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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Blass, A., Gurevich, Y.: On the unique satisfiability problem. Information and Control 55(1-3), 80–88 (1982)
Friedman, E.: Corral puzzles are NP-complete. Technical report, Stetson University, DeLand, FL 32723 (2002)
Friedman, E.: Pearl puzzles are NP-complete. Technical report, Stetson University, DeLand, FL 32723 (2002)
Friedman, E.: Spiral galaxies puzzles are NP-complete. Technical report, Stetson University, DeLand, FL 32723 (2002)
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)
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)
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)
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)
Valiant, L.G.: The complexity of computing the permanent. Theoretical Computer Science 8, 189–201 (1979)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
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)