Biased random walks

Yossi Azar, Andrei Z. Broder, Anna R. Karlin, Nathan Linial, Steven Phillips

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

20 Scopus citations


How much can an imperfect source of randomness affect an algorithm? We examine several simple questions of this type concerning the long-term behavior of a random walk on a finite graph. In our setup, at each step of the random walk a "controller" can, with a certain small probability, fix the next step, thus introducing a bias. We analyze the extent to which the bias can affect the limit behavior of the walk. The controller is assumed to associate a real, nonnegative, "benefit" with each state, and to strive to maximize the long-term expected benefit. We derive tight bounds on the maximum of this objective function over all controller's strategies, and present polynomial time algorithms for computing the optimal controller strategy.

Original languageAmerican English
Title of host publicationProceedings of the 24th Annual ACM Symposium on Theory of Computing, STOC 1992
PublisherAssociation for Computing Machinery
Number of pages9
ISBN (Electronic)0897915119
StatePublished - 1 Jul 1992
Event24th Annual ACM Symposium on Theory of Computing, STOC 1992 - Victoria, Canada
Duration: 4 May 19926 May 1992

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
VolumePart F129722
ISSN (Print)0737-8017


Conference24th Annual ACM Symposium on Theory of Computing, STOC 1992

Bibliographical note

Publisher Copyright:
© 1992 ACM.


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