Algorithms for Random Generation and Counting: A Markov Chain Approach

A. Sinclair

ISBN 10: 1461267072 / ISBN 13: 9781461267072

Edité par Springer-Verlag New York Inc., 2012

This item is printed on demand. New copy - Usually dispatched within 5-9 working days 280. N° de réf. du vendeur C9781461267072

Synopsis :

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.

Détails bibliographiques

Titre : Algorithms for Random Generation and ...
Éditeur : Springer-Verlag New York Inc.
Date d'édition : 2012
Reliure : Paperback / softback
Etat : New