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International Workshop on Algorithms and Computation

WALCOM 2021: WALCOM: Algorithms and Computation pp 321–332Cite as

Mathematical Characterizations and Computational Complexity of Anti-slide Puzzles

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12635))

Abstract

For a given set of pieces, an anti-slide puzzle asks us to arrange the pieces so that none of the pieces can slide. In this paper, we investigate the anti-slide puzzle in 2D. We first give mathematical characterizations of anti-slide puzzles and show the relationship between the previous work. Using a mathematical characterization, we give a polynomial time algorithm for determining if a given arrangement of polyominoes is anti-slide or not in a model. Next, we prove that the decision problem whether a given set of polyominoes can be arranged to be anti-slide or not is strongly NP-complete even if every piece is x-monotone. On the other hand, we show that a set of pieces cannot be arranged to be anti-slide if all pieces are convex polygons.

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Acknowledgements

This work is partially supported by JSPS KAKENHI Grant Numbers 17H06287 and 18H04091. The authors thank Prof. Yoshio Okamoto, who mentioned that the techniques in [8] can be used to prove Theorem 4.

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Authors and Affiliations

  1. School of Information Science, Japan Advanced Institute of Science and Technology (JAIST), Ishikawa, Japan

    Ko Minamisawa & Ryuhei Uehara

  2. Department of Mathematical Science, Tokai University, Kanagawa, Japan

    Masao Hara

Authors
  1. Ko Minamisawa
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  2. Ryuhei Uehara
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  3. Masao Hara
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Corresponding author

Correspondence to Ko Minamisawa .

Editor information

Editors and Affiliations

  1. Japan Advanced Institute of Science and Technology, Ishikawa, Japan

    Ryuhei Uehara

  2. University of Sydney, Sydney, NSW, Australia

    Seok-Hee Hong

  3. Indian Statistical Institute, kolkata, India

    Subhas C. Nandy

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Minamisawa, K., Uehara, R., Hara, M. (2021). Mathematical Characterizations and Computational Complexity of Anti-slide Puzzles. In: Uehara, R., Hong, SH., Nandy, S.C. (eds) WALCOM: Algorithms and Computation. WALCOM 2021. Lecture Notes in Computer Science(), vol 12635. Springer, Cham. https://doi.org/10.1007/978-3-030-68211-8_26

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  • DOI: https://doi.org/10.1007/978-3-030-68211-8_26

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-68210-1

  • Online ISBN: 978-3-030-68211-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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