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)


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.


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


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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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