.1017/S0963548300004405]
	4	P. Gács. Compatible sequences and a slow Winkler percolation. www.arXiv.org/abs/(MATH).PR/0011008, 2000.
	5	P. Gács. Clairvoyant scheduling of random walks. www.arXiv.org/abs/(MATH).PR/0109152, 2001.
	6	Peter Winkler, Dependent percolation and colliding random walks, Random Structures & Algorithms, v.16 n.1, p.58-84, Jan.1.2000 [doi>10.1002/(SICI)1098-2418(200001)16:1<58::AID-RSA5>3.0.CO;2-E]