Read e-book online Algorithms for Random Generation and Counting: A Markov PDF

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 collage of Edin­ burgh in June 1988, with an extra bankruptcy summarising more moderen advancements. many of the fabric has seemed within the kind 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 constructions, and producing them uniformly at random. of their specific shape, those prob­ lems seem to be intractable for plenty of very important buildings, so curiosity has keen on discovering effective randomised algorithms that clear up them ap­ proxim~ly, with a small likelihood of mistakes. for many typical buildings the 2 difficulties are in detail hooked up at this point of approximation, so it really is ordinary to check them jointly. on the middle of the monograph is a unmarried algorithmic paradigm: sim­ ulate a Markov chain whose states are combinatorial constructions and which converges to a identified chance distribution over them. this system has purposes not just in combinatorial counting and new release, but in addition in numerous different components akin to statistical physics and combinatorial optimi­ sation. The potency of the process in any software relies crucially at the fee 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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