Finding all solutions and instances of numberlink and slitherlink by ZDDs

Ryo Yoshinaka, Toshiki Saitoh, Jun Kawahara, Koji Tsuruma, Hiroaki Iwashita, Shin Ichi Minato

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)176-213
Number of pages38
JournalAlgorithms
Volume5
Issue number2
DOIs
Publication statusPublished - 2012 Jun
Externally publishedYes

Keywords

  • Instance generations
  • Link puzzles
  • Numberlink
  • Slitherlink
  • Solvers

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Numerical Analysis
  • Computational Theory and Mathematics
  • Computational Mathematics

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