A semidefinite programming-based heuristic for graph coloring

Discrete Applied Mathematics

Volumn 156, Issue 2, 2008, Pages 180-189

  Dukanovic, Igor ^a   Rendl, Franz ^b  

^a UNIVERSITY OF MARIBOR   (Slovenia)

^b UNIVERSITY OF KLAGENFURT   (Austria)

Author keywords

Graph (vertex) coloring; Lov sz theta function; Lov sz theta number

Indexed keywords

COMPUTER PROGRAMMING; GRAPH THEORY; NUMERICAL METHODS; POLYNOMIALS; PROBLEM SOLVING;

CHROMATIC NUMBER; GRAPH COLORING; LOVASZ THETA NUMBER; SEMIDEFINITE PROGRAMMING;

HEURISTIC ALGORITHMS;

EID: 37049015975     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dam.2006.07.014     Document Type: Article

References (27)

1. Benson S., and Ye Y. Approximating maximum stable set and minimum graph coloring problems with the positive semidefinite relaxation. Applications and Algorithms of Complementarity (2000), Kluwer Academic Publishers, Dordrecht 1-18
2. Bradley P.S., Mangasarian O.L., and Street W.N. Clustering via concave minimization. In: Mozer M.C., Jordan M.I., and Petsche T. (Eds). Advances in Neural Information Processing Systems vol. 9 (1997), The MIT Press, Cambridge, MA 368
3. Brélaz D. New methods to color the vertices of a graph. Comm. ASM 22 4 (1979) 252-256
4. Brown J.R. Chromatic scheduling and the chromatic number problem. Management Sci. 19 4 (1972) 456-463
5. Burer S., and Monteiro R.D.C. A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization. Math. Programming 95 (2003) 329-357
6. de Klerk E., Pasechnik D.V., and Warners J.P. On approximate graph colouring and max-k-cut algorithms based on the θ-function. J. Combin. Optim. 8 (2004) 267-294
7. De Werra D. Heuristics for graph coloring. Computing 7 (1990) 191-208
8. I. Dukanovic, Semidefinite programming applied to graph coloring problem, Ph.D. Thesis, University of Klagenfurt, Austria, 2007, forthcoming.
9. I. Dukanovic, F. Rendl, Semidefinite programming relaxations for graph coloring and maximal clique problems, Math. Programming 109 (2007) 345-365.
10. Fleurent C., and Ferland J.A. Genetic and hybrid algorithms for graph coloring. Ann. Oper. Res. 63 (1996) 437-461
11. Galinier P., and Hao J.K. Hybrid evolutionary algorithms for graph coloring. J. Combin. Optim. 3 (1999) 379-397
12. Garey M.R., and Johnson D.S. Computers and Intractability: a Guide to the Theory of NP-Completeness (1979), W.H. Freeman, New York
13. Glass C.A., and Pruegel-Bennett A. Genetic algorithm for graph coloring: exploration of Galinier and Hao's algorithm. J. Combin. Optim. 7 (2003) 229-236
14. Goemans M.X. Semidefinite programming in combinatorial optimization. Math. Programming 79 (1997) 143-162
15. Helmberg C., and Rendl F. A spectral bundle method for semidefinite programming. SIAM J. Optim. 10 (2000) 673-696
16. Herrmann F., and Hertz A. Finding the chromatic number by means of critical graphs. ACM J. Experimental Algorithms 7 (2002) 10
17. Hertz A., and De Werra D. Using tabu search for graph coloring. Computing 39 (1987) 345-351
18. Karger D., Motwani R., and Sudan M. Approximate graph coloring by semidefinite programming. J. Assoc. Comput. Mach. 45 (1998) 246-265
19. Kubale M., and Jackowski B. A generalized implicit enumeration algorithm for graph coloring. Comm. ACM 28 4 (1985) 412-418
20. Lovász L. On the Shannon capacity of a graph. IEEE Trans. Inform. Theory 25 (1979) 1-7
21. Mehrotra A., and Trick M.A. A column generation approach for exact graph coloring. INFORMS J. Comput. 8 (1996) 344-354
22. Meurdesoif P. Strengthening the Lovász θ (over(G, -)) bound for graph coloring. Math. Programming 102 (2005) 577-588
23. Peemöller J. A correction to Brélaz's modification of Brown's coloring algorithm. Comm. ACM 26 8 (1983) 593-597
24. J. Povh, F. Rendl, A. Wiegele, A boundary point method to solve semidefinite programs, Computing 78 (2006) 277-286.
25. Todd M.J. Semidefinite optimization. Acta Numer. 10 (2001) 515-560
26. Toh K.C., and Kojima M. Solving some large scale semidefinite programs via the conjugate residual method. SIAM J. Optim. 12 (2002) 669-691
27. M. Trick, Network resources for coloring a graph. http://mat.gsia.cmu.edu/COLOR/color.html, 1994.