On the Size of the Zero-Suppressed Binary Decision Diagram that Represents All the Subtrees in a Tree

  • Norihito Yasuda
  • Masaaki Nishino
  • Shin-ichi Minato
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8643)


This paper presents a method of constructing a ZDD that represents all connected subtrees in the given tree and analyzes the size of the resulting ZDD. We show that the size of the ZDD is bounded by \(O(nh)\) for a tree with \(n\)-nodes and \(h\)-height. Furthermore, by properly ordering the ZDD variables, we can further reduce the size to \(O(n\log n)\), which is surprisingly small compared to represent at most \(O(2^n)\) subtrees.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Norihito Yasuda
    • 1
  • Masaaki Nishino
    • 2
  • Shin-ichi Minato
    • 1
    • 3
  1. 1.JST ERATO Minato Discrete Structure Manipulation System ProjectSapporoJapan
  2. 2.NTT Communication Science LaboratoriesKyotoJapan
  3. 3.Hokkaido UniversitySapporoJapan

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