Certifying algorithms for recognizing interval graphs and permutation graphs

SIAM Journal on Computing

Volumn 36, Issue 2, 2006, Pages 326-353

  Kratsch, Dieter ^a   Moconnell, Ross M ^b   Mehlhorn, Kurt ^c   Spinrad, Jeremy P ^d  

^a UNIVERSITÉ DE LORRAINE   (France)

^b Department of Computer Science   (United States)

^c MAX PLANCK INSTITUTE FOR INFORMATICS   (Germany)

^d VANDERBILT UNIVERSITY   (United States)

Author keywords

Certificates; Certifying algorithms; Interval graphs; Permutation graphs

Indexed keywords

ALGORITHMS FAILURE; CERTIFYING ALGORITHMS; INTERVAL GRAPHS; PERMUTATION GRAPHS;

ALGORITHMS; COMPUTATIONAL METHODS; LINEAR SYSTEMS; PROBLEM SOLVING;

GRAPH THEORY;

EID: 33845544501     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539703437855     Document Type: Article

References (28)

1. M. BLUM AND S. KANNAN, Designing programs that check their work, in Proceedings of the 21st Symposium on the Theory of Computation, ACM, New York, 1989, pp. 86-97.
2. K. S. BOOTH AND G.S. LUEKER, Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms, J. Comput. System Sci., 13 (1976), pp. 335-379.
3. A. BRANDSTÄDT, V. B. LE, AND,J. P. SPINRAD, Graph Classes: A Survey, SIAM Monogr. Discrete Math. Appl. 3, SIAM, Philadelphia, 1999.
4. D. G. CORNEIL, S. OLARIU, AND L. STEWART, The ultimate interval graph recognition algorithm?, in Proceedings of the Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, ACM, New York, SIAM, Philadelphia, 1998, pp. 175-180.
5. D. G. CORNEIL, Y. PERL, AND L. K. STEWART, A linear recognition algorithm for cographs, SIAM J. Comput., 14 (1985), pp. 926-934.
6. G. A DIRAC, On rigid circuit graphs, Abh. Math. Sem. Univ. Hamburg, 25 (1961), pp. 71-76.
7. T. GALLAI, Transitiv orientierbare Graphen, Acta Math. Acad. Sci. Hungar., 18 (1967), pp. 25-66.
8. M. C. GOLUMBIC, Algorithmic Graph Theory and Perfect Graphs, Academic Press, New York, 1980.
9. M. HABIB, R. M. MCCONNELL, C. PAUL, AND L. VIENNOT, Lex-BFS and partition refinement, with applications to transitive orientation, interval graph recognition, and consecutive ones testing, Theoret. Comput. Sci., 234 (2000), pp. 59-84.
10. D. HAREL AND R. E. TARJAN, Fast algorithms for finding nearest common ancestors, SIAM J. Comput., 13 (1984), pp. 338-355.
11. W. L. HSU, A simple test for interval graphs, in Graph-theoretic Concepts in Computer Science, Lecture Notes in Comput. Sci. 657, Springer, Berlin, 1993, pp. 11-16.
12. W. L. HSU AND R. M. MCCONNELL, PC trees and circular-ones arrangements, Theoret. Comput. Sci., 296 (2003), pp. 99-116.
13. N. KORTE AND R. H. MÖHRING, An incremental linear-time algorithm for recognizing interval graphs, SIAM J. Comput., 18 (1989), pp. 68-81.
14. D. C. KOZEN, The Design and Analysis of Algorithms, Springer, Berlin, 1991.
15. C. LEKKERKERKER AND D. BOLAND, Representation of finite graphs by a set of intervals on the real line, Fund. Math., 51 (1962), pp. 45-64.
16. A. LUBIW, Doubly lexical orderings of matrices, SIAM J. Comput., 16 (1987), pp. 854-879.
17. R. M. MCCONNELL AND F. DE MONTGOLFIER, On the Common Factors in a Set of Linear Orders, Technical report CS-04-102, Colorado State University, Fort Collins, CO, 2004.
18. R. M. MCCONNELL AND J. P. SPINRAD, Modular decomposition and transitive orientation, Discrete Math., 201 (1999), pp. 189-241.
19. K. MEHLHORN AND S. NÄHER, The LEDA Platform for Combinatorial and Geometric Computing, Cambridge University Press, Cambridge, UK, 1999.
20. K. MEHLHORN, S. NÄHER, T. SCHILZ, M. SEEL, R. SEIDEL, AND C. UHRIG, Checking geometric programs or verification of geometric structures, Comput. Geom., 12 (1999), pp. 85-103.
21. K. MEHLHORN, S. NÄHER, AND C. UHRIG, The LEDA platform for combinatorial and geometric computing, in Proceedings of the 24th International Colloquium on Automata, Languages, and Programming (ICALP '97), Lecture Notes in Comput. Sci. 1256, Springer-Verlag, Berlin, 1997, pp. 7-16.
22. R. PAIGE AND R. E. TARJAN, Three partition refinement algorithms, SIAM J. Comput., 16 (1987), pp. 973-989.
23. A. PNUELI, A. LEMPEL, AND S. EVEN, Transitive orientation of graphs and identification of permutation graphs, Canad. J. Math., 23 (1971), pp. 160-175.
24. F. S. ROBERTS, Graph Theory and Its Applications to Problems of Society, SIAM, Philadelphia, 1978.
25. D. J. ROSE, R. E. TARJAN, AND G. S. LUEKER, Algorithmic aspects of vertex elimination on graphs, SIAM J. Comput., 5 (1976), pp. 266-283.
26. J. P. SPINRAD, Doubly lexical ordering of dense 0-1 matrices, Inform. Process. Lett., 45 (1993), pp. 229-235.
27. R. E. TARJAN AND M. YANNAKAKIS, Addendum: Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs, SIAM J. Comput., 14 (1985), pp. 254-255.
28. H. WASSERMAN AND M. BLUM, Software reliability via run-time result-checking, J. ACM, 44 (1997), pp. 826-849.