An efficient algorithm for the transversal hypergraph generation

Journal of Graph Algorithms and Applications

Volumn 9, Issue 2, 2005, Pages 239-264

  Kavvadias, Dimitris J ^a   Stavropoulos, Elias C ^a  

^a UNIVERSITY OF PATRAS   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM FOR SOLVING; EXPERIMENTAL COMPARISON; EXPERIMENTAL EVALUATION; HYPER GRAPH; HYPEREDGES; LARGE PROBLEMS; MEMORY REQUIREMENTS; MINIMAL HITTING SET; PROBLEM INSTANCES; TIME BOUND;

PROBLEM SOLVING;

EID: 27844519832     PISSN: 15261719     EISSN: 15261719     Source Type: Journal    
DOI: 10.7155/jgaa.00107     Document Type: Article

References (39)

1. J. Bailey, T. Manoukian, and K. Ramamohanarao. A fast algorithm for computing hypergraph transversals and its application in mining emerging patersn. In Proc. of the 3rd IEEE International Conference on Mining (ICDM 2003), pages 485-488. IEEE Computer Society, December 2003.
2. R. Ben-Eliyahu and R. Dechter. On computing minimal models. Annals of Mathematics and Artificial Intelligence, 18:3-27, 1996.
3. C. Berge. Hypergraphs: Combinatorics of Finite Sets, volume 45 of North Holland Mathematical Library. Elsevier Science Publishers B.V., Amsterdam, 1989.
4. J. C. Bioch and T. Ibaraki. Complexity of identification and dualization of positive Boolean functions. Information and Computation, 123:50-63, 1995.
5. B. Bollobás. Combinatorics: Set Systems, Hypergraphs, Families of Vectors and Combinatorial Probability. Cambridge University Press, Great Britain, 1986.
6. E. Boros, K. Elbassioni, V. Gurvich, and L. Khachiyan. An efficient implementation of a quasi-polynomial algorithm for generating hypergraph transversals. In Proc. of the 11th European Symposioum on Algorithms (ESA 2003), volume 2432 of LNCS, pages 556-567. Springer, 2003.
7. N. H. Bshouty, R. Cleve, R. Gavaldà, S. Kannan, and C. Tamon. Oracles and queries that are sufficient for exact learning. Journal of Computer Systems and Sciences, 52:421-433, 1996.
8. M. Cadoli. The complexity of model checking for circumscriptive formulae. Information Processing Letters, 44(3):113-118, 1992.
9. Z.-Z. Chen and S. Toda. The complexity of selecting maximal solutions. Information and Computation, 119:231-239, 1995.
10. J. de Kleer, A. K. Mackworth, and R. Reiter. Characterizing diagnosis and systems. Artificial Intelligence, 56:197-222, 1992.
11. J. Diaz and J. Toŕan. Classes of bounded nondeterminism. Mathematical Systems Theory, 23:21-32, 1990.
12. C. Domingo, N. Mishra, and L. Pitt. Efficient read-restricted monotone CNF/DNF dualization by learning with membership queries. Machine Learning, 37(1):88-110, 1999.
13. J.-G. Dumas, F. Heckenbach, D. Saunders, and V. Welker. Computing simplicial homology based on efficient Smith Normal Form algorithms. In Algebra, Geometry, and Software Systems, pages 177-206, 2003.
14. T. Eiter and G. Gottlob. Identifying the minimal transversals of a hypergraph and related problems. SIAM Journal of Computing, 24(6):1278-1304, December 1995.
15. T. Eiter and G. Gottlob. Hypergraph transversal computation and related problems in Logic and AI. In Proc. of the 8th European Conference on Logics in Artificial Intelligence (JELIA 2002), volume 2424 of LNCS/LNAI, pages 549-564. Springer, 2002.
16. T. Eiter, G. Gottlob, and K. Makino. New results on monotone dualization and generating hypergraph transversals. In Proc. of the 34th ACM Symposium on Theory of Computing (STOC 2002), pages 14-22, Montreal, Quebec, Canada, May 2002.
17. T. Eiter, G. Gottlob, and K. Makino. New results on monotone dualization and generating hypergraph transversals. SIAM J. Computing, 32(2):514-537, 2003.
18. M. L. Fredman and L. Khachiyan. On the complexity of dualization of monotone disjunctive normal forms. Journal of Algorithms, 21:618-628, 1996.
19. M. R. Garey and D. S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman and Company, San Francisco, 1979.
20. L. A. Goldberg. Efficient Algorithms for Listing Combinatorial Structures. BCS Distinguished Dissertations in Computer Science. Cambridge University Press, Great Britain, 1993.
21. J. Goldsmith, M. A. Levy, and M. Mundhenk. Limited nondeterminism. ACM SIGACT News, 27(2):20-29, June 1996.
22. D. Gunopulos, R. Khardon, H. Mannila, S. Saluja, H. Toivonen, and R. S. Sharma. Discovering all most specific sentences. ACM Transactions on Database Systems, 28(2):140-174, June 2003.
23. D. Gunopulos, R. Khardon, H. Mannila, and H. Toivonen. Data mining, hypergraph transversals, and machine learning. In Proc. of Sixteenth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, pages 209-216, Tucson, Arizona, USA, May 1997. ACM Press.
24. V. Gurvich and L. Khachiyan. On generating the irredundant conjunctive and disjunctive normal forms of monotone Boolean functions. Discrete Applied Mathematics, 96-97:363-373, 1999.
25. D. S. Johnson, M. Yannakakis, and C. H. Papadimitriou. On generating all maximal independent sets. Information Processing Letters, 27:119-123, March 1988.
26. D. Kavvadias, C. H. Papadimitriou, and M. Sideri. On Horn envelopes and hypergraph transversals. In Proc. of 4th Annual International Symposium on Algorithms and Computation (ISAAC'93), volume 762 of LNCS, pages 399-405, Hong Kong, 1993. Springer.
27. D. Kavvadias and M. Sideri. The inverse satisfiability problem. SIAM Journal of Computing, 28(1):152-163, 1998.
28. D. J. Kavvadias, M. Sideri, and E. C. Stavropoulos. Generating all maximal models of a Boolean expression. Information Processing Letters, 74(3-4):157-162, May 2000.
29. D. J. Kavvadias and E. C. Stavropoulos. Evaluation of an algorithm for the transversal hypergraph problem. In J. S. Vitter and C. D. Zaroliagis, editors, Proc. of 3th International Workshop on Algorithm Engineering (WAE99), volume 1668 of LNCS, pages 72-84, London, UK, 1999. Springer-Verlag.
30. 2 n]. Information Processing Letters, 85(1):1-6, January 2003.
31. C. M. R. Kintala and P. Fischer. Refining nondeterminism in relativized polynomial-time bounded computations. SIAM J. Computing, 9:46-53, 1980.
32. E. L. Lawler. Covering problems: duality relations and a new method of solution. SIAM Journal of Applied Mathematics, 14(5):1115-1132, September 1966.
33. H. Mannila and K.-J. Räihä. Design by example: An application of Armstrong relations. Journal of Computer and System Sciences, 33:126-141, 1986.
34. C. H. Papadimitriou. NP-completeness: A retrospective. In Proc. of 24th International Colloquium on Automata, Languages, and Programming, volume 1256 of LNCS, pages 2-6, Bologna, Italy, July 1997.
35. R. Reiter. A theory of diagnosis from first principles. Artificial Intelligence, 32(1):57-95, 1987.
36. S. Sarkar and N. Savarajan. Hypergraph models for cellular mobile communication systems. IEEE Transactions on Vehicular Technology, 47(2):460-471, May 1998.
37. B. Selman and H. A. Kautz. Model-preference default theories. Artificial Intelligence, 45:287-322, 1990.
38. B. Selman and H. A. Kautz. Knowledge compilation and theory approximation. Journal of the ACM, 43(2):193-224, 1996.
39. B. Zanuttini. Approximation of relations by propositional formulas: Complexity and semantics. In S. Koenig and R. Holte, editors, Proc. of the SARA 2002, volume 2371 of LNCS, pages 242-255. Springer-Verlag, 2002.