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Approximating the Permanent
A randomised approximation scheme for the permanent of a 0–1s presented. The task of estimating a permanent is reduced to that of almost uniformly generating perfect matchings in a graph; the latterExpand
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Improved Approximation Algorithms for MAX k-CUT and MAX BISECTION
Polynomial-time approximation algorithms with non-trivial performance guarantees are presented for the problems of (a) partitioning the vertices of a weighted graph into k blocks so as to maximiseExpand
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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
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Random Generation of Combinatorial Structures from a Uniform Distribution
Abstract The class of problems involving the random generation of combinatorial structures from a uniform distribution is considered. Uniform generation problems are, in computational difficulty,Expand
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A Very Simple Algorithm for Estimating the Number of k-Colorings of a Low-Degree Graph
  • M. Jerrum
  • Mathematics, Computer Science
  • Random Struct. Algorithms
  • 1 September 1995
A fully polynomial randomized approximation scheme is presented for estimating the number of (vertex) k‐colorings of a graph of maximum degree Δ, when k ≥ 2Δ + 1. © 1995 John Wiley & Sons, Inc.
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Polynomial-Time Approximation Algorithms for the Ising Model
The paper presents a randomised algorithm which evaluates the partition function of an arbitrary ferromagnetic Ising system to any specified degree of accuracy. The running time of the algorithm in...
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A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries
We present a polynomial-time randomized algorithm for estimating the permanent of an arbitrary n × n matrix with nonnegative entries. This algorithm---technically a "fully-polynomial randomizedExpand
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The Monte Carlo Markov Chain method: an approach to approximate counting and integration
Thermoset coating compositions are made from an aqueous solution or dispersion of a polymer of a hydroxyalkyl acrylate catalyzed with a titanium chelate. Films useful as protective and decorativeExpand
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The Markov chain Monte Carlo method: an approach to approximate counting and integration
In the area of statistical physics, Monte Carlo algorithms based on Markov chain simulation have been in use for many years. The validity of these algorithms depends crucially on the rate ofExpand
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Large Cliques Elude the Metropolis Process
  • M. Jerrum
  • Mathematics, Computer Science
  • Random Struct. Algorithms
  • 1992
In a random graph on n vertices, the maximum clique is likely to be of size very close to 2 lg n. However, the clique produced by applying the naive “greedy” heuristic to a random graph is unlikelyExpand
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