Biased Random Walks

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.

• Type: Conference
• Year: 1992
• Where: STOC
• Authors: Yossi Azar, Andrei Z. Broder, Anna R. Karlin, Nathan Linial, Steven Phillips
• Keywords: Algorithms, Certain Small Probability, Long-term Expected Benefit, Random Walk, STOC 1992