CsegGraph: A graph colouring instance generator

International Journal of Computer Mathematics

Volumn 86, Issue 10-11, 2009, Pages 1956-1967

  Hossain, Shahadat ^a  

^a UNIVERSITY OF LETHBRIDGE   (Canada)

Author keywords

Column segments graph; Mathematical derivative; Sparse matrix

Indexed keywords

CHROMATIC NUMBER; COLUMN-SEGMENTS GRAPH; INSTANCE GENERATOR; INTERSECTION GRAPH; MATHEMATICAL DERIVATIVES; SPARSE MATRICES; SPARSITY PATTERNS; UNDIRECTED GRAPH;

COMPUTER SCIENCE; MATHEMATICAL TECHNIQUES;

GRAPH THEORY;

EID: 76249125631     PISSN: 00207160     EISSN: 10290265     Source Type: Journal    
DOI: 10.1080/00207160903023565     Document Type: Conference Paper

References (24)

1. R.F. Boisvert, R. Pozo, K. Remington, R. Barrett, and J.J. Dongarra, The matrix market: A web resource for test matrix collections, in Quality of Numerical Software, Assessment and Enhancement, R.F. Boisvert, ed., Chapman and Hall, London, 1997, pp. 125-137.
2. D. Brélaz, New methods to color the vertices of a graph, Commun. ACM 22 (1979), pp. 251-256.
3. T.N. Bui, T.H. Nguyen, C.M. Patel, and K.A.T. Phan, An ant-based algorithm for coloring graphs, Discrete Appl. Math. 156 (2008), pp. 190-200.
4. M. Caramia and P. Dell'Olmo, Coloring graphs by iterated local search traversing feasible and infeasible solutions, Discrete Appl. Math. 156 (2008), pp. 201-217.
5. T.F. Coleman and J.J. Moré, Estimation of sparse Jacobian matrices and graph colouring problems, SIAM J. Numer. Anal. 20 (1983), pp. 187-209.
6. T.F. Coleman, B.S. Garbow, and J.J. Moré, Software for estimating sparse Jacobian matrices, ACM Trans. Math. Softw. 10 (1984), pp. 329-345.
7. J. Culberson and I. Gent, Frozen development in graph coloring, Theor. Comput. Sci. 265 (2001), pp. 227-264.
8. J. Dongarra, A. Lumsdaine, R. Pozo, and K. Remington, A sparse matrix library in C++ for high performance architectures, in Proceedings of the Second Object Oriented Numerics Conference, 1994, pp. 214-218.
9. I.S. Duff, R.G. Grimes, and J.G. Lewis, Sparse matrix test problems,ACM Trans. Math. Softw. 15 (1989), pp. 1-14.
10. P. Galinier, A. Hertz, and N. Zufferey, An adaptive memory algorithm for the k-coloring problem, Discrete Appl. Math. 156 (2008), pp. 267-279.
11. M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, W.H. Freeman & Co., NewYork, 1979.
12. A.H. Gebremedhin, F. Manne, and A. Pothen, What color is your Jacobian? Graph coloring for computing derivatives, SIAM Rev. 47 (2005), pp. 629-705.
13. A. Griewank, Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, Number 19 in Frontiers in Applied Mathematics SIAM, Philadelphia, PA, 2000.
14. S. Hossain and T. Steihaug, Sparsity issues in the computation of Jacobian matrices, in Proceedings of the International Symposium on Symbolic and Algebraic Computing (ISSAC), T. Mora, ed., ACM, New York, 2002, pp. 123-130.
15. S. Hossain and T. Steihaug, Graph coloring in the estimation of sparse derivative matrices: Instances and applications, Discrete Appl. Math. 156 (2008), pp. 280-288.
16. S. Hossain and T. Steihaug, Optimal direct determination of sparse Jacobian matrices. Tech. Rep. 254, Department of Informatics, University of Bergen, Norway, October 2003, Optim. Methods Softw., to appear.
17. 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, Oper. Res. 39 (1991), 378-406.
18. D.S. Johnson, A. Mehrotra, and M.A. Trick, Preface: Special issue on computational methods for graph coloring and its generalizations, Discrete Appl. Math. 156 (2008), pp. 145-146.
19. S. Kugele, Efficient solving of combinatorial problems using sat-solvers, Master's thesis, Technische Universität München, October 2006. Available at www7.in.tum.de/um/bibdb/kugele/kugele-diploma06.pdf (accessed May 2009).
20. A. Mehrotra and M.A. Trick, A column generation approach for graph coloring, INFORMS J. Comput. 8 (1996), pp. 344-354.
21. I. Méndez-Díaz and P. Zabala, A branch-and-cut algorithm for graph coloring, Discrete Appl. Math. 154 (2006), pp. 826-847.
22. I. Méndez-Díaz and P. Zabala, A cutting plane algorithm for graph coloring. Discrete Appl. Math. 156 (2008), pp. 159-179.
23. G.N. Newsam and J.D. Ramsdell, Estimation of sparse Jacobian matrices, SIAM J. Alg. Disc. Methods 4 (1983), pp. 404-417.
24. A. Van Gelder, Another look at graph colouring via propositional satisfiability. Discrete Appl. Math. 156 (2008), pp. 230-243.