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Chromatic Scheduling and the Chromatic Number Problem

Author

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  • J. Randall Brown

    (Kent State University)

Abstract

The chromatic scheduling problem may be defined as any problem in which the solution is a partition of a set of objects. Since the partitions may not be distinct, redundant solutions can be generated when partial enumeration techniques are applied to chromatic scheduling problems. The necessary theory is developed to prevent redundant solutions in the application of partial enumeration techniques to chromatic scheduling problems with indistinguishable partitions and distinct objects. The chromatic number problem, which is the problem of finding the chromatic number of any graph, is a particular case of the chromatic scheduling problem. Two algorithms, basic and look-ahead, are developed for the chromatic number problem. Computational experience is given for each algorithm.

Suggested Citation

  • J. Randall Brown, 1972. "Chromatic Scheduling and the Chromatic Number Problem," Management Science, INFORMS, vol. 19(4-Part-1), pages 456-463, December.
    • Handle: RePEc:inm:ormnsc:v:19:y:1972:i:4-part-1:p:456-463
    DOI: 10.1287/mnsc.19.4.456
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    Cited by:

    1. 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.
    2. 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.
    3. Benjamin McClosky & John D. Arellano & Illya V. Hicks, 2015. "Co-2-plex vertex partitions," Journal of Combinatorial Optimization, Springer, vol. 30(3), pages 729-746, October.
    4. 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.
    5. 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.
    6. Isnaini Rosyida & Jin Peng & Lin Chen & Widodo Widodo & Ch. Rini Indrati & Kiki A. Sugeng, 2018. "An uncertain chromatic number of an uncertain graph based on $$\alpha $$ α -cut coloring," Fuzzy Optimization and Decision Making, Springer, vol. 17(1), pages 103-123, March.
    7. 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.
    8. Severino F. Galán, 2017. "Simple decentralized graph coloring," Computational Optimization and Applications, Springer, vol. 66(1), pages 163-185, January.
    9. 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.
    10. 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.
    11. Muñoz, Susana & Teresa Ortuño, M. & Ramírez, Javier & Yáñez, Javier, 2005. "Coloring fuzzy graphs," Omega, Elsevier, vol. 33(3), pages 211-221, June.

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