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Fast compilation of graph substructures for counting and enumeration

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Abstract

In this paper, we propose a new compilation method called merging frontier-based search for s–t simple paths on a graph. Recently, Nishino et al. proposed a top-down construction algorithm, which compiles s–t simple paths into a zero-suppressed SDD (ZSDD), and they showed that this method is more efficient than simpath by Knuth. However, since the method of Nishino et al. uses ZSDD as a tractable representation, it requires complicated steps for compilation. In this paper, we propose structured Z-d-DNNF, which is a super set of ZSDD. Though this representation relaxed the restriction of ZSDD, it supports important queries like model counting and model enumeration. Using this representation instead of ZSDD, we show that more efficient compilation can be realized for s–t simple paths.

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Notes

  1. Since, in our paper, the elements that appears in a vtree are edges, they are denoted by E instead of I.

  2. http://www.graphdrawing.org/download/rome-graphml.tgz

  3. The implementation was obtained from https://github.com/kunisura/TdZdd.

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Author information

Authors and Affiliations

  1. Graduate School of Information Science and Technology, Hokkaido University, Sapporo, Japan

    Teruji Sugaya

  2. NTT Communication Science Laboratories, NTT Corporation, Kyoto, Japan

    Masaaki Nishino & Norihito Yasuda

  3. Graduate School of Informatics, Kyoto University, Kyoto, Japan

    Shin-ichi Minato

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

Correspondence to Teruji Sugaya.

Additional information

Communicated by Joe Suzuki.

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Sugaya, T., Nishino, M., Yasuda, N. et al. Fast compilation of graph substructures for counting and enumeration. Behaviormetrika 45, 423–450 (2018). https://doi.org/10.1007/s41237-018-0056-x

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  • DOI: https://doi.org/10.1007/s41237-018-0056-x

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