Alistair Sinclair

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A randomised approximation scheme for the permanent of a 0-1 matrix is presented. The task of estimating a permanent is reduced to that of almost uniformly generating perfect matchings in a graph; the latter is accomplished by simulating a Markov chain whose states are the matchings in the graph. For a wide class of 0-1 matrices the approximation scheme is(More)
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 of convergence to equilibrium of the Markov chain being simulated. Unfortunately, the classical theory of stochastic processes hardly touches on the sort of non-asymptotic(More)
The paper presents a randomised algorithm which evaluates the partition function of an arbitrary ferromagnetic Ising system to any speci ed degree of accuracy. The running time of the algorithm increases only polynomially with the size of the system (i.e., the number of sites) and a parameter which controls the accuracy of the result. Further approximation(More)
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, for self-reducible structures, almost uniform generation is possible in polynomial time provided only that randomised approximate counting to within some arbitrary(More)
Will reading habit influence your life? Many say yes. Reading algorithms for random generation and counting a markov chain approach progress in theoretical computer science is a good habit; you can develop this habit to be such interesting way. Yeah, reading habit will not only make you have any favourite activity. It will be one of guidance of your life.(More)
We study the ability of decentralized, local dynamics in non-cooperative games to rapidly reach an approximate Nash equilibrium. For symmetric congestion games in which the edge delays satisfy a "bounded jump" condition, we show that convergence to an ε-Nash equilibrium occurs within a number of steps that is polynomial in the number of players and(More)