A Branch-and-Cut algorithm for graph coloring

Discrete Applied Mathematics

Volumn 154, Issue 5 SPEC. ISS., 2006, Pages 826-847

  Méndez Díaz, Isabel ^a   Zabala, Paula ^a  

^a UNIVERSIDAD DE BUENOS AIRES   (Argentina)

Author keywords

Branch and Cut algorithms; Graph coloring; Integer programming

Indexed keywords

GRAPH THEORY; INTEGER PROGRAMMING; MATHEMATICAL MODELS;

BRANCH-AND-CUT ALGORITHMS; GRAPH COLORING;

ALGORITHMS;

EID: 33644602434     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dam.2005.05.022     Document Type: Article

References (34)

1. K. Aardal, A. Hipolito, C. van Hoesel, B. Jansen, C. Roos, T. Terlaky, A Branch-and-Cut algorithm for the frequency assignment problem, Research Memorandum 96/011, Maastricht University, 1996.
2. D. Applegate, R. Bixby, V. Chvátal, W. Cook, On the solution of traveling salesman problems, Documenta Mathematica Journal der Deutschen Mathematiker-Vereinigung, International Congress of Mathematicians (1998) 645-656.
3. E. Balas, S. Ceria, G. Cornuéjols, and G.G. Pataki Polyhedral methods for the maximum clique problem D. Johnson M. Trick Cliques, Coloring, and Satisfiability, DIMACS Series on Discrete Mathematics and Theoretical Computer Science vol. 26 1996 11 27
4. F. Barahona, L. Ladányi, Branch-and-Cut Based on the volume algorithm: Steiner trees in graphs and max cut, IBM Research Report RC22221, 2001.
5. U. Blasum, W. Hochstättler, Application of the Branch and Cut method to the vehicle routing problem, Zentrum für Angewandte Informatik Köln Technical Report zpr2000-386, 2000.
6. D. Brélatz New methods to color the vertices of a graph Comm. ACM 22 1979 251 256
7. P. Coll, J. Marenco, I. Méndez-Díaz, and P. Zabala Facets of the graph coloring polytope Ann. Oper. Res. 116 2002 79 90
8. CPLEX Linear Optimization 6.0 with mixed integer & barrier solvers, ILOG, 1997-1998.
9. G.J. Chaitin, M. Auslander, A.K. Chandra, J. Cocke, M.E. Hopkins, and P. Markstein Register allocation via coloring Computer Languages 6 1981 47 57
10. J. Culberson, Graph coloring bibliography, < http://web.cs.ualberta. ca/ ∼ joe >.
11. D. de Werra Heuristics for graph coloring Computing 7 1990 191 208
12. DIMACS Instances, < http://mat.gsia.cmu.edu/COLOR02 >.
13. F. Glover, M. Parker, and J. Ryan Coloring by tabu branch and bound D. Johnson M. Trick Coloring Cliques Coloring and Satisfiability, DIMACS Series on Discrete Mathematics and Theoretical Computer Science vol. 26 1996 285 308
14. A. Herz, and D. de Werra Using tabu search techniques for graph coloring Computing 39 1987 345 351
15. T. Jensen, B. Toft, Graph coloring problems, Wiley-Interscience, Series in Discrete Mathematics and Optimization, Wiley, New York, 1995.
16. D. Johnson, M. Trick (Eds.), Cliques, Coloring, and Satisfiability, DIMACS Series on Discrete Mathematics and Theoretical Computer Science, vol. 26, 1996.
17. M. Junger, and S. Thienel The ABACUS system for Branch-and-Cut-and-Price algorithms in integer programming and combinatorial optimization Software Practice and Experience 30 11 2000 1325 1352
18. R. Karp Reducibility among combinatorial problems R. Miller J. Thatcher Complexity of Computer Computations 1972 85 104
19. A. Koster, Frequency Assignment, Models and Algorithms, Ph.D. Thesis, Universiteit Maastricht, 1999.
20. M. Kubale, and B. Jackowski A generalized implicit enumeration algorithm for graph coloring Commun. ACM 28 4 1985 412 418
21. F.T. Leighton A graph coloring algorithm for large scheduling problems J. Res. Natl. Bur. Standards 84 1979 489 506
22. C. Mannino, and A. Sassano An exact algorithm for the maximum stable set problem Comput. Optimization and Applications 3 1994 243 258
23. J. McHugh Algorithmic Graph Theory 1990 Prentice-Hall Englewood Cliffs, NJ
24. A. Mehrotra, and M. Trick A column generation approach for graph coloring INFORMS J. Comput. 8 4 1996 344 353
25. I. Méndez-Díaz, Problema de Coloreo de Grafos-Un Estudio Poliedral y un Algoritmo Branch-and-Cut, Tesis Doctoral, Universidad de Buenos Aires, Argentina, 2003.
26. I. Méndez-Díaz, and P. Zabala A polyhedral approach for graph coloring Electronics Notes in Discrete Mathematics 7 2001
27. I. Méndez-Díaz, P. Zabala, Polyhedral results for graph coloring, TR 02-001 Departamento de Computación, Universidad de Buenos Aires, 2002.
28. G. Nemhauser, and G. Sigismondi A strong cutting plane/branch-and-bound algorithm for node packing J. Oper. Res. Soc. 43 5 1992 443 457
29. G. Nemhauser, and L. Wolsey Integer and Combinatorial Optimization 1988 Wiley New York
30. M.W. Padberg On the facial structure of set packing polyhedral Math. Prog. 5 1973 199 215
31. T.J. Sager, and S. Lin A pruning procedure for exact graph coloring ORSA J. Comput. 3 3 1991 226 230
32. A. Sassano On the facial structure of the set covering polytope Math. Prog. 44 1989 181 202
33. E. Sewell An improved algorithm for exact graph coloring D. Johnson M. Trick DIMACS Series on Discrete Mathematics and Theoretical Computer Science vol. 26 1996 359 373
34. L. Wolsey Integer Programming 1998 Wiley New York