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Algorithm Case Studies

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Guide to Graph Colouring

Part of the book series: Texts in Computer Science ((TCS))

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Abstract

In this chapter, we present detailed descriptions of six different high-performance algorithms for the graph colouring problem. We also compare the performance of these algorithms over a wide range of graphs to gauge their relative strengths and weaknesses. The considered problem instances include random, flat, planar, and scale-free graphs, together with some real-world graphs from the fields of timetabling and social networking.

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Notes

  1. 1.

    Note that in some cases a Kempe chain will contain all vertices in both colour classes, that is, the graph induced by \(S_i\cup S_j\) will form a connected bipartite graph. Kempe chains of this type are known as total, and interchanging their colours serves no purpose since this only results in the two colour classes being relabelled. Consequently, total Kempe chains are ignored by the algorithm.

  2. 2.

    These parameters can be altered in our source code, however.

  3. 3.

    As in Chap. 3, statistical significance is claimed here according to the nonparametric related samples Wilcoxon signed-rank test (for pairwise comparisons), and the related samples Friedman’s two-way analysis of variance by ranks (for group comparisons). For the remainder of this chapter, statistical significance is claimed at the 1% level.

  4. 4.

    Using a 3.0 GHz Windows 7 machine with 3.87 GB RAM.

  5. 5.

    Consequently, the reported results for TabuCol and PartialCol in Table 5.3 are produced using an initial k generated by executing the Greedy algorithm with a random permutation of the vertices.

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Authors and Affiliations

  1. Cardiff School of Mathematics, Cardiff University, Cardiff, UK

    R. M. R. Lewis

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Correspondence to R. M. R. Lewis .

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Lewis, R.M.R. (2021). Algorithm Case Studies. In: Guide to Graph Colouring. Texts in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-030-81054-2_5

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  • DOI: https://doi.org/10.1007/978-3-030-81054-2_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-81053-5

  • Online ISBN: 978-3-030-81054-2

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