Lex-BFS and partition refinement, with applications to transitive orientation, interval graph recognition and consecutive ones testing

Theoretical Computer Science

Volumn 234, Issue 1-2, 2000, Pages 59-84

  Habib, Michel ^a   McConnell, Ross ^b   Paul, Christophe ^a   Viennot, Laurent ^c  

^a LIRMM   (France)

^b The University of Colorado Denver   (United States)

^c UNIVERSITÉ PARIS DIDEROT   (France)

Author keywords

Algorithm; Boolean matrix; Data structure; Graph; Partition refinement

Indexed keywords

EID: 0002482188     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(97)00241-7     Document Type: Article

References (16)

1. C. Berge, Graphes et Hypergraphes, Dunod, Paris, 1970.
2. K.S. Booth, G.S. Lueker, Testing for the consecutive ones property, interval graphs and graph planarity using pq-tree algorithm, J. Comput. System Sci. 13 (1976) 335-379.
3. A. Brandstädt, Classes of bipartite graphs related to chordal graphs, Discrete Appl. Math. 32 (1991) 51-60.
4. A. Cournier, M. Habib, A new linear algorithm of modular decomposition, in: Trees in Algebra and Programming - CAAP 94, Edinburgh, Lecture Notes in Computer Science, vol. 787, Springer, Berlin, 1994, pp. 68-84.
5. E. Dahlhaus, J. Gustedt, R.M. McConnell, Efficient and practical modular decomposition, in: Proc. 7th Ann. ACM-SIAM Symp. on Discrete Algorithm, SIAM, Philadelphia, 1997, pp. 26-35.
6. P. Galinier, M. Habib, C. Paul, Chordal graphs and their clique graph, in: M. Nagl (Ed.), Graph-Theoretic Concepts in Computer Science, WG'95, Lecture Notes in Computer Science, vol. 1017, Aachen, Germany, June 1995, Proc. 21st Internat. Workshop WG'95, Springer, Berlin.
7. T. Gallai, Transitiv orientierbare graphen, Acta Math. Acad. Sci. Hungar. 18 (1967) 25-66.
8. F. Gavril, The intersection graphs of a path in a tree are exactly the chordal graphs, J. Combin. Theory 16 (1974) 47-56.
9. M.C. Golumbic, Algorithms Graph Theory and Perfect Graphs, Academic Press, New York University, 1980.
10. Hsu, Ma, Substitution decomposition on chordal graphs and applications, in: Proc. 2nd ACM-SIGSAM Internat. Symp. on Symbolic Algebraic Comput., Lecture Notes in Computer Science, vol. 557, Springer, Berlin.
11. N. Korte, R. Möhring, An incremental linear-time algorithm for recognizing interval graphs, SIAM J. Comput. 18 (1989) 68-81.
12. R.M. McConnell, J.P. Spinrad, Linear-time modular decomposition and efficient transitive orientation of comparability graphs, in: Proc. 5th Annual ACM-SIAM Symp. on Discrete Algorithms, Arlington, VA, 1994, pp. 536-545.
13. R.M. McConnell, J.P. Spinrad, Linear-time modular decomposition and efficient transitive orientation of undirected graphs, in: Proc. 7th Annual ACM-SIAM Symp. Discrete Algorithm, SIAM, Philadelphia, 1997, pp. 19-35.
14. R. Paige, R.E. Tarjan, Three partition refinement algorithms, SIAM J. Comput. 16 (1987) 973-989.
15. D.J. Rose, R. Endre Tarjan, George S. Leuker, Algorithmic aspects of vertex elimination on graphs, SIAM J. Comput. 5 (1976) 266-283.
16. J.P. Spinrad, Graph partitioning, 1986.