Encyclopedia of Algorithms

Living Edition
| Editors: Ming-Yang Kao

Counting by ZDD

Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27848-8_734-1

Years and Authors of Summarized Original Work

1986; R. E. Bryant

1993; S. Minato

2009; D. E. Knuth

2013; S. Minato

2013; T. Inoue, H. Iwashita, J. Kawahara, and S. Minato

Problem Definition

We consider a framework of the problems to enumerate all the subsets of a given graph, each subset of which satisfies a given constraint. For example, enumerating all Hamilton cycles, all spanning trees, all paths between two vertices, all independent sets of vertices, etc. When we assume a graph G = (V, E) with the vertex set \(V =\{ v_{1},v_{2},\ldots ,v_{n}\}\)


BDD Binary decision diagram ZDD Zero-suppressed BDD Graph algorithm Dynamic programming Enumeration Indexing Data compression 
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Recommended Reading

  1. 1.
    Bryant RE (1986) Graph-based algorithms for Boolean function manipulation. IEEE Trans Comput C-35(8):677–691CrossRefGoogle Scholar
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    Doi S et al (2012) Time with class! let’s count! (the art of 1064 – understanding vastness –). YouTube video, http://www.youtube.com/watch?v=Q4gTV4r0zRs
  3. 3.
    Inoue T et al (2013) Graphillion. http://graphillion.org/
  4. 4.
    Inoue T, Iwashita H, Kawahara J, Minato S (2013) Graphillion: ZDD-based software library for very large sets of graphs. In: Proceedings of the workshop on synthesis and simulation meeting and international interchange (SASIMI-2013), R4-6, Sapporo, pp 237–242Google Scholar
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    Inoue T, Takano K, Watanabe T, Kawahara J, Yoshinaka R, Kishimoto A, Tsuda K, Minato S, Hayashi Y (2014) Distribution loss minimization with guaranteed error bound. IEEE Trans Smart Grid 5(1):102–111Google Scholar
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    Iwashita H, Nakazawa Y, Kawahara J, Uno T, Minato S (2013) Efficient computation of the number of paths in a grid graph with minimal perfect hash functions. TCS technical reports TCS-TR-A-10-64, Division of Computer Science, Hokkaido UniversityGoogle Scholar
  7. 7.
    Knuth DE (2009) Bitwise tricks & techniques; binary decision diagrams. The art of computer programming, vol 4, fascicle 1. Addison-Wesley, Upper Saddle RiverGoogle Scholar
  8. 8.
    Minato S (1993) Zero-suppressed BDDs for set manipulation in combinatorial problems. In: Proceedings of 30th ACM/IEEE design automation conference (DAC’93), Dallas, pp 272–277Google Scholar
  9. 9.
    Minato S (2013) Techniques of BDD/ZDD: brief history and recent activity. IEICE Trans Inf Syst E96-D(7):1419–1429CrossRefGoogle Scholar
  10. 10.
    OEIS-simpath (2013) Number of nonintersecting (or self-avoiding) rook paths joining opposite corners of an n ×n grid, the on-line encyclopedia of integer sequences. https://oeis.org/A007764

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Graduate School of Information Science and TechnologyHokkaido UniversitySapporoJapan