no. 1
Coloration de graphes : fondements et applications
RAIRO - Operations Research - Recherche Opérationnelle, Tome 37 (2003) no. 1, pp. 29-66.

Les modèles classiques de coloration doivent leur notoriété en grande partie à leurs applications à des problèmes de type emploi du temps ; nous présentons les concepts de base des colorations ainsi qu'une série de variations et de généralisations motivées par divers problèmes d'ordonnancement dont les élaborations d'horaires scolaires. Quelques algorithmes exacts et heuristiques seront présentés et nous esquisserons des méthodes basées sur la recherche Tabou pour trouver des solutions approchées pour des problèmes de grande taille. Enfin nous mentionnons l'application des colorations à la confection de calendriers de ligues de sport et à des problèmes de transferts de fichiers informatiques. Ce texte est une version étendue de [37].

The classical colouring models are well known thanks in large part to their applications to scheduling type problems; we describe the basic concepts of colourings together with a number of variations and generalisations arising from scheduling problems such as the creation of school schedules. Some exact and heuristic algorithms will be presented, and we will sketch solution methods based on tabu search to find approximate solutions to large problems. Finally we will also mention the use of colourings for creating schedules in sports leagues and for computer file transfer problems. This paper is an extended version of [37].

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Werra, Dominique de; Kobler, Daniel. Coloration de graphes : fondements et applications. RAIRO - Operations Research - Recherche Opérationnelle, Tome 37 (2003) no. 1, pp. 29-66. doi : 10.1051/ro:2003013. http://archive.numdam.org/articles/10.1051/ro:2003013/

[1] N. Alon et M. Tarsi, Colorings and orientations of graphs. Combinatorica 12 (1992) 125-134. | MR | Zbl

[2] M. Bellare, O. Goldreich et M. Sudan, Free bits, PCPs and non-approximability - towards tight results. SIAM J. Comput. 27 (1998) 804-915. | Zbl

[3] C. Berge, Graphes. Gauthier-Villars, Paris (1983). | MR | Zbl

[4] C. Berge, Hypergraphes. Gauthier-Villars, Paris (1987). | MR | Zbl

[5] C. Berge et V. Chvátal, Topics on Perfect Graphs. Ann. Discrete Math. 21 (1984). | MR | Zbl

[6] M. Biró, M. Hujter et Zs. Tuza, Precoloring extension. I. Interval graphs. Discrete Math. 100 (1992) 267-279. | MR | Zbl

[7] H.L. Bodlaender, K. Jansen et G. Woeginger, Scheduling with incompatible jobs. Discrete Appl. Math. 55 (1994) 219-232. | MR | Zbl

[8] V. Chvátal, Perfectly ordered graphs, in Topics on Perfect Graphs. North Holland Math. Stud. 88, Annals Discrete Math. 21 (1984) 63-65. | MR | Zbl

[9] E.G. Coffman Jr., M.G. Garey, D.S. Johnson et A.S. Lapaugh, Scheduling file transfers. SIAM J. Comput. 14 (1985) 744-780. | MR | Zbl

[10] O. Coudert, Exact Coloring of Real-Life Graphs is Easy, in Proc. of 34th ACM/IEEE Design Automation Conf. ACM Press, New York (1997) 121-126.

[11] N. Dubois et D. De Werra, EPCOT: An Efficient Procedure for Coloring Optimally with Tabu Search. Comput. Math. Appl. 25 (1993) 35-45. | MR | Zbl

[12] K. Easton, G. Nemhauser et M. Trick, The traveling tournament problem: description and benchmarks. GSIA, Carnegie Mellon University (2002). | Zbl

[13] C. Fleurent et J.A. Ferland, Genetic and Hybrid Algorithms for Graph Coloring, édité par G. Laporte et I.H. Osman (éds). Metaheuristics in Combinatorial Optimization, Ann. Oper. Res. 63 (1996) 437-461. | Zbl

[14] M.G. Garey et D.S. Johnson, The complexity of near-optimal graph coloring. J. ACM 23 (1976) 43-49. | MR | Zbl

[15] M.G. Garey, D.S. Johnson et L. Stockmeyer, Some simplified NP-complete graph problems. Theoret. Comput. Sci. 1 (1976) 237-267. | MR | Zbl

[16] F. Glover et M. Laguna, Tabu Search. Kluwer Academic Publ. (1997). | MR | Zbl

[17] M.C. Golumbic, Algorithmic Graph Theory and Perfect Graphs. Academic Press, New York (1984). | Zbl

[18] M. Grötschel, L. Lovasz et A. Schrijver, Geometric Algorithms and Combinatorial Optimization. Springer-Verlag, Berlin (1988). | MR | Zbl

[19] M.M. Halldórsson, A still better performance guarantee for approximate graph coloring. Inform. Process. Lett. 45 (1993) 19-23. | MR | Zbl

[20] P. Hansen, A. Hertz et J. Kuplinsky, Bounded Vertex Colorings of Graphs. Discrete Math. 111 (1993) 305-312. | MR | Zbl

[21] P. Hansen, J. Kuplinsky et D. De Werra, Mixed Graph Coloring. Math. Meth. Oper. Res. 45 (1997) 145-160. | MR | Zbl

[22] A.J.W. Hilton et D. De Werra, A sufficient condition for equitable edge-colourings of simple graphs. Discrete Math. 128 (1994) 179-201. | MR | Zbl

[23] E.L. Lawler, Combinatorial Optimization: Networks and Matroids. Holt, Rinehart and Winston, New York (1976). | MR | Zbl

[24] F. Leighton, A Graph Coloring Algorithm for Large Scheduling Problems. J. Res. National Bureau Standards 84 (1979) 742-774. | MR | Zbl

[25] M. Middendorf et F. Pfeiffer, On the complexity of recognizing perfectly orderable graphs, Discrete Mathematics 80 (1990) 327-333. | MR | Zbl

[26] A. Pnueli, A. Lempel et S. Even, Transitive orientation of graphs and identification of permutation graphs. Canadian J. Math. 23 (1971) 160-175. | MR | Zbl

[27] F.S. Roberts, Discrete Mathematical Models. Prentice-Hall, Englewood Cliffs (1976). | Zbl

[28] Zs. Tuza, Graph colorings with local constraints - a survey, Discussiones Mathematicae - Graph Theory 17 (1997) 161-228. | Zbl

[29] V.G. Vizing, On an estimate of the chromatic class of a p-graph (en russe), Metody Discret Analiz. 3 (1964) 25-30. | MR

[30] D.J.A. Welsh et M.B. Powell, An upper bound on the chromatic number of a graph and its application to timetabling problems, Computer J. 10 (1967) 85-87. | Zbl

[31] D. De Werra, Some models of graphs for scheduling sports competitions, Discrete Applied Mathematics 21 (1988) 47-65. | MR | Zbl

[32] D. De Werra, The combinatorics of timetabling, European Journal of Operational Research 96 (1997) 504-513. | Zbl

[33] D. De Werra, On a multiconstrained model for chromatic scheduling, Discrete Applied Mathematics 94 (1999) 171-180. | MR | Zbl

[34] D. De Werra, Ch. Eisenbeis, S. Lelait et B. Marmol, On a graph-theoretical model for cyclic register allocation, Discrete Applied Mathematics 93 (1999) 191-203. | MR | Zbl

[35] D. De Werra et Y. Gay, Chromatic scheduling and frequency assignment, Discrete Applied Mathematics 49 (1994) 165-174. | MR | Zbl

[36] D. De Werra et A. Hertz, Consecutive colorings of graphs, Zeischrift für Operations Research 32 (1988) 1-8. | MR | Zbl

[37] D. De Werra et D. Kobler, Coloration et ordonnencement chromatique, ORWP 00/04, Ecole Polytechnique Fédérale de Lausanne, 2000.

[38] X. Zhou et T. Nishizeki, Graph Coloring Algorithms, IEICE Trans. on Information and Systems E83-D (2000) 407-417.

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