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Finding All Solutions and Instances of Numberlink and Slitherlink by ZDDs
Graduate School of Informatics, Kyoto University, Kyoto, 606-8501, Japan
ERATO MINATO Project, Japan Science and Technology Agency, Kitaku North 14, West 9, Sapporo, 060-0814, Hokkaido, Japan
Graduate School of Information Science and Technology, Hokkaido University, Kitaku North 14, West 9, Sapporo, 060-0814, Hokkaido, Japan
* Author to whom correspondence should be addressed.
Received: 16 November 2011; in revised form: 29 February 2012 / Accepted: 19 March 2012 / Published: 5 April 2012
Abstract: Link puzzles involve finding paths or a cycle in a grid that satisfy given local and global properties. This paper proposes algorithms that enumerate solutions and instances of two link puzzles, Slitherlink and Numberlink, by zero-suppressed binary decision diagrams (ZDDs). A ZDD is a compact data structure for a family of sets provided with a rich family of set operations, by which, for example, one can easily extract a subfamily satisfying a desired property. Thanks to the nature of ZDDs, our algorithms offer a tool to assist users to design instances of those link puzzles.
Keywords: link puzzles; Slitherlink; Numberlink; solvers; instance generations
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MDPI and ACS Style
Yoshinaka, R.; Saitoh, T.; Kawahara, J.; Tsuruma, K.; Iwashita, H.; Minato, S.-I. Finding All Solutions and Instances of Numberlink and Slitherlink by ZDDs. Algorithms 2012, 5, 176-213.
Yoshinaka R, Saitoh T, Kawahara J, Tsuruma K, Iwashita H, Minato S-I. Finding All Solutions and Instances of Numberlink and Slitherlink by ZDDs. Algorithms. 2012; 5(2):176-213.
Yoshinaka, Ryo; Saitoh, Toshiki; Kawahara, Jun; Tsuruma, Koji; Iwashita, Hiroaki; Minato, Shin-ichi. 2012. "Finding All Solutions and Instances of Numberlink and Slitherlink by ZDDs." Algorithms 5, no. 2: 176-213.