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An Unconstrained Quadratic Binary Programming Approach to the Vertex Coloring Problem

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  • Gary Kochenberger
  • Fred Glover
  • Bahram Alidaee
  • Cesar Rego

Abstract

The vertex coloring problem has been the subject of extensive research for many years. Driven by application potential as well as computational challenge, a variety of methods have been proposed for this difficult class of problems. Recent successes in the use of the unconstrained quadratic programming (UQP) model as a unified framework for modeling and solving combinatorial optimization problems have motivated a new approach to the vertex coloring problem. In this paper we present a UQP approach to this problem and illustrate its attractiveness with preliminary computational experience. Copyright Springer Science + Business Media, Inc. 2005

Suggested Citation

  • Gary Kochenberger & Fred Glover & Bahram Alidaee & Cesar Rego, 2005. "An Unconstrained Quadratic Binary Programming Approach to the Vertex Coloring Problem," Annals of Operations Research, Springer, vol. 139(1), pages 229-241, October.
    • Handle: RePEc:spr:annopr:v:139:y:2005:i:1:p:229-241:10.1007/s10479-005-3449-7
    DOI: 10.1007/s10479-005-3449-7
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    References listed on IDEAS

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    1. R. D. McBride & J. S. Yormark, 1980. "An Implicit Enumeration Algorithm for Quadratic Integer Programming," Management Science, INFORMS, vol. 26(3), pages 282-296, March.
    2. Glover, Fred & Alidaee, Bahram & Rego, Cesar & Kochenberger, Gary, 2002. "One-pass heuristics for large-scale unconstrained binary quadratic problems," European Journal of Operational Research, Elsevier, vol. 137(2), pages 272-287, March.
    3. Billionnet, A. & Sutter, A., 1994. "Minimization of a quadratic pseudo-Boolean function," European Journal of Operational Research, Elsevier, vol. 78(1), pages 106-115, October.
    4. Fred Glover & Gary A. Kochenberger & Bahram Alidaee, 1998. "Adaptive Memory Tabu Search for Binary Quadratic Programs," Management Science, INFORMS, vol. 44(3), pages 336-345, March.
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    Cited by:

    1. Fred Glover & Gary Kochenberger & Rick Hennig & Yu Du, 2022. "Quantum bridge analytics I: a tutorial on formulating and using QUBO models," Annals of Operations Research, Springer, vol. 314(1), pages 141-183, July.
    2. Lü, Zhipeng & Glover, Fred & Hao, Jin-Kao, 2010. "A hybrid metaheuristic approach to solving the UBQP problem," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1254-1262, December.
    3. Alidaee, Bahram & Kochenberger, Gary & Lewis, Karen & Lewis, Mark & Wang, Haibo, 2008. "A new approach for modeling and solving set packing problems," European Journal of Operational Research, Elsevier, vol. 186(2), pages 504-512, April.
    4. Alidaee, Bahram & Glover, Fred & Kochenberger, Gary & Wang, Haibo, 2007. "Solving the maximum edge weight clique problem via unconstrained quadratic programming," European Journal of Operational Research, Elsevier, vol. 181(2), pages 592-597, September.
    5. Rupaj Kumar Nayak & Nirmalya Kumar Mohanty, 2019. "Improved row-by-row method for binary quadratic optimization problems," Annals of Operations Research, Springer, vol. 275(2), pages 587-605, April.
    6. Sidi Mohamed Douiri & Souad Elbernoussi, 2012. "The Unconstrained Binary Quadratic Programming for the Sum Coloring Problem," Modern Applied Science, Canadian Center of Science and Education, vol. 6(9), pages 1-26, September.
    7. Wang, Yang & Lü, Zhipeng & Glover, Fred & Hao, Jin-Kao, 2012. "Path relinking for unconstrained binary quadratic programming," European Journal of Operational Research, Elsevier, vol. 223(3), pages 595-604.
    8. Neng Fan & Panos Pardalos, 2010. "Linear and quadratic programming approaches for the general graph partitioning problem," Journal of Global Optimization, Springer, vol. 48(1), pages 57-71, September.

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