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

By A. Sinclair

This monograph is a marginally revised model of my PhD thesis [86], com­ pleted within the division of machine technological know-how on the college of Edin­ burgh in June 1988, with an extra bankruptcy summarising more moderen advancements. the various fabric has seemed within the type of papers [50,88]. The underlying subject of the monograph is the examine of 2 classical difficulties: counting the weather of a finite set of combinatorial buildings, and producing them uniformly at random. of their distinct shape, those prob­ lems seem to be intractable for plenty of vital constructions, so curiosity has fascinated about discovering effective randomised algorithms that resolve them ap­ proxim~ly, with a small likelihood of mistakes. for many average constructions the 2 difficulties are in detail attached at this point of approximation, so it's 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 system has purposes not just in combinatorial counting and new release, but additionally in numerous different components resembling statistical physics and combinatorial optimi­ sation. The potency of the strategy in any software relies crucially at the cost 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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