Coloring graphs by iterated local search traversing feasible and infeasible solutions

Discrete Applied Mathematics

Volumn 156, Issue 2, 2008, Pages 201-217

  Caramia, Massimiliano ^a   Dell'Olmo, Paolo ^b  

^a UNIVERSITY OF ROME TOR VERGATA   (Italy)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Graph coloring benchmarks; Heuristics; Local search; Vertex coloring

Indexed keywords

BENCHMARKING; HEURISTIC ALGORITHMS; OPTIMIZATION; PROBLEM SOLVING; SEARCH ENGINES;

GRAPH COLORING BENCHMARKS; LOCAL SEARCH; PERTURBATION SUBROUTINE; VERTEX COLORING;

GRAPH THEORY;

EID: 37049034859     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dam.2006.07.013     Document Type: Article

References (37)

1. Bianco L., Caramia M., and Dell'Olmo P. Solving a preemptive scheduling problem using coloring technique. In: Weglarz J. (Ed). Project Scheduling Recent Models, Algorithms and Applications (1998), Kluwer Academic Publishers, Dordrecht
2. Blazewicz J., Ecker K.H., Pesch E., Schmidt G., and Weglarz J. Scheduling Computer and Manufacturing Processes (1996), Springer, Berlin
3. Brelaz D. New methods to color the vertices of a graph. Comm. ACM 22 (1979) 251-256
4. Brown J.R. Chromatic scheduling and the chromatic number problem. Manag. Sci. 19 (1972) 456-463
5. M. Caramia, P. Dell'Olmo, A fast and simple local search for graph coloring, in: Proceedings of the Third Workshop on Algorithm Engineering (WAE'99), Lecture Notes in Computer Science, vol. 1668, Springer, Berlin, 1999, pp. 319-333.
6. Caramia M., and Dell'Olmo P. Iterative coloring extension of a maximum clique. Naval Res. Logist. 48 (2001) 518-550
7. Caramia M., and Dell'Olmo P. Constraint propagation in graph coloring. J. Heuristics 8 (2002) 83-107
8. Caramia M., Dell'Olmo P., and Italiano G.F. CHECKCOL: improved local search for graph coloring. J. Discrete Algorithms 4 2 (2006) 277-298
9. Chams M., Hertz A., and de Werra D. Some experiments with simulated annealing for coloring graphs. European J. Oper. Res. 32 (1987) 260-266
10. Christofides N. Graph Theory. An Algorithmic Approach (1975), Academic Press, London
11. Coffman E.G. An introduction to combinatorial models of dynamic storage allocation. SIAM Rev. 25 (1983) 311-325
12. Coloring the Queen Graphs, 〈http://www.cs.concordia.ca/∼chvatal/queengraphs.html〉.
13. Dailey D.P. Uniqueness of colorability and colorability of planar 4-regular graphs are NP-complete. Discrete Math. 30 (1980) 289-293
14. C. Desrosiers, P. Galinier, A. Hertz, Efficient algorithms for finding critical subgraphs, Technical Report G-2004-31, Les Cahiers du GERAD, 2004.
15. De Werra D. An introduction to timetabling. European J. Oper. Res. 19 (1985) 151-162
16. I.M. Diaz, P. Zabala, A branch and cut algorithm for graph coloring, in: Proceedings of the Computational Symposium on Graph Coloring and its Generalization, Ithaca, New York, September 2002 〈http://mat.gsia.cmu.edu/COLOR02〉.
17. Dorne R., and Hao J.K. Tabu search for graph coloring, T-colorings and set T-colorings. Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization (1999), Kluwer Academic Publishers, Dordrecht 77-92
18. Eiben A.E., Van Der Hauw J.K., and Van Hemert J.I. Graph coloring with adaptive evolutionary algorithms. J. Heuristics 4 (1998) 25-46
19. Fleurent C., and Ferland J.A. Genetic and hybrid algorithms for graph coloring. Ann. Oper. Res. 63 (1995) 437-461
20. P. Galiner, A. Hertz, N. Zufferey, An adaptive memory algorithm for the k-colouring problem, Technical Report G-2003-35, Les Cahiers du GERAD, 2003.
21. Galinier P., and Hao J.K. Hybrid evolutionary algorithms for graph coloring. J. Combin. Optim. 3 4 (1999) 379-397
22. Garey M.R., and Johnson D.S. Computers and Intractability: A Guide to the Theory of NP-completeness (1979), W.H. Freeman & Company, New York
23. Garey M.R., Johnson D.S., and Stockmeyer L. Some simplified NP-complete graph problems. Theoret. Comput. Sci. 1 (1976) 237-267
24. Hermann F., and Hertz A. Finding the chromatic number by means of critical graphs. ACM J. Experimental Algorithms 7 10 (2002) 1-9
25. Hertz A., and De Werra D. Using tabu search techniques for graph coloring. Computing 39 (1987) 345-351
26. Johnson D.R., Aragon C.R., McGeoch L.A., and Schevon C. Optimization by simulated annealing: an experimental evaluation; part ii, graph coloring and number partitioning. Oper. Res. 39 (1991) 378-406
27. Kannan S., and Proebsting T. Register allocation in structured programs. J. Algorithms 29 (1998) 223-237
28. Krawczyk H., and Kubale M. An approximation algorithm for diagnostic test scheduling in multicomputer systems. IEEE Trans. Comput. C-34 (1985) 869-872
29. Leighton F.T. J. Res. Nat. Bur. Standards 84 (1979) 489-505
30. Lewandowski G. Experiments with parallel graph coloring heuristics. In: Johnson D.S., and Trick M.A. (Eds). DIMACS Series in Discrete Mathematics and Theoretical Computer Science vol. 26 (1996), American Mathematical Society, Providence, RI
31. C. Lund, M. Yannakakis, On the hardness of approximating minimization problems, in: Proceedings of the 25th Annual ACM Symposium on Theory of Computing, 1993, pp. 286-293 (Full version in J. ACM 41 (5) (1994) 960-981).
32. Mehrotra A., and Trick M.A. A column generation approach for graph coloring. INFORMS J. Comput. 8 (1996) 344-354
33. C. Morgenstern, Distributed coloration neighborhood search, Discrete Mathematics and Theoretical Computer Science, vol. 26, American Mathematical Society, Providence, RI, 1996, pp. 335-358.
34. Mycielski J. Sur le coloriage des graphes. Colloq. Math. 3 (1955) 161-162
35. Sager T.J., and Lin S. A pruning procedure for exact graph coloring. ORSA J. Comput. 3 (1993) 226-230
36. Sewell E.C. An improved algorithm for exact graph coloring. In: Johnson D.S., and Trick M.A. (Eds). DIMACS Series in Computer Mathematics and Theoretical Computer Science vol. 26 (1996), American Mathematical Society, Providence, RI 359-373
37. A. Van Gelder, Another look at graph coloring via propositional satisfiability, in: Proceedings of the Computational Symposium on Graph Coloring and its Generalization, Ithaca, New York, September 2002 〈http://mat.gsia.cmu.edu/COLOR02〉.