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On the Markov Chain Simulation Method for Uniform Combinatorial Distributions and Simulated Annealing

Published online by Cambridge University Press:  27 July 2009

David Aldous
David Aldous
Affiliation:
Department of StatisticsUniversity of California Berkeley, California
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Abstract

Uniform distributions on complicated combinatorial sets can be simulated by the Markov chain method. A condition is given for the simulations to be accurate in polynomial time. Similar analysis of the simulated annealing algorithm remains an open problem. The argument relies on a recent eigenvalue estimate of Alon [4]; the only new mathematical ingredient is a careful analysis of how the accuracy of sample averages of a Markov chain is related to the second-largest eigenvalue.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 1 , Issue 1 , January 1987 , pp. 33 - 46
Copyright
Copyright © Cambridge University Press 1987

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