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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Crama, Y., Hammer, P., Ibaraki, T.: Cause-effect relationships and partially defined Boolean functions. Annals of Operations Research 16(1), 299–325 (1988)
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)
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)
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)
Knuth, D.E.: The Art of Computer Programming Volume 4a. Addison-Wesley Professional, New Jersey (2011)
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)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Toda, T., Takeuchi, S., Tsuda, K., Minato, Si. (2015). Superset Generation on Decision Diagrams. In: Rahman, M.S., Tomita, E. (eds) WALCOM: Algorithms and Computation. WALCOM 2015. Lecture Notes in Computer Science, vol 8973. Springer, Cham. https://doi.org/10.1007/978-3-319-15612-5_28
Download citation
DOI: https://doi.org/10.1007/978-3-319-15612-5_28
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-15611-8
Online ISBN: 978-3-319-15612-5
eBook Packages: Computer ScienceComputer Science (R0)