## Abstract

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 language | American English |
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Pages (from-to) | 1-18 |

Number of pages | 18 |

Journal | Combinatorica |

Volume | 16 |

Issue number | 1 |

DOIs | |

State | Published - 1996 |