By A. Sinclair

ISBN-10: 1461267072

ISBN-13: 9781461267072

This monograph is a touch revised model of my PhD thesis [86], com­ pleted within the division of desktop technological know-how on the college of Edin­ burgh in June 1988, with an extra bankruptcy summarising newer advancements. a few of the fabric has seemed within the type of papers [50,88]. The underlying subject matter of the monograph is the research of 2 classical difficulties: counting the weather of a finite set of combinatorial buildings, and producing them uniformly at random. of their specific shape, those prob­ lems seem to be intractable for plenty of very important constructions, so curiosity has concerned about discovering effective randomised algorithms that clear up them ap­ proxim~ly, with a small likelihood of mistakes. for many normal buildings the 2 difficulties are in detail attached at this point of approximation, so it really is common to check them jointly. on the center of the monograph is a unmarried algorithmic paradigm: sim­ ulate a Markov chain whose states are combinatorial constructions and which converges to a recognized likelihood distribution over them. this method has functions not just in combinatorial counting and iteration, but additionally in numerous different components corresponding to statistical physics and combinatorial optimi­ sation. The potency of the process in any program relies crucially at the price of convergence of the Markov chain.

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Algorithms for Random Generation and Counting: A Markov Chain Approach (Progress in Theoretical Computer Science) by A. Sinclair

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