The mixing time of Glauber dynamics for coloring regular trees

The mixing time of Glauber dynamics for coloring regular trees

We consider Metropolis Glauber dynamics for sampling proper q‐colorings of the n‐vertex complete b‐ary tree when 3 ≤ q ≤ b/(2lnb). We give both upper and lower bounds on the mixing time. Our upper bound is nO(b/ log b) and our lower bound is nΩ(b/(q log b)), where the constants implicit in the O() a...

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Veröffentlicht in:Random structures & algorithms 2010-07, Vol.36 (4), p.464-476
Hauptverfasser: Goldberg, Leslie Ann, Jerrum, Mark, Karpinski, Marek
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
Coloring
coloring trees
Dynamics
Glauber dynamics
Lower bounds
mixing time
Reproduction
Sampling
Trees
Upper bounds
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Zusammenfassung:We consider Metropolis Glauber dynamics for sampling proper q‐colorings of the n‐vertex complete b‐ary tree when 3 ≤ q ≤ b/(2lnb). We give both upper and lower bounds on the mixing time. Our upper bound is nO(b/ log b) and our lower bound is nΩ(b/(q log b)), where the constants implicit in the O() and Ω() notation do not depend upon n, q or b. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 2010
ISSN:1042-9832
1098-2418
1098-2418
DOI:10.1002/rsa.20303