Algorithms for Random Generation and Cou
β A. Sinclair
π Library
π
1993
π BirkhΓ€user Boston
π English
β¦ LIBER β¦
π
Algorithms for Random Generation and Counting: A Markov Chain Approach
β Scribed by Alistair Sinclair (auth.)
- Publisher
- BirkhΓ€user Basel
- Year
- 1993
- Tongue
- English
- Leaves
- 155
- Series
- Progress in Theoretical Computer Science
- Edition
- 1
- Category
- Library
β¬ Acquire This Volume
No coin nor oath required. For personal study only.
β¦ Synopsis
This monograph is a slightly revised version of my PhD thesis [86], comΒ pleted in the Department of Computer Science at the University of EdinΒ burgh in June 1988, with an additional chapter summarising more recent developments. Some of the material has appeared in the form of papers [50,88]. The underlying theme of the monograph is the study of two classical problems: counting the elements of a finite set of combinatorial structures, and generating them uniformly at random. In their exact form, these probΒ lems appear to be intractable for many important structures, so interest has focused on finding efficient randomised algorithms that solve them apΒ proxim~ly, with a small probability of error. For most natural structures the two problems are intimately connected at this level of approximation, so it is natural to study them together. At the heart of the monograph is a single algorithmic paradigm: simΒ ulate a Markov chain whose states are combinatorial structures and which converges to a known probability distribution over them. This technique has applications not only in combinatorial counting and generation, but also in several other areas such as statistical physics and combinatorial optimiΒ sation. The efficiency of the technique in any application depends crucially on the rate of convergence of the Markov chain.
β¦ Table of Contents
Front Matter....Pages i-viii
Synopsis....Pages 1-6
Preliminaries....Pages 7-41
Markov chains and rapid mixing....Pages 42-62
Direct Applications....Pages 63-100
Indirect Applications....Pages 101-125
Back Matter....Pages 126-147
β¦ Subjects
Math Applications in Computer Science; Probability Theory and Stochastic Processes; Algorithm Analysis and Problem Complexity; Algorithms; Computational Mathematics and Numerical Analysis; Applications of Mathematics
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