Tiling with bars under tomographic constraints
Theoretical Computer Science
Tilings of rectangles with T-tetrominoes
Theoretical Computer Science - Combinatorics of the discrete plane and tilings
Tilings with trichromatic colored-edges triangles
Theoretical Computer Science - Combinatorics of the discrete plane and tilings
Efficiency test of pseudorandom number generators using random walks
Journal of Computational and Applied Mathematics
ACM Transactions on Algorithms (TALG)
Distributed selfish load balancing
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Rapidly Mixing Markov Chains with Applications in Computer Science and Physics
Computing in Science and Engineering
Disjoint Decomposition of Markov Chains and Sampling Circuits in Cayley Graphs
Combinatorics, Probability and Computing
Path coupling without contraction
Journal of Discrete Algorithms
Randomly coloring planar graphs with fewer colors than the maximum degree
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Torpid mixing of local Markov chains on 3-colorings of the discrete torus
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Slow Mixing of Markov Chains Using Fault Lines and Fat Contours
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Sampling biased lattice configurations using exponential metrics
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Sampling Eulerian orientations of triangular lattice graphs
Journal of Discrete Algorithms
Mixing time for the solid-on-solid model
Proceedings of the forty-first annual ACM symposium on Theory of computing
Convergence to equilibria in distributed, selfish reallocation processes with weighted tasks
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Theoretical Computer Science
Approximating fixation probabilities in the generalized Moran process
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
A Deterministic Polynomial-Time Approximation Scheme for Counting Knapsack Solutions
SIAM Journal on Computing
Time hierarchies for sampling distributions
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
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Consider the following Markov chain, whose states are all domino tilings of a 2n× 2n chessboard: starting from some arbitrary tiling, pick a 2×2 window uniformly at random. If the four squares appearing in this window are covered by two parallel dominoes, rotate the dominoes $90^{\rm o}$ in place. Repeat many times. This process is used in practice to generate a random tiling and is a widely used 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. This 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.