New lower and upper bounds for graph treewidth

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2647, Issue , 2003, Pages 70-80

  Clautiaux, François ^a   Carlier, Jacques ^a   Moukrim, Aziz ^a   Nègre, Stéphane ^b  

^a CNRS   (France)

^b Institut Supérieur de Sciences et Techniques   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; OPTIMIZATION; POLYNOMIAL APPROXIMATION;

ARBITRARY GRAPHS; COMPUTATIONAL EXPERIMENT; COMPUTING TIME; GRAPH COLORINGS; LOWER AND UPPER BOUNDS; OPTIMIZATION PROBLEMS; POLYNOMIAL-TIME; TREE DECOMPOSITION;

HEURISTIC METHODS;

EID: 35248894380     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-44867-5_6     Document Type: Article

References (18)

1. The second dimacs implementation challenge: NP-hard problems: Maximum clique, graph coloring, and satisfiability, 1992-1993.
2. S. Arnborg and A. Proskurowki, Characterisation and recognition of partial 3-trees, SIAM J. Alg. Disc. Meth. 7 (1986), 305-314.
3. H. Bodlaender, A linear time algorithm for finding tree-decompositions of small treewidth, SIAM J. Comput. 25 (1996), 1305-1317.
4. _, Necessary edges in k-chordalisation of graphs, Tech. Report UU-CS-2000-27, Institute for Information and Computing Sciences, Utrecht University, 2000.
5. H. Bodlaender and R. Möhring, The pathwidth and treewidth of cographs, SIAM J. Disc. Math. 6 (1993), 181-188.
6. J. Carlier and C. Lucet, A decomposition algorithm for network reliability evaluation, Discrete Applied Mathematics 65 (1993), 141-156.
7. F. Clautiaux, A. Moukrim, S. Nègre, and J. Carlier, A tabu search minimising upper bounds for graph treewidth, Report, 2003.
8. D. Fulkerson and O. Gross, Incidence matrices and interval graphs, Pacific J. Math. 15 (1965), 835-855.
9. F. Gavril, Algorithms for minimum coloring, maximum clique, minimum coloring cliques and maximum independent set of a chordal graph, SIAM J. Comput. 1 (1972), 180-187.
10. F. Jensen, S. Lauritzen, and K. Olesen, Bayesian updating in causal probabilistic networks by local computations, Computational Statistics Quaterly 4 (1990), 269-282.
11. A. Koster, Frequency assignment, models and algorithms, Ph.D. thesis, Universiteit Maastricht, 1999.
12. A. Koster, H. Bodlaender, and S. van Hoesel, Treewidth: Computational experiments, Fundamenta Informaticae 49 (2001), 301-312.
13. C. Lucet, J. F. Manouvrier, and J. Carlier, Evaluating network reliability and 2-edge-connected reliability in linear time for bounded pathwidth graphs, Algorithmica 27 (2000), 316-336.
14. C. Lucet, F. Mendes, and A. Moukrim, Méthode de décomposition appliquée à la coloration de graphes, ROADEF, 2002.
15. N. Robertson and P. Seymour, Graph minors. ii algorithmic aspects of tree-width, Journal of Algorithms 7 (1986), 309-322.
16. D. Rose, Triangulated graphs and the elimination process, J Math. Anal. Appl. 32 (1970), 597-609.
17. _, A graph-theoretic study of the numerical solution of sparse positive definite systems of linear equations, Graph Theory and Computing (R. C. Reed, ed.), Academic Press (1972), 183-217.
18. D. Rose, E. Tarjan, and G. Lueker, Algorithmic aspects of vertex elimination on graphs, SIAM J. Comput. 5 (1976), 146-160.