Skip to main content
SpringerLink
Log in
Book cover

International Symposium on Experimental Algorithms

SEA 2013: Experimental Algorithms pp 91–102Cite as

Hypergraph Transversal Computation with Binary Decision Diagrams

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7933))

Abstract

We study a hypergraph transversal computation: given a hypergraph, the problem is to generate all minimal transversals. This problem is related to many applications in computer science and various algorithms have been proposed. We present a new efficient algorithm using the compressed data structures BDDs and ZDDs, and we analyze the time complexity for it. By conducting computational experiments, we show that our algorithm is highly competitive with existing algorithms.

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

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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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 

  2. Eiter, T., Makino, K., Gottlob, G.: Computational aspects of monotone dualization: A brief survey. Discrete Applied Mathematics 156, 2035–2049 (2008)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  4. Gurvich, V., Khachiyan, L.: On generating the irredundant conjunctive and disjunctive normal forms of monotone Boolean functions. Discrete Applied Mathematics 96-97, 363–373 (1999)

    Article  MathSciNet  Google Scholar 

  5. Khachiyan, L., Boros, E., Elbassioni, K., Gurvich, V.: An efficient implementation of a quasi-polynomial algorithm for generating hypergraph transversals and its application in joint generation. Discrete Applied Mathematics 154, 2350–2372 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  6. Murakami, K., Uno, T.: Efficient algorithms for dualizing large-scale hypergraphs. In: Proc. of the Meeting on Algorithm Engineering & Experiments, ALENEX, New Orleans, Louisiana, USA, pp. 1–13 (January 2013)

    Google Scholar 

  7. Dong, G., Li, J.: Mining border descriptions of emerging patterns from dataset pairs. Knowledge and Information Systems 8, 178–202 (2005)

    Article  Google Scholar 

  8. Bailey, J., Manoukian, T., Ramamohanarao, K.: A fast algorithm for computing hypergraph transversals and its application in mining emerging patterns. In: Proc. of the 3rd IEEE International Conference on Data Mining, pp. 485–488. IEEE Computer Society (November 2003)

    Google Scholar 

  9. Kavvadias, D., Stavropoulos, E.: An efficient algorithm for the transversal hypergraph generation. Journal of Graph Algorithms and Applications 9(2), 239–264 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  10. Hérbert, C., Bretto, A., Crémilleux, B.: A data mining formalization to improve hypergraph minimal transversal computation. Fundamental Informaticae 80, 415–433 (2007)

    Google Scholar 

  11. Knuth, D.: The Art of Computer Programming, vol. 4A. Addison-Wesley Professional, New Jersey (2011)

    Google Scholar 

  12. Bryant, R.: Graph-based algorithms for Boolean function manipulation. IEEE Transaction on Computers 35, 677–691 (1986)

    Article  MATH  Google Scholar 

  13. Yoshinaka, R., Kawahara, J., Denzumi, S., Arimura, H., Minato, S.: Counterexamples to the long-standing conjecture on the complexity of BDD binary operations. Information Processing Letters 112, 636–640 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  14. Minato, S.: Zero-suppressed BDDs for set manipulation in combinatorial problems. In: Proc. of 30th ACM/IEEE Design Automation Conference, DAC 1993, Dallas, Texas, USA, pp. 272–277 (June 1993)

    Google Scholar 

  15. Toda, T.: HTC-BDD: Hypergraph Transversal Computation with Binary Decision Diagrams (2013), http://kuma-san.net/htcbdd.html (accessed on March 28)

  16. Murakami, K., Uno, T.: Hypergraph Dualization Repository (2013), http://research.nii.ac.jp/~uno/dualization.html (accessed on January 19)

  17. Khachiyan, L., Boros, E., Elbassioni, K., Gurvich, V.: A global parallel algorithm for the hypergraph transversal problem. Information Processing Letters 101, 148–155 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  18. Coudert, O.: Solving graph optimization problems with ZBDDs. In: Proc. of the 1997 European Conference on Design and Test, Paris, France, pp. 224–228 (March 1997)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. ERATO MINATO Discrete Structure Manipulation System Project, Japan Science and Technology Agency, Hokkaido University, Sapporo, 060-0814, Japan

    Takahisa Toda

Authors
  1. Takahisa Toda
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute for Systems Analysis and Computer Science (IASI), National Research Council (CNR), Viale Manzoni 30, 00185, Rome, Italy

    Vincenzo Bonifaci

  2. Department of Computer and Systems Science, Sapienza University of Rome, Via Ariosto 25, 00185, Rome, Italy

    Camil Demetrescu  & Alberto Marchetti-Spaccamela  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Toda, T. (2013). Hypergraph Transversal Computation with Binary Decision Diagrams. In: Bonifaci, V., Demetrescu, C., Marchetti-Spaccamela, A. (eds) Experimental Algorithms. SEA 2013. Lecture Notes in Computer Science, vol 7933. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38527-8_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-38527-8_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38526-1

  • Online ISBN: 978-3-642-38527-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation