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A Large Neighborhood Search Heuristic for Graph Coloring

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Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems (CPAIOR 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4510))

Abstract

We propose a new local search heuristic for graph coloring that searches very large neighborhoods. The heuristic is based on solving a MAX-CUT problem at each step. While the MAX-CUT problem is formally hard, fast heuristics that give “good” cuts are available to solve this. We provide computational results on benchmark instances. The proposed approach is based on similar heuristics used in computer vision.

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References

  1. Avanthay, C., Hertz, A., Zufferey, N.: A variable neighborhood search for graph coloring. European Journal of Operational Research 151, 379–388 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  2. Boykov, Y., Veksler, O., Zabih, R.: Fast approximate energy minimization via graph cuts. IEEE Transactions on Pattern Analysis and Machine Intelligence 23(11), 1222–1239 (2001)

    Article  Google Scholar 

  3. Bui, T.N., Patel, C.M.: An Ant System Algorithm for Coloring Graphs. In: Johnson, D.S., Mehrotra, A., Trick, M. (eds.) Proceedings of the Computational Symposium on Graph Coloring and its Generalizations, Ithaca, NY (2002)

    Google Scholar 

  4. Burer, S., Monteiro, R.D.C., Zhang, T.: Rank-two relaxation heuristics for MAX-CUT and other binary quadratic programs. SIAM Journal on Optimization 12, 503–521 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  5. Chiarandini, M., Dumitrescu, I., Stuetzle, T.: Local search for the colouring graph problem. A computational study. Technical Report AIDA-03-01, FG Intellektik, TU Darmstadt (2003)

    Google Scholar 

  6. Chiarandini, M., Stuetzle, T.: An application of Iterated Local Search to Graph Coloring Problem. In: Johnson, D.S., Mehrotra, A., Trick, M. (eds.) Proceedings of the Computational Symposium on Graph Coloring and its Generalizations, Ithaca, NY (2002)

    Google Scholar 

  7. CirCut: A Fortran 90 Code for Max-Cut, Max-Bisection and More, http://www.caam.rice.edu/~zhang/circut/

  8. COLOR02/03/04: Graph Coloring and its Generalizations, http://mat.gsia.cmu.edu/COLOR04

  9. Croitoru, C., Luchian, H., Gheorghies, O., Apetrei, A.: A New Genetic Graph Coloring Heuristic. In: Johnson, D.S., Mehrotra, A., Trick, M. (eds.) Proceedings of the Computational Symposium on Graph Coloring and its Generalizations, Ithaca, NY (2002)

    Google Scholar 

  10. Galinier, P., Hertz, A.: A Survey of Local Search Methods for Graph Coloring. Computers & Operations Research 33, 2547–2562 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  11. Galinier, P., Hertz, A., Zufferey, N.: Adaptive Memory Algorithms for Graph Coloring. In: Johnson, D.S., Mehrotra, A., Trick, M. (eds.) Proceedings of the Computational Symposium on Graph Coloring and its Generalizations, Ithaca, NY (2002)

    Google Scholar 

  12. Garey, M.R., Johnson, D.S.: Computers and Interactibility: A Guide to the Theory of NP-Completeness. W.H. Freeman, San Francisco (1979)

    MATH  Google Scholar 

  13. Goemans, M.X., Williamson, D.P.: Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. Journal of ACM 42, 1115–1145 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  14. Mehrotra, A., Trick, M.: A column generation approach for graph coloring. INFORMS Journal On Computing 8(4), 344–354 (1996)

    MATH  Google Scholar 

  15. Phan, V., Skiena, S.: Coloring Graphs With a General Heuristic Search Engine. In: Johnson, D.S., Mehrotra, A., Trick, M. (eds.) Proceedings of the Computational Symposium on Graph Coloring and its Generalizations, Ithaca, NY (2002)

    Google Scholar 

  16. Thompson, P.M., Psaraftis, H.N.: Cyclic transfer algorithms for multivehicle routing and scheduling problems. Operations Research 41, 70–79 (1993)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA,15213, USA

    Michael A. Trick & Hakan Yildiz

Authors
  1. Michael A. Trick
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  2. Hakan Yildiz
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Pascal Van Hentenryck Laurence Wolsey

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© 2007 Springer Berlin Heidelberg

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Trick, M.A., Yildiz, H. (2007). A Large Neighborhood Search Heuristic for Graph Coloring. In: Van Hentenryck, P., Wolsey, L. (eds) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. CPAIOR 2007. Lecture Notes in Computer Science, vol 4510. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72397-4_25

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  • DOI: https://doi.org/10.1007/978-3-540-72397-4_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72396-7

  • Online ISBN: 978-3-540-72397-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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