Skip to main content

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2942))

Abstract

Hypergraph Transversals have been studied in Mathematics for a long time, cf. [2]. Generating minimal transversals of a hypergraph is an important problem which has many applications in Computer Science, especially in database Theory, Logic, and AI. We briefly survey some results on problems which are known to be related to computing the transversal hypergraph, where we focus on problems in database theory, propositional Logic and AI (for a more detailed survey and further references cf. [10]).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Benzaken, C.: Algorithme de dualisation d’une fonction booléenne. Revue Francaise de Traitment de l’Information – Chiffres 9(2), 119–128 (1966)

    MathSciNet  Google Scholar 

  2. Berge, C.: Hypergraphs. North Holland, Amsterdam (1989)

    MATH  Google Scholar 

  3. Bioch, C., Ibaraki, T.: Complexity of identification and dualization of positive Boolean functions. Information and Computation 123, 50–63 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  4. Boros, E., Elbassioni, K., Gurvich, V., Khachiyan, L.: An efficient incremental algorithm for generating all maximal independent sets in hypergraphs of bounded dimension. Parallel Processing Letters 10(4), 253–266 (2000)

    Article  MathSciNet  Google Scholar 

  5. Boros, E., Gurvich, V., Hammer, P.L.: Dual subimplicants of positive Boolean functions. Optimization Methods and Software 10, 147–156 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  6. Boros, E., Gurvich, V., Khachiyan, L., Makino, K.: On the complexity of generating maximal frequent and minimal infrequent sets. In: Alt, H., Ferreira, A. (eds.) STACS 2002. LNCS, vol. 2285, pp. 133–141. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  7. Boros, E., Hammer, P., Ibaraki, T., Kawakami, K.: Polynomial time recognition of 2-monotonic positive Boolean functions given by an oracle. SIAM J. Comput. 26(1), 93–109 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  8. Domingo, C., Mishra, N., Pitt, L.: Efficient read-restricted monotone CNF/DNF dualization by learning with membership queries. Machine Learning 37 (1999)

    Google Scholar 

  9. Eiter, T., Gottlob, G.: Identifying the minimal transversals of a hypergraph and related problems. SIAM Journal on Computing 24(6), 1278–1304 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  10. Eiter, T., Gottlob, G.: Hypergraph Transversal Computation and Related Problems in Logic and AI. In: Flesca, S., Greco, S., Leone, N., Ianni, G. (eds.) JELIA 2002. LNCS (LNAI), vol. 2424, pp. 549–564. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  11. Eiter, T., Gottlob, G., Makino, K.: New results on monotone dualization and generating hypergraph transversals. SIAM Journal on Computing 32(2), 514–537 (2003); Preprint available as Computer Science Repository Report (CoRR) nr. cs. DS/0204009, (A shorter version has appeared in Proc. ACM STOC 2002, pp. 14–22 (2002), http://arxiv.org/abs/cs/0204009

    Article  MATH  MathSciNet  Google Scholar 

  12. Eiter, T., Makino, K.: On computing all abductive explanations. In: Proc. 18th National Conference on Artificial Intelligence (AAAI 2002), AAAI Press, Menlo Park (2002)

    Google Scholar 

  13. Eiter, T., Makino, K., Ibaraki, T.: Decision lists and related Boolean functions. Theoretical Computer Science 270(1-2), 493–524 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  14. Fagin, R.: Degrees of acyclicity for hypergraphs and relational database schemes. Journal of the ACM 30, 514–550 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  15. Fredman, M., Khachiyan, L.: On the complexity of dualization of monotone disjunctive normal forms. Journal of Algorithms 21, 618–628 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  16. Gaur, D., Krishnamurti, R.: Self-duality of bounded monotone Boolean functions and related problems. In: Arimura, H., Sharma, A.K., Jain, S. (eds.) ALT 2000. LNCS (LNAI), vol. 1968, pp. 209–223. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  17. Gogic, G., Papadimitriou, C., Sideri, M.: Incremental recompilation of knowledge. J. Artificial Intelligence Research 8, 23–37 (1998)

    MATH  MathSciNet  Google Scholar 

  18. Goldsmith, J., Levy, M., Mundhenk, M.: Limited nondeterminism. SIGACT News 27(2), 20–29 (1978)

    Article  Google Scholar 

  19. Gottlob, G., Libkin, L.: Investigations on Armstrong relations, dependency inference, and excluded functional dependencies. Acta Cybernetica 9(4), 385–402 (1990)

    MATH  MathSciNet  Google Scholar 

  20. Gunopulos, D., Khardon, R., Mannila, H., Toivonen, H.: Data mining, hypergraph transversals, and machine learning. In: Proc. 16th ACM Symp. on Principles of Database Systems (PODS 1997), pp. 209–216 (1997)

    Google Scholar 

  21. Kavvadias, D., Papadimitriou, C., Sideri, M.: On Horn envelopes and hypergraph transversals. In: Ng, K.W., Balasubramanian, N.V., Raghavan, P., Chin, F.Y.L. (eds.) ISAAC 1993. LNCS, vol. 762, pp. 399–405. Springer, Heidelberg (1993)

    Google Scholar 

  22. Khardon, R.: Translating between Horn representations and their characteristic models. J. Artificial Intelligence Research 3, 349–372 (1995)

    MATH  Google Scholar 

  23. Makino, K., Ibaraki, T.: A fast and simple algorithm for identifying 2-monotonic positive Boolean functions. Journal of Algorithms 26, 291–302 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  24. Mannila, H., Räihä, K.-J.: Design by Example: An application of Armstrong relations. Journal of Computer and System Sciences 22(2), 126–141 (1986)

    Article  Google Scholar 

  25. Mannila, H., Räihä, K.-J.: Dependency Inference. In: VLDB 1987, pp. 155–158 (1987)

    Google Scholar 

  26. Mannila, H., Räihä, K.-J.: On the Complexity of Inferring Functional Dependencies. Discrete Applied Mathematics 40(2), 223–237 (1992)

    Article  Google Scholar 

  27. Mishra, N., Pitt, L.: Generating all maximal independent sets of boundeddegree hypergraphs. In: Proc. Tenth Annual Conference on Computational Learning Theory (COLT 1997), pp. 211–217 (1997)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gottlob, G. (2004). Hypergraph Transversals. In: Seipel, D., Turull-Torres, J.M. (eds) Foundations of Information and Knowledge Systems. FoIKS 2004. Lecture Notes in Computer Science, vol 2942. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24627-5_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-24627-5_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20965-2

  • Online ISBN: 978-3-540-24627-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics