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The Bag-Based Search: A Meta-Algorithm to Construct Tractable Logical Circuits for Graphs Based on Tree Decomposition

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Combinatorial Optimization and Applications (COCOA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14462))

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Abstract

Tractable logical circuits (TLCs) have attracted more attention in the AI field as bases of knowledge representation and tractable probabilistic modeling. We propose the bag-based search (BBS), a new meta-algorithm for constructing a TLC that accepts all subgraphs of a given input graph that satisfies a target graph property. We implemented BBS examples for various graph properties, including independent set, k-edgeset, dominating set, k-matchings, and spanning trees, and applied them to artificial and real-world graphs. The experimental results showed that BBS generated significantly smaller circuits than ZDDs obtained by the frontier-based search (FBS).

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Notes

  1. 1.

    Appendix is provided on the author’s website.

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Authors and Affiliations

  1. NTT Communication Science Laboratories, Kyoto, Japan

    Masakazu Ishihata

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  1. Masakazu Ishihata
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Correspondence to Masakazu Ishihata .

Editor information

Editors and Affiliations

  1. University of Texas at Dallas, Richardson, TX, USA

    Weili Wu

  2. Beijing Normal University, Zhuhai, China

    Jianxiong Guo

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Ishihata, M. (2024). The Bag-Based Search: A Meta-Algorithm to Construct Tractable Logical Circuits for Graphs Based on Tree Decomposition. In: Wu, W., Guo, J. (eds) Combinatorial Optimization and Applications. COCOA 2023. Lecture Notes in Computer Science, vol 14462. Springer, Cham. https://doi.org/10.1007/978-3-031-49614-1_25

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  • DOI: https://doi.org/10.1007/978-3-031-49614-1_25

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-49613-4

  • Online ISBN: 978-3-031-49614-1

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