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A Hybrid Approach for Exact Coloring of Massive Graphs

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Integration of Constraint Programming, Artificial Intelligence, and Operations Research (CPAIOR 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11494))

Abstract

The graph coloring problem appears in numerous applications, yet many state-of-the-art methods are hardly applicable to real world, very large, networks. The most efficient approaches for massive graphs rely on “peeling” the graph of its low-degree vertices and focus on the maximum k-core where k is some lower bound on the chromatic number of the graph. However, unless the graphs are extremely sparse, the cores can be very large, and lower and upper bounds are often obtained using greedy heuristics.

In this paper, we introduce a combined approach using local search to find good quality solutions on massive graphs as well as locate small subgraphs with potentially large chromatic number. The subgraphs can be used to compute good lower bounds, which makes it possible to solve optimally extremely large graphs, even when they have large k-cores.

G. Katsirelos—The second author was partially supported by the french “Agence nationale de la Recherche”, project DEMOGRAPH, reference ANR-16-C40-0028.

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Notes

  1. 1.

    http://www.info.univ-angers.fr/~porumbel/graphs/.

  2. 2.

    denotes our implementation of the Dsatur heuristic.

  3. 3.

    Ties broken by overall degree.

  4. 4.

    Sources available at: https://bitbucket.org/gkatsi/minicsp.

  5. 5.

    Sources available at: https://bitbucket.org/gkatsi/gc-cdcl/src/master/.

  6. 6.

    Personnal communication with the authors.

  7. 7.

    email-Eu-core, email-EuAll, Gnutella08/09, bitcoinalpha, bitcoinotc, facebook, gplus, CollegeMsg and sx-superuser.

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Author information

Authors and Affiliations

  1. LAAS-CNRS, Université de Toulouse, CNRS, Toulouse, France

    Emmanuel Hebrard

  2. MIAT, UR-875, INRA, Toulouse, France

    George Katsirelos

Authors
  1. Emmanuel Hebrard
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  2. George Katsirelos
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Corresponding author

Correspondence to Emmanuel Hebrard .

Editor information

Editors and Affiliations

  1. Ecole Polytechnique de Montréal, Montréal, QC, Canada

    Louis-Martin Rousseau

  2. University of Western Macedonia, Kozani, Greece

    Kostas Stergiou

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Hebrard, E., Katsirelos, G. (2019). A Hybrid Approach for Exact Coloring of Massive Graphs. In: Rousseau, LM., Stergiou, K. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2019. Lecture Notes in Computer Science(), vol 11494. Springer, Cham. https://doi.org/10.1007/978-3-030-19212-9_25

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  • DOI: https://doi.org/10.1007/978-3-030-19212-9_25

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-19211-2

  • Online ISBN: 978-3-030-19212-9

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