# Alistair Sinclair

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 probability distribution. Such a sampling procedure lies at the heart of efficient probabilistic algorithms for a wide variety of problems, such as approximating the size ofâ€¦ (More)
• SIAM J. Comput.
• 1989
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 isâ€¦ (More)
• SIAM J. Comput.
• 1993
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 approximationâ€¦ (More)
• WG
• 1987
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 arbitraryâ€¦ (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.â€¦ (More)
• ISTCS
• 1993
Let A be a Las Vegas algorithm, i.e., A is a randomized algorithm that always produces the correct answer when it stops but whose running time is a random variable. We consider the problem of minimizing the expected time required to obtain an answer from A using strategies which simulate A as follows: run A for a fixed amount of time t1 , then run Aâ€¦ (More)
• SODA
• 2007
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 &#949;-Nash equilibrium occurs within a number of steps that is polynomial in the number of players andâ€¦ (More)