A more rapidly mixing Markov chain for graph colorings
proceedings of the eighth international conference on Random structures and algorithms
Faster random generation of linear extensions
Discrete Mathematics - Special issue on partial ordered sets
Markov Chain Algorithms for Planar Lattice Structures
SIAM Journal on 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
Compact error-resilient computational DNA tiling assemblies
DNA'04 Proceedings of the 10th international conference on DNA computing
Random lattice triangulations: structure and algorithms
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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Monotonic surfaces spanning finite regions of Zd arise in many contexts, including DNA-based self-assembly, card-shuffling and lozenge tilings. We explore how we can sample these surfaces when the distribution is biased to favor higher surfaces. We show that a natural local chain is rapidly mixing with any bias for regions in Z2, and for bias λ d2 in Zd, when d 2. Moreover, our bounds on the mixing time are optimal on d-dimensional hyper-cubic regions. The proof uses a geometric distance function and introduces a variant of path coupling in order to handle distances that are exponentially large.