Maximal label search algorithms to compute perfect and minimal elimination orderings

SIAM Journal on Discrete Mathematics

Volumn 23, Issue 1, 2008, Pages 428-446

  Berry, A ^a   Krueger, R ^b   Simonet, G ^c  

^a UNIVERSITÉ BLAISE PASCAL   (France)

^b UNIVERSITY OF TORONTO   (Canada)

^c LIRMM   (France)

Author keywords

Elimination scheme; Graph search; Maximal label search; Meo; Minimal triangulation; Peo

Indexed keywords

CHORDAL GRAPHS; COMPLEXITY ANALYSIS; ELIMINATION SCHEME; GENERIC ALGORITHM; GRAPH SEARCH; GRAPH SEARCH ALGORITHM; INPUT GRAPHS; MINIMAL ELIMINATION ORDERING; MINIMAL TRIANGULATIONS; SEARCH ALGORITHMS; VERTEX LABELING;

COMPUTER PROGRAMMING; LABELS; LEARNING ALGORITHMS; TRIANGULATION;

COMPUTATION THEORY;

EID: 77952603944     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/070684355     Document Type: Article

References (19)

1. A. Berry, J. Blair, P. Heggernes, and B. Peyton, Maximum cardinality search for computing minimal triangulations of graphs, Algorithmica, 39 (2004), pp. 287-298. (Pubitemid 40871659)
2. A. Berry and J.-P. Bordat, Separability generalizes Dirac's theorem, Discrete Appl. Math., 84 (1998), pp. 43-53. (Pubitemid 128387138)
3. A. Berry and J.-P. Bordat, Moplex elimination orderings, in Proceedings of the First Cologne-Twente Workshop on Graphs and Combinatorial Optimization, Electron. Notes Discrete Math. 8, J. Hurink, S. Pickl, H. Broersma, and U. Faigle, eds., Elseiver, Amsterdam, 2001, pp. 6-9.
4. A. Berry, R. Krueger, and G. Simonet, Ultimate generalizations of LexBFS and LEX M, in Proceedings of the 31st International Workshop on Graph-Theoretic Concepts in Computer Science 2005 (WG 2005), Lect. Notes Comput. Sci. 3787, Springer-Verlag, New York, 2005, pp. 199-213. (Pubitemid 43848614)
5. J. R. S. Blair, P. Heggernes, and J. A. Telle, A practical algorithm for making filled graphs minimal, Theoret. Comput. Sci. A, 250-1/2 (2001), pp. 125-141. (Pubitemid 32674084)
6. H. L. Bodlaender and A. M. C. A. Koster, On the maximum cardinality search lower bound for treewidth, Discrete Appl. Math., 155 (2007), pp. 1348-1372.
7. D. G. Corneil, Lexicographic breadth first search - a survey, in Proceedings of the 30th International Workshop on Graph Theory (WG2004), Lect. Notes Comput. Sci. 3353, Springer-Verlag, New York, 2004, pp. 1-19.
8. D. G. Corneil and R. M. Krueger, Unified view of graph searching, SIAM J. Discrete Math., 22 (2008), pp. 1259-1276.
9. D. G. Corneil, S. Olariu, and L. Stewart, Linear time algorithms for dominating pairs in asteroidal triple-free graphs, SIAM J. Comput., 28 (1999), pp. 1284-1297.
10. E. Dahlhaus, P. L. Hammer, F. Maffray, and S. Olariu, On Domination Elimination Orderings and Domination Graphs, in Proceedings of WG 1994, London, 1994, pp. 81-92.
11. D. R. Fulkerson and O. A. Gross, Incidence matrixes and interval graphs, Pacific J. Math., 15 (1965), pp. 835-855.
12. T. Ohtsuki, A fast algorithm for finding an optimal ordering in the vertex elimination on a graph, SIAM J. Comput., 5 (1976), pp. 133-145.
13. T. Ohtsuki, L. K. Cheung, and T. Fujisawa, Minimal triangulation of a graph and optimal pivoting order in a sparse matrix, J. Math. Anal. Appl., 54 (1976), pp. 622-633.
14. D. Rose, R. E. Tarjan, and G. Lueker, Algorithmic aspects of vertex elimination on graphs, SIAM J. Comput., 5 (1976), pp. 266-283.
15. D. R. Shier, Some aspects of perfect elimination orderings in chordal graphs, Discrete Appl. Math., 7 (1984), pp. 325-331.
16. R. E. Tarjan and M. Yannakakis, Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs, SIAM J. Comput., 13 (1984), pp. 566-579. (Pubitemid 15514404)
17. P. van Emde Boas, Preserving order in a forest in less than logarithmic time and linear space, Inform. Process. Lett., 6 (1977), pp. 80-82.
18. P. van Emde Boas, R. Kaas, and E. Zijlstra, Design and implementation of an efficient priority queue, Math. Syst. Theory, 10 (1977), pp. 99-127.
19. Y. Villanger, Lex M versus MCS-M, Discrete Math., 306 (2004), pp. 393-400. (Pubitemid 43289243)