Evasive random walks and the clairvoyant demon

Authors:
Aaron Abrams;Henry Landau;Zeph Landau;James Pommersheim;Eric Zaslow
Affiliations:
Mathematics Department, University of California, Berkeley, Berkeley, CA;-;Sloan Center for Theoretical Neurobiology, Department of Physiology, Box 0444, University of California, San Francisco, 513 Parnassus Avenue, San Francisco, CA;Department of Mathematics, Pomona College, 610 N. College Ave., Claremont, CA;Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL
Venue:
Random Structures & Algorithms
Year:
2002

Citing 3
Cited 0

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Abstract

A pair of random walks (R, S) on the vertices of a graph G is successful if two tokens moving one at a time can be scheduled (moving only one token at a time) to travel along R and S without colliding. We consider questions related to P. Winkler's clairvoyant demon problem, which asks whether for random walks R and S on G, Pr[(R, S) is successful] 0. We introduce the notion of an evasive walk on G: a walk S so that for a random walk R on G, Pr[(R, S) is successful] 0. We characterize graphs G having evasive walks, giving explicit constructions on such G. Also, we show that on a cycle, the tokens must collide quickly with high probability.