Clique partitioning of interval graphs with submodular costs on the cliques

RAIRO - Operations Research

Volumn 41, Issue 3, 2007, Pages 275-287

  Gijswijt, Dion ^a   Jost, Vincent ^b   Queyranne, Maurice ^b  

^a EÖTVÖS LORÁND UNIVERSITY   (Hungary)

^b CNRS   (France)

Author keywords

Batch scheduling; Bipartite matchings; Chromatic entropy; Circular arc graphs; Interval graphs; Max coloring; Partial q coloring; Partition into cliques; Probabilist coloring; Split graphs; Submodular functions

Indexed keywords

ALGORITHMS; COST FUNCTIONS; DYNAMIC PROGRAMMING; PROBLEM SOLVING; SET THEORY; THEOREM PROVING;

BATCH SCHEDULING; BIPARTITE MATCHINGS; CHROMATIC ENTROPY; CIRCULAR ARC GRAPHS; MAX-COLORING; PARTIAL Q-COLORING; PARTITION INTO CLIQUES; PROBABILIST COLORING; SPLIT GRAPHS; SUBMODULAR FUNCTIONS;

GRAPH THEORY;

EID: 34548388787     PISSN: 03990559     EISSN: 28047303     Source Type: Journal    
DOI: 10.1051/ro:2007024     Document Type: Conference Paper

References (21)

1. N. Alon and A. Orlitsky, Source coding and graph entropies. IEEE Trans Inform Theory 42 (1996) 1329-1339.
2. L. Becchetti, P. Korteweg, A. Marchetti-Spaccamela, M. Skutella, L. Stougie and A. Vitaletti, Latency contrained aggregation in sensor networks. Workshop of Combinatorial Optimization, Aussois (2006).
3. M. Boudhar, Dynamic Scheduling on a Single Batch Processing Machine with Split Compatibility Graphs. J. Math. Model. Algorithms 2 (2003) 17-35.
4. P. Brucker and S. Knust, Complexity results of scheduling problems. www.mathematik.uni-osnabrueck. de/research/OR/class/
5. K. Cameron, A min-max relation for the partial q-colourings of a graph. II: Box perfection. Discrete Math. 74 (1989) 15-27.
6. J. Cardinal, S. Fiorini and G. Joret, Minimum entropy coloring. ISAAC, Led. Notes Comput. Sci. 3827 (2005) 819-828.
7. F. Della Croce, B. Escoffier, C. Murat and V. Th. Paschos, Probabilistic coloring of bipartite and split graphs. ICCSA'05, Lect. Notes Comput. Sci. 3483 (2005) 202-211
8. (see also Cahiers du Lamsade No. 218).
9. M. Demange, D. de Werra, J. Monnot and V.T. Paschos, Time slot scheduling of compatible jobs. Cahiers du Lamsade No. 182, (2001),
10. (accepted in J. Scheduling).
11. E. Desgrippes, Coordination entre la production et la distribution dans une chaîne logistique. Laboratoire GILCO - Grenoble (2005).
12. J. Edmonds and R. Giles, A min-max relation for submodular functions on graphs. Ann. Discrete Math. 1 (1977) 185-204.
13. B. Escoffier, J. Monnot and V. Th. Paschos, Weighted Coloring: Further Complexity and Approximability Results. ICTCS (2005) 205-214.
14. G. Finke, V. Jost, M. Queyranne and A. Sebo, Batch processing with interval graph compatibilities between tasks. Cahier du Leibniz No. 108, Laboratoire Leibniz-IMAG, Grenoble (2004)
15. (accepted in Discrete Appl. Math.).
16. M.C. Golumbic, Algorithmic Graph Theory and Perfect Graphs. Academic Press (1980).
17. D.J. Guan and Xuding Zhu, A Coloring Problem for Weighted Graphs. Inf. Process. Lett. 61 (1997) 77-81.
18. Y.T. Herer and M. Penn, Characterizations of natural submodular graphs: A polynomially solvable class of the TSP. Proc. Am. Math. Soc. 123 (1995) 673-679.
19. V. Jost, Ordonnancement chromatique: Polyèdres, Complexité et Classification. Ph.D. thesis, Laboratoire Leibniz-IMAG - UJF - Grenoble (2006).
20. A. Schrijver, Combinatorial Optimization: Polyhedra and Efficiency. Springer (2003).
21. M. Yannakakis and F. Gavril, The maximum k-colorable subgraph problem for chordal graphs. Inf. Process. Lett. 24 (1987) 133-137.