Minimizing Unsatisfaction in Colourful Neighbourhoods
Data Structures and Algorithms
2009-11-13 v3 Disordered Systems and Neural Networks
Computational Complexity
Abstract
Colouring sparse graphs under various restrictions is a theoretical problem of significant practical relevance. Here we consider the problem of maximizing the number of different colours available at the nodes and their neighbourhoods, given a predetermined number of colours. In the analytical framework of a tree approximation, carried out at both zero and finite temperatures, solutions obtained by population dynamics give rise to estimates of the threshold connectivity for the incomplete to complete transition, which are consistent with those of existing algorithms. The nature of the transition as well as the validity of the tree approximation are investigated.
Keywords
Cite
@article{arxiv.0704.3835,
title = {Minimizing Unsatisfaction in Colourful Neighbourhoods},
author = {K. Y. Michael Wong and David Saad},
journal= {arXiv preprint arXiv:0704.3835},
year = {2009}
}