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ZDD-Based Algorithmic Framework for Solving Shortest Reconfiguration Problems

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Integration of Constraint Programming, Artificial Intelligence, and Operations Research (CPAIOR 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13884))

Abstract

This paper proposes an algorithmic framework for solving various combinatorial reconfiguration problems by using zero-suppressed binary decision diagrams (ZDDs), a data structure for representing families of sets. In general, a reconfiguration problem checks if there is a step-by-step transformation between two given feasible solutions (e.g., independent sets of an input graph) of a fixed search problem, such that all intermediate results are also feasible and each step obeys a fixed reconfiguration rule (e.g., adding/removing a single vertex to/from an independent set). The solution space formed by all feasible solutions can be exponential in the input size, and indeed, many reconfiguration problems are known to be PSPACE-complete. This paper shows that an algorithm in the proposed framework efficiently conducts breadth-first search by compressing the solution space using ZDDs, and that it finds a shortest transformation between two given feasible solutions if such a transformation exists. Moreover, the proposed framework provides rich information on the solution space, such as its connectivity and all feasible solutions that are reachable from a specified one. Finally, we demonstrate that the proposed framework can be applied to various reconfiguration problems, and experimentally evaluate its performance.

Partially supported by JSPS KAKENHI Grant Numbers JP18H04091, JP19H01103, JP19H04068, JP19K11814, JP20K11666, JP20K11748, JP20H05793 and JP20H05794, Japan.

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Notes

  1. 1.

    https://core-challenge.github.io/2022/.

  2. 2.

    https://core-challenge.github.io/2022result/.

  3. 3.

    https://github.com/Shin-ichi-Minato/SAPPOROBDD.

  4. 4.

    https://github.com/junkawahara/ddreconf-experiments2023.

  5. 5.

    https://github.com/junkawahara/ddreconf.

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Author information

Authors and Affiliations

  1. Graduate School of Information Sciences, Tohoku University, Sendai, Japan

    Takehiro Ito & Akira Suzuki

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

    Jun Kawahara

  3. Graduate School of Science and Technology, Nara Institute of Science and Technology, Ikoma, Japan

    Yu Nakahata

  4. Information Infrastructure and Digital Transformation Initiatives Headquarters, Kobe University, Kobe, Japan

    Takehide Soh

  5. Graduate School of Information Sciences, University of Hyogo, Kobe, Japan

    Junichi Teruyama

  6. Graduate School of Informatics and Engineering, The University of Electro-Communications, Chofu, Japan

    Takahisa Toda

Authors
  1. Takehiro Ito
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  2. Jun Kawahara
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  3. Yu Nakahata
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  4. Takehide Soh
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  5. Akira Suzuki
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  6. Junichi Teruyama
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  7. Takahisa Toda
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Corresponding author

Correspondence to Jun Kawahara .

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Editors and Affiliations

  1. Department of Management, University of Toronto Scarborough and Rotman School of Management, University of Toronto, Toronto, ON, Canada

    Andre A. Cire

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Ito, T. et al. (2023). ZDD-Based Algorithmic Framework for Solving Shortest Reconfiguration Problems. In: Cire, A.A. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2023. Lecture Notes in Computer Science, vol 13884. Springer, Cham. https://doi.org/10.1007/978-3-031-33271-5_12

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  • DOI: https://doi.org/10.1007/978-3-031-33271-5_12

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