Approximately counting up to four (extended abstract)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Random generation of embedded graphs and an extension to Dobrushin uniqueness (extended abstract)
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Graph orientations with no sink and an approximation for a hard case of #SAT
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Determinant algorithms for random planar structures
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Random three-dimensional tilings of Aztec octahedra and tetrahedra: an extension of domino tilings
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Ribbon tile invariants from the signed area
Journal of Combinatorial Theory Series A
Random Structures & Algorithms
Parallel 'Go with the Winners' Algorithms in the LogP Model
IPPS '97 Proceedings of the 11th International Symposium on Parallel Processing
A Note on Bounding the Mixing Time by Linear Programming
RANDOM '98 Proceedings of the Second International Workshop on Randomization and Approximation Techniques in Computer Science
Random dyadic tilings of the unit square
Random Structures & Algorithms - Special issue: Proceedings of the tenth international conference "Random structures and algorithms"
Theoretical Computer Science - Special issue: Tilings of the plane
The bounded eight-vertex model
Theoretical Computer Science - Special issue: Tilings of the plane
Parallel 'go with the winners' algorithms in distributed memory models
Journal of Parallel and Distributed Computing - Special section best papers from the 2002 international parallel and distributed processing symposium
Convergence of the Iterated Prisoner's Dilemma Game
Combinatorics, Probability and Computing
Domino tilings and related models: space of configurations of domains with holes
Theoretical Computer Science - Combinatorics of the discrete plane and tilings
Coupling and self-stabilization
Distributed Computing - Special issue: DISC 04
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Consider the following Markov chain, whose states are all domino tilings of a 2n/spl times/2n chessboard: starting from some arbitrary tiling, pick a 2/spl times/2 window uniformly at random. If the four squares appearing in this window are covered by two parallel dominoes, rotate the dominoes in place. Repeat many times. This process is used in practice to generate a random tiling and is a key tool in the study of the combinatorics of tilings and the behavior of dimer systems in statistical physics. Analogous Markov chains are used to randomly generate other structures on various two-dimensional lattices. The paper presents techniques which prove for the first time that, in many interesting cases, a small number of random moves suffice to obtain a uniform distribution.