Corpus ID: 4780474

# Rapid mixing of Glauber dynamics for colorings below Vigoda's 11/6 threshold

@article{Delcourt2018RapidMO,
title={Rapid mixing of Glauber dynamics for colorings below Vigoda's 11/6 threshold},
author={Michelle Delcourt and Guillem Perarnau and Luke Postle},
journal={ArXiv},
year={2018},
volume={abs/1804.04025}
}
• Published 11 April 2018
• Mathematics, Computer Science
• ArXiv
A well-known conjecture in computer science and statistical physics is that Glauber dynamics on the set of $k$-colorings of a graph $G$ on $n$ vertices with maximum degree $\Delta$ is rapidly mixing for $k \geq \Delta +2$. In FOCS 1999, Vigoda showed rapid mixing of flip dynamics with certain flip parameters on the set of proper $k$-colorings for $k > \frac{11}{6}\Delta$, implying rapid mixing for Glauber dynamics. In this paper, we obtain the first improvement beyond the $\frac{11}{6}\Delta… Expand Improved Bounds for Randomly Sampling Colorings via Linear Programming • Computer Science, Physics • SODA • 2019 Two approaches are used to give two proofs that the Glauber dynamics is rapidly mixing for any$k\ge\left(\frac{11}{6} - \epsilon_0\right)\Delta$for some absolute constant$k > 2 \Delta$. Expand Frozen$(\Delta+1)$-colourings of bounded degree graphs • Mathematics • 2018 Let$G$be a graph of maximum degree$\Delta$and$k$be an integer. The$k$-recolouring graph of$G$is the graph whose vertices are$k$-colourings of$G$and where two$k$-colourings are adjacentExpand The Glauber dynamics for edges colourings of trees • Computer Science, Mathematics • Random Struct. Algorithms • 2020 This paper shows that for k ≥ ∆ + 1 the Glauber dynamics for k-edge-colourings of T mixes in polynomial time in n, and bound on the number of colours is best possible as the chain is not even ergodic for k ≤ ∆. Expand A Simple Parallel and Distributed Sampling Technique: Local Glauber Dynamics • Computer Science, Mathematics • DISC • 2018 This work proposes a simple local update rule based on the Glauber dynamics that leads to efficient parallel and distributed algorithms for sampling from Gibbs distributions and can sample a uniform proper coloring with$(2+\eps)\Delta$colors in$O(\log n) rounds, for any constant $\eps >0$. Expand
Weighted counting of solutions to sparse systems of equations
• Mathematics, Computer Science
• Combinatorics, Probability and Computing
• 2019
An algorithm is presented which, for a set X defined by a system of homogeneous linear equations with at most r variables per equation and at most c equations per variable, computes w(X) within relative error ∊ > 0 in (rc)O(ln n-ln ∊) time. Expand
Frozen (Δ + 1)-colourings of bounded degree graphs
• Mathematics
• 2020
Let G be a graph of maximum degree ∆ and k be an integer. The k-recolouring graph of G is the graph whose vertices are k-colourings of G and where two k-colourings are adjacent if they differ atExpand
Approximation schemes for randomly sampling colorings
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Reconfiguration and combinatorial games
Cette these explore des problematiques liees aux jeux. Les jeux qui nous interessent sont ceux pour lesquels il n'y a pas d'information cachee: tout les joueurs ont acces a toute l'informationExpand

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