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International Conference on Fun with Algorithms

FUN 2007: Fun with Algorithms pp 198–212Cite as

The Troubles of Interior Design–A Complexity Analysis of the Game Heyawake

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 4475)

Abstract

Heyawake is one of many recently popular Japanese pencil puzzles. We investigate the computational complexity of the problem of deciding whether a given puzzle instance has a solution or not. We show that Boolean gates can be emulated via Heyawake puzzles, and that it is possible to reduce the Boolean Satisfiability problem to Heyawake. It follows that the problem in question is \(\textsf{NP}\)-complete.

Keywords

  • Spiral Galaxy
  • Wire Grid
  • Interior Design
  • 3CNF Formula
  • Original Construction

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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  • DOI: 10.1007/978-3-540-72914-3_18
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References

  1. Blass, A., Gurevich, Y.: On the unique satisfiability problem. Information and Control 55(1-3), 80–88 (1982)

    MathSciNet  CrossRef  MATH  Google Scholar 

  2. Friedman, E.: Corral puzzles are NP-complete. Technical report, Stetson University, DeLand, FL 32723 (2002)

    Google Scholar 

  3. Friedman, E.: Pearl puzzles are NP-complete. Technical report, Stetson University, DeLand, FL 32723 (2002)

    Google Scholar 

  4. Friedman, E.: Spiral galaxies puzzles are NP-complete. Technical report, Stetson University, DeLand, FL 32723 (2002)

    Google Scholar 

  5. Garey, M.R., Johnson, D.S.: Computers and Intractability; A Guide to the Theory of NP-Completeness. W. H. Freeman & Co, New York, NY, USA (1990)

    MATH  Google Scholar 

  6. Holzer, M., Klein, A., Kutrib, M.: On the NP-completeness of the NURIKABE pencil puzzle and variants thereof. In: Ferragnia, P., Grossi, R.: (eds.). In: Proceedings of the 3rd International Conference on FUN with Algorithms, Island of Elba, Italy, Edizioni Plus, Universitá di Pisa, pp. 77–89 (May 2004)

    Google Scholar 

  7. Seta, T.: The complexities of puzzles, cross sum and their another solution problems (asp). Senior thesis, Univ. of Tokyo, Dept. of Information Science, Faculty of Science, Hongo 7-3-1, Bunkyo-ku, Tokyo 113, Japan (February 2001)

    Google Scholar 

  8. Ueda, N., Nagao, T.: NP-completeness results for nonogram via parsimonious reductions, Technical Report TR96-008, Dept. of Computer Science, Tokyo Institute of Technology (1996)

    Google Scholar 

  9. Valiant, L.G.: The complexity of computing the permanent. Theoretical Computer Science 8, 189–201 (1979)

    MathSciNet  CrossRef  MATH  Google Scholar 

  10. Yato, T.: Complexity and completeness of finding another solution and its application to puzzles. Master’s thesis, Univ. of Tokyo, Dept. of Information Science, Faculty of Science, Hongo 7-3-1, Bunkyo-ku, Tokyo 113, Japan (January 2003)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institut für Informatik, Technische Universität München, Boltzmannstrasse 3, D-85748 Garching bei München, Germany

    Markus Holzer & Oliver Ruepp

Authors
  1. Markus Holzer
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  2. Oliver Ruepp
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Editor information

Editors and Affiliations

  1. Dipartimento di Sistemi e Informatica, Università degli Studi di Firenze, Viale Morgagni 65, 50134, Firenze, Italy

    Pierluigi Crescenzi

  2. Dipartimento di Informatica, Università degli Studi di Pisa, Largo Bruno Pontecorvo 3, 56127, Pisa, Italy

    Giuseppe Prencipe

  3. Dipartimento di Ingegneria dell’Informazione, Università degli Studi di Padova, Via Gradenigo 6/B, 35131, Padova, Italy

    Geppino Pucci

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© 2007 Springer Berlin Heidelberg

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Holzer, M., Ruepp, O. (2007). The Troubles of Interior Design–A Complexity Analysis of the Game Heyawake. In: Crescenzi, P., Prencipe, G., Pucci, G. (eds) Fun with Algorithms. FUN 2007. Lecture Notes in Computer Science, vol 4475. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72914-3_18

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  • DOI: https://doi.org/10.1007/978-3-540-72914-3_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72913-6

  • Online ISBN: 978-3-540-72914-3

  • eBook Packages: Computer ScienceComputer Science (R0)