An exact approach for the Vertex Coloring Problem

Discrete Optimization

Volumn 8, Issue 2, 2011, Pages 174-190

  Malaguti, Enrico ^a   Monaci, Michele ^b   Toth, Paolo ^a  

^a UNIVERSITY OF BOLOGNA   (Italy)

^b UNIVERSITY OF PADOVA   (Italy)

Author keywords

Branch and Price; Column generation; Computational experiments; Vertex Coloring

Indexed keywords

ADJACENT VERTICES; BRANCH AND PRICE; BRANCH-AND-PRICE ALGORITHMS; COLUMN GENERATION; COMPUTATIONAL EXPERIMENT; COMPUTATIONAL EXPERIMENTS; EXACT ALGORITHMS; EXACT APPROACH; OPTIMALITY; SET COVERINGS; UNDIRECTED GRAPH; VERTEX COLORING; VERTEX COLORING PROBLEMS;

ALGORITHMS; COLOR; EXPERIMENTS;

HEURISTIC METHODS;

EID: 79955602725     PISSN: 15725286     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.disopt.2010.07.005     Document Type: Article

References (34)

1. M.R. Garey, and D.S. Johnson Computers and Intractability: A Guide to the Theory of NP-Completeness 1979 W. H. Freeman & Co. New York
2. F.T. Leighton A graph coloring algorithm for large scheduling problems Journal of Research of the National Bureau of Standards 84 1979 489 503
3. N. Zufferey, P. Amstutz, and P. Giaccari Graph colouring approaches for a satellite range scheduling problem Journal of Scheduling 11 2008 263 277
4. D. de Werra An introduction to timetabling European Journal of Operational Research 19 1985 151 162
5. F.C. Chow, and J.L. Hennessy The priority-based coloring approach to register allocation ACM Transactions on Programming Languages and Systems 12 1990 501 536
6. A. Gamst Some lower bounds for a class of frequency assignment problems IEEE Transactions on Vehicular Technology 35 1986 8 14 (Pubitemid 16614221)
7. T.K. Woo, S.Y.W. Su, and R. Newman Wolfe Resource allocation in a dynamically partitionable bus network using a graph coloring algorithm IEEE Transactions on Communications 39 2002 1794 1801
8. I. Mndez-Daz, and P. Zabala A branch-and-cut algorithm for graph coloring Discrete Applied Mathematics 154 2006 826 847
9. I. Mndez-Daz, and P. Zabala A cuttting plane algorithm for graph coloring Discrete Applied Mathematics 156 2008 159 179 (Pubitemid 350251593)
10. A. Mehrotra, and M.A. Trick A column generation approach for graph coloring INFORMS Journal on Computing 8 1996 344 354
11. E. Malaguti, and P. Toth A survey on vertex coloring problems International Transactions in Operational Research 17 2010 1 34
12. F. Hermann, and A. Hertz Finding the chromatic number by means of critical graphs ACM Journal of Experimental Algorithmics 7 2002 1 9
13. A. Hertz, and D. de Werra Using tabu search techniques for graph coloring Computing 39 1987 345 351 (Pubitemid 18562739)
14. D.S. Johnson, C.R. Aragon, L.A. McGeoch, and C. Schevon Optimization by simulated annealing: an experimental evaluation; part II, graph coloring and number partitioning Operations Research 39 1991 378 406
15. L. Davis Handbook of Genetic Algorithms 1998 Van Nostrand Reinhold New York
16. C.A. Morgenstern Distibuted coloration neighborhood search D.S. Johnson, M.A. Trick, Cliques, Coloring, and Satisfiability: 2nd DIMACS Implementation Challange, 1993 DIMACS Series in Discrete Mathematics and Theoretical Computer Science 1996 American Mathematical Society 335 358
17. P. Galinier, and J.K. Hao Hybrid evolutionary algorithms for graph coloring Journal of Combinatorial Optimization 3 1999 379 397 (Pubitemid 129575323)
18. N. Funabiki, and T. Higashino A minimal-state processing search algorithm for graph coloring problems IEICE Transactions on Fundamentals E83-A 2000 1420 1430
19. P. Galinier, A. Hertz, and N. Zufferey An adaptative memory algorithm for the k-coloring problem Discrete Applied Mathematics 156 2008 267 279 (Pubitemid 350251597)
20. I. Blchliger, and N. Zufferey A reactive tabu search using partial solutions for the graph coloring problem Computers & Operations Research 35 2008 960 975 (Pubitemid 47368857)
21. M. Plumettaz, D. Schindl, N. Zufferey, Ant local search and its efficient adaptation to graph colouring, Journal of the Operational Research Society (2010) (in press).
22. E. Malaguti, M. Monaci, and P. Toth A metaheuristic approach for the vertex coloring problem INFORMS Journal on Computing 20 2008 302 316
23. R. Brown Chromatic scheduling and the chromatic number problem Management Science 19 1972 456 463
24. D. Brlatz New methods to color the vertices of a graph Communications of the ACM 22 1979 251 256
25. E.C. Sewell An improved algorithm for exact graph coloring D.S. Johnson, M.A. Trick, Cliques, Coloring, and Satisfiability: 2nd DIMACS Implementation Challange, 1993 DIMACS Series in Discrete Mathematics and Theoretical Computer Science 1996 American Mathematical Society 359 373
26. P. Hansen, M. Labb, and D. Schindl Set covering and packing formulations of graph coloring: algorithms and first polyhedral results Discrete Optimization 6 2009 135 147
27. A. Caprara, M. Fischetti, and P. Toth A heuristic method for the set covering problem Operations Research 47 1999 730 743 (Pubitemid 30544593)
28. P.R.J. stergrd A new algorithm for the maximum-weight clique problem Nordic Journal of Computing 8 2001 424 436
29. I.M. Bomze, M. Budinich, P.M. Pardalos, and M. Pelillo The maximum clique problem D.Z. Du, P.M. Pardalos, Handbook of Combinatorial Optimization suppl. vol. A 1999 1 74
30. A. Grosso, M. Locatelli, and W. Pullan Simple ingredients leading to very efficient heuristics for the maximum clique problem Journal of Heuristics 14 2008 587 612
31. A.A. Farley A note on bounding a class of linear programming problems, including cutting stock problems Operations Research 38 1990 922 923
32. J.M. Valrio de Carvalho Using extra dual cuts to accelerate column generation INFORMS Journal on Computing 17 2005 175 182
33. A.A. Zykov On some properties of linear complexes Matematicheskij Sbornik 24 1949 163 188
34. D.S. Johnson, and M.A. Trick Cliques, Coloring, and Satisfiability: 2nd DIMACS Implementation Challange, 1993 DIMACS Series in Discrete Mathematics and Theoretical Computer Science 1996 American Mathematical Society