International Workshop on Algorithms and Computation

WALCOM 2015: WALCOM: Algorithms and Computation pp 317-322 | Cite as

Superset Generation on Decision Diagrams

  • Takahisa Toda
  • Shogo Takeuchi
  • Koji Tsuda
  • Shin-ichi Minato
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8973)

Abstract

Generating all supersets from a given set family is important, because it is closely related to identifying cause-effect relationship. This paper presents an efficient method for superset generation by using the compressed data structures BDDs and ZDDs effectively. We analyze the size of a BDD that represents all supersets. As a by-product, we obtain a non-trivial upper bound for the size of a BDD that represents a monotone Boolean function in a fixed variable ordering.

Keywords

superset binary decision diagram zero-suppressed binary decision diagram cause-effect relationship Boolean completion 

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References

  1. 1.
    Crama, Y., Hammer, P., Ibaraki, T.: Cause-effect relationships and partially defined Boolean functions. Annals of Operations Research 16(1), 299–325 (1988)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Kovalerchuk, B., Triantaphyllou, E., Ruiz, J.F., Torvik, V.I., Vityaev, E.: The reliability issue of computer-aided breast cancer diagnosis. Computers and Biomedical Research 33(4), 296–313 (2000)CrossRefGoogle Scholar
  3. 3.
    Kovalerchuk, B., Vityaev, E., Triantaphyllou, E.: How can AI procedures become more effective for manufacturings? In: Proc. of the Artificial Intelligence and Manufacturing Research Planning Workshop, Albuquerque, New, Mexico, pp. 103–111 (June 1996)Google Scholar
  4. 4.
    Judson, D.: Statistical rule induction in the presence of prior information: The bayesian record linkage problem. In: Triantaphyllou, E., Felici, G. (eds.) Data Mining and Knowledge Discovery Approaches Based on Rule Induction Techniques. Massive Computing, vol. 6, pp. 655–694. Springer US (2006)Google Scholar
  5. 5.
    Knuth, D.E.: The Art of Computer Programming Volume 4a. Addison-Wesley Professional, New Jersey (2011)Google Scholar
  6. 6.
    Toda, T.: Fast compression of large-scale hypergraphs for solving combinatorial problems. In: Fürnkranz, J., Hüllermeier, E., Higuchi, T. (eds.) DS 2013. LNCS, vol. 8140, pp. 281–293. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  7. 7.
    Huang, J., Darwiche, A.: Using DPLL for efficient OBDD construction. In: Hoos, H.H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, pp. 157–172. Springer, Heidelberg (2005)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Takahisa Toda
    • 1
  • Shogo Takeuchi
    • 2
  • Koji Tsuda
    • 2
    • 3
    • 4
  • Shin-ichi Minato
    • 2
    • 5
  1. 1.Graduate School of Information SystemsThe University of Electro-CommunicationsChofuJapan
  2. 2.ERATO MINATO Discrete Structure Manipulation System Project, Japan Science and Technology AgencyHokkaido UniversitySapporoJapan
  3. 3.Graduate School of Frontier SciencesThe University of TokyoKashiwaJapan
  4. 4.Computational Biology Research CenterNational Institute of Advanced Industrial Science and Technology (AIST)TokyoJapan
  5. 5.Graduate School of Information Science and TechnologyHokkaido UniversitySapporoJapan

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