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

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Book cover Trends and Applications in Knowledge Discovery and Data Mining (PAKDD 2014)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8643))

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Abstract

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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Author information

Authors and Affiliations

  1. JST ERATO Minato Discrete Structure Manipulation System Project, Sapporo, Japan

    Norihito Yasuda & Shin-ichi Minato

  2. NTT Communication Science Laboratories, Kyoto, Japan

    Masaaki Nishino

  3. Hokkaido University, Sapporo, Japan

    Shin-ichi Minato

Authors
  1. Norihito Yasuda
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  2. Masaaki Nishino
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  3. Shin-ichi Minato
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Corresponding author

Correspondence to Norihito Yasuda .

Editor information

Editors and Affiliations

  1. National Chiao Tung University, Hsinchu, Taiwan

    Wen-Chih Peng

  2. Google Research, Mountain View, California, USA

    Haixun Wang

  3. University of Melbourne, Melbourne, Victoria, Australia

    James Bailey

  4. National Cheng Kung University, Tainan, Taiwan

    Vincent S. Tseng

  5. Japan Advanced Institute of Science and Technology, Nomi City, Japan

    Tu Bao Ho

  6. Nanjing University, Nanjing, China

    Zhi-Hua Zhou

  7. National Chengchi University, Taipei, Taiwan

    Arbee L.P. Chen

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© 2014 Springer International Publishing Switzerland

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Yasuda, N., Nishino, M., Minato, Si. (2014). On the Size of the Zero-Suppressed Binary Decision Diagram that Represents All the Subtrees in a Tree. In: Peng, WC., et al. Trends and Applications in Knowledge Discovery and Data Mining. PAKDD 2014. Lecture Notes in Computer Science(), vol 8643. Springer, Cham. https://doi.org/10.1007/978-3-319-13186-3_45

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  • DOI: https://doi.org/10.1007/978-3-319-13186-3_45

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-13185-6

  • Online ISBN: 978-3-319-13186-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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