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Algorithms for Random Generation and Counting: A Markov Chain Approach - Softcover

 
9781461203247: Algorithms for Random Generation and Counting: A Markov Chain Approach

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Synopsis

Synopsis.- 1 Preliminaries.- 1.1 Some basic definitions.- 1.2 Notions of tractability.- 1.3 An extended model.- 1.4 Counting, generation and self-reducibility.- 1.5 An interesting class of relations.- 2 Markov chains and rapid mixing.- 2.1 The Markov chain approach to generation problems.- 2.2 Conductance and the rate of convergence.- 2.3 A characterisation of rapid mixing.- 3 Direct Applications.- 3.1 Some simple examples.- 3.2 Approximating the permanent.- 3.3 Monomer-dimer systems.- 3.4 Concluding remarks.- 4 Indirect Applications.- 4.1 A robust notion of approximate counting.- 4.2 Self-embeddable relations.- 4.3 Graphs with specified degrees.- Appendix: Recent developments.

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  • PublisherBirkhäuser
  • Publication date2011
  • ISBN 10 1461203244
  • ISBN 13 9781461203247
  • BindingPaperback
  • LanguageEnglish

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