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Approximating the Permanent
TLDR
A randomised approximation scheme for the permanent of a 0–1s presented, demonstrating that the matchings chain is rapidly mixing, apparently the first such result for a Markov chain with genuinely c... Expand
Approximate counting, uniform generation and rapidly mixing Markov chains
The paper studies effective approximate solutions to combinatorial counting and uniform generation problems. Using a technique based on the simulation of ergodic Markov chains, it is shown that, forExpand
A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries
TLDR
A polynomial-time randomized algorithm for estimating the permanent of an arbitrary n × n matrix with nonnegative entries computes an approximation that is within arbitrarily small specified relative error of the true value of the permanent. Expand
Polynomial-Time Approximation Algorithms for the Ising Model
TLDR
A randomised algorithm which evaluates the partition function of an arbitrary ferromagnetic Ising system to any specified degree of accuracy is presented. Expand
Improved Bounds for Mixing Rates of Marcov Chains and Multicommodity Flow
  • A. Sinclair
  • Mathematics, Computer Science
  • Comb. Probab. Comput.
  • 1 December 1992
TLDR
A new upper bound on the mixing rate is presented, based on the solution to a multicommodity flow problem in the Markov chain viewed as a graph, and improved bounds are obtained for the runtimes of randomised approximation algorithms for various problems, including computing the permanent of a 0–1 matrix, counting matchings in graphs, and computing the partition function of a ferromagnetic Ising system. Expand
The Markov chain Monte Carlo method: an approach to approximate counting and integration
TLDR
The introduction of analytical tools with the aim of permitting the analysis of Monte Carlo algorithms for classical problems in statistical physics has spurred the development of new approximation algorithms for a wider class of problems in combinatorial enumeration and optimization. Expand
Algorithms for Random Generation and Counting: A Markov Chain Approach
  • A. Sinclair
  • Mathematics, Computer Science
  • Progress in Theoretical Computer Science
  • 1 February 1993
TLDR
The Markov chain approach to generation problems, and a robust notion of approximate counting, and self-embeddable relations, are presented. Expand
Optimal speedup of Las Vegas algorithms
TLDR
The authors describe a simple universal strategy S/sup univ/, with the property that, for any algorithm A, T(A,S/Sup univ/)=O (l/sub A/log(l/ sub A/)), which is the best performance that can be achieved, up to a constant factor, by any universal strategy. Expand
Improved Bounds for Mixing Rates of Markov Chains and Multicommodity Flow ( Extended Abstract )
In recent years, Markov chain simulation has emerged as a powerful algorithmic paradigm. Its chief application is to the random sampling of combinatorial structures from a specified probabilityExpand
Approximate Counting, Uniform Generation and Rapidly Mixing Markov Chains
TLDR
The general techniques of the paper are used to derive an almost uniform generation procedure for labelled graphs with a given degree sequence which is valid over a much wider range of degrees than previous methods: this in turn leads to randomised approximate counting algorithms for these graphs with very good asymptotic behaviour. Expand
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