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

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 maximise… Expand

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

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

A randomised algorithm which evaluates the partition function of an arbitrary ferromagnetic Ising system to any specified degree of accuracy is presented.Expand

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

It is shown that the Metropolis process takes super-polynomial time to locate a clique that is only slightly bigger than that produced by the greedy heuristic, which is one step above the greedy one in its level of sophistication.Expand

The results show that for two general kinds of concept class the V-C dimension is polynomially bounded in the number of real numbers used to define a problem instance, and that in the continuous case, as in the discrete, the real barrier to efficient learning in the Occam sense is complexity- theoretic and not information-theoretic.Expand