The Glauber Dynamics for Colourings of Bounded Degree Trees

Authors:
Brendan Lucier;Michael Molloy;Yuval Peres
Affiliations:
Dept of Computer Science, University of Toronto,;Dept of Computer Science, University of Toronto,;Microsoft Research,
Venue:
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Year:
2009

Citing 6
Cited 1

Approximating the permanent

SIAM Journal on Computing
A very simple algorithm for estimating the number of k-colorings of a low-degree graph

Random Structures & Algorithms
Very rapidly mixing Markov Chains for 2&Dgr;-colorings and for independent sets in a graph with maximum degree 4

Random Structures & Algorithms
Mixing

FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Randomly coloring planar graphs with fewer colors than the maximum degree

Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Fast mixing for independent sets, colorings, and other models on trees

Random Structures & Algorithms

Phase transition for the mixing time of the Glauber dynamics for coloring regular trees

SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms

Quantified Score

Hi-index	0.00

Visualization

Abstract

We study the Glauber dynamics Markov chain for k -colourings of trees with maximum degree Δ. For k *** 3, we show that the mixing time on every tree is at most n O (1 + Δ/(k logΔ)). This bound is tight up to the constant factor in the exponent, as evidenced by the complete tree. Our proof uses a weighted canonical paths analysis and a variation of the block dynamics that exploits the differing relaxation times of blocks.