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Algorithms 2012, 5(2), 176-213; doi:10.3390/a5020176
Article

Finding All Solutions and Instances of Numberlink and Slitherlink by ZDDs

1
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2,3,* , 2,3
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 and
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1 Graduate School of Informatics, Kyoto University, Kyoto, 606-8501, Japan 2 ERATO MINATO Project, Japan Science and Technology Agency, Kitaku North 14, West 9, Sapporo, 060-0814, Hokkaido, Japan 3 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 / Revised: 29 February 2012 / Accepted: 19 March 2012 / Published: 5 April 2012
(This article belongs to the Special Issue Puzzle/Game Algorithms)
Download PDF [298 KB, uploaded 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 link puzzles; Slitherlink; Numberlink; solvers; instance generations
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
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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.

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