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Combining CP and ILP in a Tree Decomposition of Bounded Height for the Sum Colouring Problem

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Integration of AI and OR Techniques in Constraint Programming (CPAIOR 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10335))

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Abstract

The Sum Colouring Problem is an \({\mathcal {NP}}\)-hard problem derived from the well-known graph colouring problem. It consists in finding a proper colouring which minimizes the sum of the assigned colours rather than the number of those colours. This problem often arises in scheduling and resource allocation. In this paper, we conduct an in-depth evaluation of ILP and CP’s capabilities to solve this problem, with several improvements. Moreover, we propose to combine ILP and CP in a tree decomposition with a bounded height. Finally, those methods are combined in a portfolio approach to take advantage from their complementarity.

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Notes

  1. 1.

    http://mat.gsia.cmu.edu/COLOR02.

  2. 2.

    ftp://dimacs.rutgers.edu/pub/challenge/graph/benchmarks/color/.

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Acknowledgements

This work has been supported by the ANR project SoLStiCe (ANR-13-BS02-0002-01).

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Authors and Affiliations

  1. Université de Lyon - LIRIS, Lyon, France

    Maël Minot, Samba Ndojh Ndiaye & Christine Solnon

  2. Université Lyon 1, LIRIS, UMR5205, 69622, Lyon, France

    Samba Ndojh Ndiaye

  3. INSA-Lyon, LIRIS, UMR5205, 69621, Lyon, France

    Maël Minot & Christine Solnon

Authors
  1. Maël Minot
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  2. Samba Ndojh Ndiaye
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  3. Christine Solnon
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Correspondence to Maël Minot .

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Editors and Affiliations

  1. University of Padua, Padua, Italy

    Domenico Salvagnin

  2. University of Bologna, Bologna, Italy

    Michele Lombardi

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Minot, M., Ndiaye, S.N., Solnon, C. (2017). Combining CP and ILP in a Tree Decomposition of Bounded Height for the Sum Colouring Problem. In: Salvagnin, D., Lombardi, M. (eds) Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2017. Lecture Notes in Computer Science(), vol 10335. Springer, Cham. https://doi.org/10.1007/978-3-319-59776-8_29

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  • DOI: https://doi.org/10.1007/978-3-319-59776-8_29

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  • Online ISBN: 978-3-319-59776-8

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