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Tackling the maximum happy vertices problem in large networks

Thiruvady, Dhananjay, Lewis, Rhyd and Morgan, Kerri 2020. Tackling the maximum happy vertices problem in large networks. 4OR: A Quarterly Journal of Operations Research 10.1007/s10288-020-00431-4
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Abstract

Abstract In this paper we consider a variant of graph colouring known as the maximum happy vertices problem. This problem involves taking a graph in which a subset of the vertices have been preassigned to colours. The objective is to then colour the remaining vertices such that the number of happy vertices is maximised, where a vertex is considered happy only when it is assigned to the same colour as all of its neighbours. We design and test a tabu search approach, which is compared to two existing state of the art methods. We see that this new approach is particularly suited to larger problem instances and finds very good solutions in very short time frames. We also propose a algorithm to find upper bounds for the problem efficiently. Moreover, we propose an algorithm for imposing additional precoloured vertices and are hence able to significantly reduce the solution space. Finally, we present an analysis of this problem and use probabilistic arguments to characterise problem hardness.

Item Type: Article
Date Type: Published Online
Status: In Press
Schools: Mathematics
Publisher: Springer Verlag (Germany)
ISSN: 1619-4500
Date of First Compliant Deposit: 20 February 2020
Date of Acceptance: 11 February 2020
Last Modified: 10 Mar 2020 20:10
URI: http://orca.cf.ac.uk/id/eprint/129862

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