Lectures in Mathematics. ETH Zürich

Counting, Sampling and Integrating: Algorithms and Complexity

Authors: Jerrum, Mark

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About this book

The subject of these notes is counting (of combinatorial structures) and related topics, viewed from a computational perspective. "Related topics" include sampling combinatorial structures (being computationally equivalent to approximate counting via efficient reductions), evaluating partition functions (being weighted counting), and calculating the volume of bodies (being counting in the limit).

A major theme of the book is the idea of accumulating information about a set of combinatorial structures by performing a random walk (i.e., simulating a Markov chain) on those structures. (This is for the discrete setting; one can also learn about a geometric body by performing a walk within it.) The running time of such an algorithm depends on the rate of convergence to equilibrium of this Markov chain, as formalised in the notion of "mixing time" of the Markov chain. A significant proportion of the volume is given over to an investigation of techniques for bounding the mixing time in cases of computational interest.

These notes will be of value not only to teachers of postgraduate courses on these topics, but also to established researchers in the field of computational complexity who wish to become acquainted with recent work on non-asymptotic analysis of Markov chains, and their counterparts in stochastic processes who wish to discover how their subject sits within a computational context. For the first time this body of knowledge has been brought together in a single volume.

Table of contents (7 chapters)

Buy this book

eBook $34.99
price for USA (gross)
  • ISBN 978-3-0348-8005-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA
  • ISBN 978-3-7643-6946-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Counting, Sampling and Integrating: Algorithms and Complexity
Authors
Series Title
Lectures in Mathematics. ETH Zürich
Copyright
2003
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel AG
eBook ISBN
978-3-0348-8005-3
DOI
10.1007/978-3-0348-8005-3
Softcover ISBN
978-3-7643-6946-0
Edition Number
1
Number of Pages
XI, 112
Number of Illustrations and Tables
7 b/w illustrations
Topics