Abstract
We present a new proof of NP-completeness for the problem of solving instances of the Japanese pencil puzzle Kakuro (also known as Cross-Sum). While the NP-completeness of Kakuro puzzles has been shown before [T. Seta. The complexity of CROSS SUM. IPSJ SIG Notes, AL-84:51–58, 2002], there are still two interesting aspects to our proof: we show NP-completeness for a new variant of Kakuro that has not been investigated before and thus improves the aforementioned result. Moreover some parts of the proof have been generated automatically, using an interesting technique involving SAT solvers.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Eén, N., Sörensson, N.: An extensible SAT-solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 502–518. Springer, Heidelberg (2004)
Friedman, E.: Corral 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 (1990)
Holzer, M., Ruepp, O.: The troubles of interior design-a complexity analysis of the game heyawake. In: Crescenzi, P., Prencipe, G., Pucci, G. (eds.) FUN 2007. LNCS, vol. 4475, pp. 198–212. Springer, Heidelberg (2007)
Lichtenstein, D.: Planar formulae and their uses. SIAM Journal on Computing 11(2), 329–343 (1982)
Papadimitriou, C.H., Yannakakis, M.: The complexity of facets (and some facets of complexity). Journal of Computer and System Sciences 28(2), 244–259 (1984)
Seta, T.: The complexities of puzzles, cross sum and their another solution problems (asp). Senior thesis, Univerity of Tokyo, Deptartment of Information Science, Faculty of Science, Hongo 7-3-1, Bunkyo-ku, Tokyo 113, Japan (February 2001)
Seta, T.: The complexity of CROSS SUM. IPSJ SIG Notes, AL-84, 51–58 (2002) (in Japanese)
Ueda, N., Nagao, T.: NP-completeness results for NONOGRAM via parsimonious reductions. Technical Report TR96-0008, Department of Computer Science, Tokyo Institut of Technology, Ôokayama 2-12-1 Meguro Tokyo 152-8552, Japan (May 1996)
Valiant, L.G., Vazirani, V.V.: NP is as easy as detecting unique solutions. Theoretical Computer Science 47(3), 85–93 (1986)
Yato, T.: Complexity and completeness of finding another solution and its application to puzzles. Master’s thesis, Univerity of Tokyo, Deptartment 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
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ruepp, O., Holzer, M. (2010). The Computational Complexity of the Kakuro Puzzle, Revisited. In: Boldi, P., Gargano, L. (eds) Fun with Algorithms. FUN 2010. Lecture Notes in Computer Science, vol 6099. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13122-6_31
Download citation
DOI: https://doi.org/10.1007/978-3-642-13122-6_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13121-9
Online ISBN: 978-3-642-13122-6
eBook Packages: Computer ScienceComputer Science (R0)