Progress in Theoretical Computer Science

Algorithms for Random Generation and Counting: A Markov Chain Approach

Authors: Sinclair, A.

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About this book

This monograph is a slightly revised version of my PhD thesis [86], com­ pleted in the Department of Computer Science at the University of Edin­ 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 prob­ lems appear to be intractable for many important structures, so interest has focused on finding efficient randomised algorithms that solve them ap­ 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: sim­ 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 optimi­ sation. The efficiency of the technique in any application depends crucially on the rate of convergence of the Markov chain.

Table of contents (5 chapters)

Buy this book

eBook $129.00
price for USA (gross)
  • ISBN 978-1-4612-0323-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.00
price for USA
  • ISBN 978-0-8176-3658-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $169.00
price for USA
  • ISBN 978-1-4612-6707-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Algorithms for Random Generation and Counting: A Markov Chain Approach
Authors
Series Title
Progress in Theoretical Computer Science
Copyright
1993
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4612-0323-0
DOI
10.1007/978-1-4612-0323-0
Hardcover ISBN
978-0-8176-3658-6
Softcover ISBN
978-1-4612-6707-2
Edition Number
1
Number of Pages
VIII, 147
Topics