Efthymiou, Charilaos (2012) A simple algorithm for random colouring G(n, d/n) using (2 + ε)d colours. In: 23rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2012, Kyoto, Japan, 17-19 Jan 2012. Published in: Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms pp. 272-280. ISSN 9781611972108.

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Abstract

Approximate random k-colouring of a graph G = (V, E) is a very well studied problem in computer science and statistical physics. It amounts to constructing a k-colouring of G which is distributed close to Gibbs distribution, i.e. the uniform distribution over all the k-colourings of G. Here, we deal with the problem when the underlying graph is an instance of Erdocombining double acute accents-Rényi random graph G(n, p), where p = d/n and d is fixed. We propose a novel efficient algorithm for approximate random k-colouring with the following properties: given an instance of G(n, d/n) and for any k ≥ (2 + ε)d, it returns a k-colouring distributed within total variation distance n -Ω(1) from the Gibbs distribution, with probability 1 - n -Ω(1). What we propose is neither a MCMC algorithm nor some algorithm inspired by the message passing heuristics that were introduced by statistical physicists. Our algorithm is of combinatorial nature. It is based on a rather simple recursion which reduces the random k-colouring of G(n, d/n) to random k-colouring simpler subgraphs first. The lower bound on the number of colours for our algorithm to run in polynomial time is significantly smaller than the corresponding bounds we have for any previous algorithm. Copyright © SIAM.

Item Type:	Conference Item (Paper)
Divisions:	Faculty of Science > Computer Science Faculty of Science > Mathematics
Journal or Publication Title:	Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
Publisher:	SIAM
ISSN:	9781611972108
Official Date:	2012
Dates:	Date Event 2012 Published
Page Range:	pp. 272-280
Status:	Not Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Conference Paper Type:	Paper
Title of Event:	23rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2012
Type of Event:	Conference
Location of Event:	Kyoto, Japan
Date(s) of Event:	17-19 Jan 2012

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