IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v48y2001i6p518-550.html
   My bibliography  Save this article

Iterative coloring extension of a maximum clique

Author

Listed:
  • Massimiliano Caramia
  • Paolo Dell'Olmo

Abstract

In this paper we present an improved branch and bound algorithm for the vertex coloring problem. The idea is to try to extend the coloring of a maximum clique to its adjacent vertices. If this succeeds, its successive neighbors are considered; in case of failure (i.e., in the case the initial colors are not sufficient), working on the subgraph induced by the maximum clique and its neighborhood, the lower bound is improved by seeking for an optimal coloring of this subgraph by branch and bound. The process is repeated iteratively until the whole graph is examined. The iterative scheme exploits a further lower bound obtained by integrating a simple algorithm into the maximum clique search, and a new method to compute upper bounds on subgraphs. Furthermore, a new branching rule and a method for the selection of the initial maximum clique are presented. Extensive computational results and comparisons with existing exact coloring algorithms on random graphs and benchmarks are given. © 2001 John Wiley & Sons, Inc. Naval Research Logistic 48: 518–550, 2001

Suggested Citation

  • Massimiliano Caramia & Paolo Dell'Olmo, 2001. "Iterative coloring extension of a maximum clique," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(6), pages 518-550, September.
    • Handle: RePEc:wly:navres:v:48:y:2001:i:6:p:518-550
    DOI: 10.1002/nav.1033
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/nav.1033
    Download Restriction: no
    File URL: https://libkey.io/10.1002/nav.1033?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. David S. Johnson & Cecilia R. Aragon & Lyle A. McGeoch & Catherine Schevon, 1991. "Optimization by Simulated Annealing: An Experimental Evaluation; Part II, Graph Coloring and Number Partitioning," Operations Research, INFORMS, vol. 39(3), pages 378-406, June.
    2. de Werra, D., 1985. "An introduction to timetabling," European Journal of Operational Research, Elsevier, vol. 19(2), pages 151-162, February.
    3. Anuj Mehrotra & Michael A. Trick, 1996. "A Column Generation Approach for Graph Coloring," INFORMS Journal on Computing, INFORMS, vol. 8(4), pages 344-354, November.
    4. Cangalovic, Mirjana & Schreuder, Jan A. M., 1991. "Exact colouring algorithm for weighted graphs applied to timetabling problems with lectures of different lengths," European Journal of Operational Research, Elsevier, vol. 51(2), pages 248-258, March.
    5. J. Randall Brown, 1972. "Chromatic Scheduling and the Chromatic Number Problem," Management Science, INFORMS, vol. 19(4-Part-1), pages 456-463, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Caramia, Massimiliano & Dell'Olmo, Paolo, 2008. "Embedding a novel objective function in a two-phased local search for robust vertex coloring," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1358-1380, September.
    2. Severino F. Galán, 2017. "Simple decentralized graph coloring," Computational Optimization and Applications, Springer, vol. 66(1), pages 163-185, January.
    3. Enrico Malaguti & Michele Monaci & Paolo Toth, 2008. "A Metaheuristic Approach for the Vertex Coloring Problem," INFORMS Journal on Computing, INFORMS, vol. 20(2), pages 302-316, May.
    4. Drexl, Andreas & Juretzka, Jan & Salewski, Frank, 1993. "Academic course scheduling under workload and changeover constraints," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 337, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    5. Vincenzo Cutello & Giuseppe Nicosia & Mario Pavone, 2007. "An immune algorithm with stochastic aging and kullback entropy for the chromatic number problem," Journal of Combinatorial Optimization, Springer, vol. 14(1), pages 9-33, July.
    6. Iztok Fister & Marjan Mernik & Bogdan Filipič, 2013. "Graph 3-coloring with a hybrid self-adaptive evolutionary algorithm," Computational Optimization and Applications, Springer, vol. 54(3), pages 741-770, April.
    7. Jagota, Arun, 1996. "An adaptive, multiple restarts neural network algorithm for graph coloring," European Journal of Operational Research, Elsevier, vol. 93(2), pages 257-270, September.
    8. Nicolas Zufferey & Olivier Labarthe & David Schindl, 2012. "Heuristics for a project management problem with incompatibility and assignment costs," Computational Optimization and Applications, Springer, vol. 51(3), pages 1231-1252, April.
    9. Xiao-Feng Xie & Jiming Liu, 2009. "Graph coloring by multiagent fusion search," Journal of Combinatorial Optimization, Springer, vol. 18(2), pages 99-123, August.
    10. M Plumettaz & D Schindl & N Zufferey, 2010. "Ant Local Search and its efficient adaptation to graph colouring," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(5), pages 819-826, May.
    11. Syam Menon & Rakesh Gupta, 2008. "Optimal Broadcast Scheduling in Packet Radio Networks via Branch and Price," INFORMS Journal on Computing, INFORMS, vol. 20(3), pages 391-399, August.
    12. Valmir C. Barbosa & Carlos A.G. Assis & Josina O. Do Nascimento, 2004. "Two Novel Evolutionary Formulations of the Graph Coloring Problem," Journal of Combinatorial Optimization, Springer, vol. 8(1), pages 41-63, March.
    13. S. Butenko & P. Festa & P. M. Pardalos, 2001. "On the Chromatic Number of Graphs," Journal of Optimization Theory and Applications, Springer, vol. 109(1), pages 69-83, April.
    14. Muñoz, Susana & Teresa Ortuño, M. & Ramírez, Javier & Yáñez, Javier, 2005. "Coloring fuzzy graphs," Omega, Elsevier, vol. 33(3), pages 211-221, June.
    15. Samir Elhedhli & Lingzi Li & Mariem Gzara & Joe Naoum-Sawaya, 2011. "A Branch-and-Price Algorithm for the Bin Packing Problem with Conflicts," INFORMS Journal on Computing, INFORMS, vol. 23(3), pages 404-415, August.
    16. P Lara-Velázquez & R López-Bracho & J Ramírez-Rodríguez & J Yáñez, 2011. "A model for timetabling problems with period spread constraints," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(1), pages 217-222, January.
    17. Bernard Gendron & Alain Hertz & Patrick St-Louis, 2007. "On edge orienting methods for graph coloring," Journal of Combinatorial Optimization, Springer, vol. 13(2), pages 163-178, February.
    18. Valls, Vicente & Perez, Angeles & Quintanilla, Sacramento, 1996. "A graph colouring model for assigning a heterogeneous workforce to a given schedule," European Journal of Operational Research, Elsevier, vol. 90(2), pages 285-302, April.
    19. Avanthay, Cedric & Hertz, Alain & Zufferey, Nicolas, 2003. "A variable neighborhood search for graph coloring," European Journal of Operational Research, Elsevier, vol. 151(2), pages 379-388, December.
    20. Drexl, Andreas & Salewski, Frank, 1997. "Distribution requirements and compactness constraints in school timetabling," European Journal of Operational Research, Elsevier, vol. 102(1), pages 193-214, October.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:navres:v:48:y:2001:i:6:p:518-550. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.