Fast and simple algorithms for recognizing chordal comparability graphs and interval graphs

SIAM Journal on Computing

Volumn 28, Issue 3, 1999, Pages 1004-1020

  Hsu, Wen Lian ^a   Ma, Tze Heng ^a  

^a INSTITUTE OF INFORMATION SCIENCE   (Taiwan)

Author keywords

Analysis of algorithms; Cardinality lexicographic ordering; Chordal graph; Cycle free poset; Graph partitioning; Graph recognition; Graph theory; Interval graph; Modular decomposition; Substitution decomposition; Transitive orientation; Triangulated graph

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; DATA STRUCTURES; ROOT LOCI; SET THEORY; TREES (MATHEMATICS);

CARDINALITY LEXICOGRAPHIC ORDERING; CHORDAL GRAPH; CYCLE FREE POSET; GRAPH PARTITIONING; GRAPH RECOGNITION; INTERVAL GRAPH; MODULAR DECOMPOSITION; SUBSTITUTION DECOMPOSITION; TRANSITIVE ORIENTATION; TRIANGULATED GRAPH;

GRAPH THEORY;

EID: 0032267125     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/s0097539792224814     Document Type: Article

References (22)

1. 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.
2. P. BUNEMAN, A characterization of rigid-circuit graphs, Discrete Math., 9 (1974), pp. 205-212.
3. D. COPPERSMITH AND S. WINOGRAD, Matrix multiplication via arithmetic progressions, in Proc. 19th Annual ACM Symposium on the Theory of Computation, ACM, New York, 1987, pp. 1-6.
4. D. CORNEIL, S. OLARIU, AND L. STEWART, The ultimate interval graph recognition algorithm?, in Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, Philadelphia, 1998, pp. 175-180.
5. D. DUFFUS, I. RIVAL, AND P. WINKLER, Minimizing setups for cycle-free ordered sets, Proc. Amer. Math. Soc., 85 (1982), pp. 509-513.
6. P. C. FISHBURN, Interval Orders and Interval Graphs, Wiley, New York, 1985.
7. D. R. FULKERSON AND O. A. GROSS, Incidence matrices and interval graphs, Pacific J. Math., 15 (1965), pp. 835-855.
8. F. GAVRIL, The intersection graphs of subtrees in trees are exactly the chordal graphs, J. Combin. Theory B, 16 (1974), pp. 47-56.
9. M. C. GOLUMBIC, Algorithmic Graph Theory and Perfect Graphs, Academic Press, New York, 1980.
10. P. C. GILMORE AND J. J. HOFFMAN, A characterization of comparability graphs and of interval graphs, Canad. J. Math., 16 (1964), pp. 539-548.
11. N. KORTE AND R. H. MÖHRING, An incremental linear-time algorithm for recognizing interval graphs, SIAM J. Comput., 18 (1989), pp. 68-81.
12. W. L. HSU AND T. H. MA, Substitution decomposition on chordal graphs and applications, in ISA '91, Algorithms: 2nd International Symposium on Algorithms, Lecture Notes in Comput. Sci. 557, Springer-Verlag, Berlin, 1991, pp. 52-60.
13. W. L. HSU, O(m · n) algorithms for the recognition and isomorphism problems on circular-arc graphs, SIAM J. Comput., 24 (1995), pp. 411-439.
14. C. G. LEKKERKERKER AND J. BOLAND, Representation of a finite graph by a set of intervals on the real line, Fund. Math., 51 (1962), pp. 45-64.
15. J. H. MULLER AND J. SPINRAD, Incremental modular decomposition, J. Assoc. Comput. Mach., 36 (1989), pp. 1-19.
16. T. H. MA AND J. SPINRAD, Cycle-free partial orders and chordal comparability graphs, Order, 8 (1991), pp. 175-183.
17. R. MCCONNELL AND J. SPINRAD, Linear-time modular decomposition and efficient transitive orientation of comparability graphs, in Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, 1994, SIAM, Philadelphia, pp. 536-545.
18. 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.
19. L. N. SHEVRIN AND N. D. FILIPPOV, Partially ordered sets and their comparability graphs, Siberian Math. J., 11 (1970), pp. 497-509.
20. J. SPINRAD, On comparability and permutation graphs, SIAM J. Comput., 14 (1985), pp. 658-670.
21. 4 trees and substitution decomposition, Disc. Appl. Math., 39 (1992), pp. 263-291.
22. R. E. TARJAN, Amortized computational complexity, SIAM J. Alg. Disc. Math., 6 (1985), pp. 306-318.