TY - GEN

T1 - Biased random walks

AU - Azar, Yossi

AU - Broder, Andrei Z.

AU - Karlin, Anna R.

AU - Linial, Nathan

AU - Phillips, Steven

N1 - Publisher Copyright:
© 1992 ACM.

PY - 1992/7/1

Y1 - 1992/7/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0026985373&partnerID=8YFLogxK

U2 - 10.1145/129712.129713

DO - 10.1145/129712.129713

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AN - SCOPUS:0026985373

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 1

EP - 9

BT - Proceedings of the 24th Annual ACM Symposium on Theory of Computing, STOC 1992

PB - Association for Computing Machinery

Y2 - 4 May 1992 through 6 May 1992

ER -