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A simple algorithm for random colouring G(n, d/n) using (2 + ε)d colours
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Efthymiou, Charilaos (2012) A simple algorithm for random colouring G(n, d/n) using (2 + ε)d colours. In: 23rd Annual ACMSIAM Symposium on Discrete Algorithms, SODA 2012, Kyoto, Japan, 1719 Jan 2012. Published in: Proceedings of the Annual ACMSIAM Symposium on Discrete Algorithms pp. 272280.
Full text not available from this repository.Abstract
Approximate random kcolouring of a graph G = (V, E) is a very well studied problem in computer science and statistical physics. It amounts to constructing a kcolouring of G which is distributed close to Gibbs distribution, i.e. the uniform distribution over all the kcolourings of G. Here, we deal with the problem when the underlying graph is an instance of Erdocombining double acute accentsRényi random graph G(n, p), where p = d/n and d is fixed. We propose a novel efficient algorithm for approximate random kcolouring with the following properties: given an instance of G(n, d/n) and for any k ≥ (2 + ε)d, it returns a kcolouring 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 kcolouring of G(n, d/n) to random kcolouring 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 ACMSIAM Symposium on Discrete Algorithms  
Publisher:  SIAM  
ISSN:  9781611972108  
Official Date:  2012  
Dates: 


Page Range:  pp. 272280  
Status:  Not Peer Reviewed  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 ACMSIAM Symposium on Discrete Algorithms, SODA 2012  
Type of Event:  Conference  
Location of Event:  Kyoto, Japan  
Date(s) of Event:  1719 Jan 2012  
URI:  http://wrap.warwick.ac.uk/id/eprint/49282 
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