Linear time split decomposition revisited

SIAM Journal on Discrete Mathematics

Volumn 26, Issue 2, 2012, Pages 499-514

  Charbit, Pierre ^a   De Montgolfier, Fabien ^a   Raffinot, Mathieu ^a  

^a UNIVERSITÉ PARIS DIDEROT   (France)

Author keywords

1 join decomposition; Graph algorithms; Graph decomposition; Graph theory; Split decomposition

Indexed keywords

GRAPH ALGORITHMS; GRAPH DECOMPOSITIONS; LINEAR TIME; LINEAR-TIME ALGORITHMS; SPLIT DECOMPOSITION; UNDIRECTED GRAPH;

ALGORITHMS; GRAPH THEORY;

FLUORINE;

EID: 84865627166     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/10080052X     Document Type: Article

References (25)

1. A. Brandstädt, V. B. Le, and J. P. Spinrad, Graph Classes: A Survey, SIAM Monogr. Discrete Appl. Math. 3, SIAM, Philadelphia, 1999.
2. P. Charbit, M. Habib, V. Limouzy, F. de Montgolfier, M. Raffinot, and M. Rao, A note on computing set overlap classes, Inform. Process. Lett., 108 (2008), pp. 186-191.
3. M. Chein, M. Habib, and M. C. Maurer, Partitive hypergraphs, Discrete Math., 37 (1981), pp. 35-50.
4. S. Cicerone and G. Di Stefano, One the extension of bipartite to parity graphs, Discrete Appl. Math., 95 (1999), pp. 181-195.
5. A. Cournier and M. Habib, A new linear algorithm for modular decomposition, in Trees in Algebra and Programming (CAAP), Lecture Notes in Comput. Sci. 787, Springer-Verlag, Berlin, New York, 1994, pp. 68-84.
6. W. H. Cunningham, Decomposition of directed graphs, SIAM J. Algebraic Discrete Methods, 3 (1982), pp. 214-228.
7. E. Dahlhaus, Efficient parallel and linear time sequential split decomposition (extended abstract), in Proceedings of the 14th Conference on Foundations of Software Technology and Theoretical Computer Science (London), Springer-Verlag, Berlin, New York, 1994, pp. 171-180.
8. E. Dahlhaus, Parallel algorithms for hierarchical clustering, and applications to split decomposition and parity graph recognition, J. Algorithms, 36 (2000), pp. 205-240.
9. C. P. Gabor, K. J. Supowit, and W.-L. Hsu, Recognizing circle graphs in polynomial time, J. ACM, 36 (1989), pp. 435-473.
10. C. Gavoille and C. Paul, Distance labeling scheme and split decomposition, Discrete Math., 273 (2003), pp. 115-130.
11. E. Gioan and C. Paul, Dynamic distance hereditary graphs using split decomposition, in Proceedings of the 18th International Symposium on Algorithms and Computation (ISAAC 2007), Lecture Notes in Comp Sci. 4835, Springer, Berlin, 2007, pp. 41-51.
12. M. Habib, C. Paul, and L. Viennot, Partition refinement techniques: An interesting algorithmic toolkit, Internat. J. Found. Comput. Sci., 10 (1999), pp. 147-170.
13. W.-L. Hsu and R. McConnell, PC-trees and circular-ones arrangements, Theoret. Comput. Sci., 296 (2003), pp. 99-116.
14. 2) algorithm for undirected split decomposition, J. Algorithms, 16 (1994), pp. 145-160.
15. R. M. McConnell, A certifying algorithm for the consecutive-ones property, in Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), SIAM, Philadelphia, ACM, New York, 2004, pp. 768-777.
16. R. McConnell and F. de Montgolfier, Linear-time modular decomposition of directed graphs, Discrete Appl. Math., 145 (2005), pp. 198-209.
17. R. McConnell and J. Spinrad, Linear-time modular decomposition and efficient transitive orientation of comparability graphs, in Proceedings of the Fifth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), SIAM, Philadelphia, ACM, New York, 1994, pp. 536-545.
18. R. H. Möhring, Algorithmic aspects of the substitution decomposition in optimization over relations, set systems and Boolean functions, Ann. Oper. Res., 6 (1985), pp. 195-225.
19. R. H. Möhring and F. J. Radermacher, Substitution decomposition for discrete structures and connections with combinatorial optimization, Ann. Discrete Math., 19 (1984), pp. 257- 356.
20. M. Rao, Set Overlap Classes Computation, Source Code, 2007. Available online at http://www.liafa.jussieu.fr/∼raffinot/overlap.html.
21. M. Rao, Coloring a graph using split decomposition, in Graph Theoretic Concepts in Computer Science, Lecture Notes in Comput. Sci. 3353, Springer-Verlag, Berlin, 2004, pp. 129-141.
22. M. Rao, Solving some np-complete problems using split decomposition, Discrete Appl. Math., 156 (2008), pp. 2768-2780.
23. J. Spinrad, Recognition of circle graphs, J. Algorithms, 16 (1994), pp. 264-282.
24. R. E. Tarjan, Decomposition by clique separators, Discrete Math., 55 (1985), pp. 221-232.
25. M. Tedder, D. G. Corneil, M. Habib, and C. Paul, Simpler linear-time modular decomposition via recursive factorizing permutations, in Proceedings of the 35th International Colloquium on Automata, Languages, and Programming (ICALP), Lecture Notes in Comput. Sci. 5125, Springer, Berlin, 2008, pp. 634-645.