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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
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
Random Generation of Combinatorial Structures from a Uniform Distribution
TLDR
It is shown that exactly uniform generation of ‘efficiently verifiable’ combinatorial structures is reducible to approximate counting (and hence, is within the third level of the polynomial hierarchy). 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 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.
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
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
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
Improved approximation algorithms for MAXk-CUT and MAX BISECTION
Polynomial-time approximation algorithms with nontrivial performance guarantees are presented for the problems of (a) partitioning the vertices of a weighted graph intok blocks so as to maximize theExpand
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