How Simple Algorithms can Solve Latin Square Completion-Type Puzzles Approximately

Kazuya Haraguchi, Hirotaka Ono

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


Among many variations of pencil puzzles, Latin square Completion-Type puzzles (LSCPs) are quite popular for puzzle fans. Concerning these puzzles, the solvability has been investigated from the viewpoint of time complexity in the last decade; it has been shown that, in most of these puzzles, it is NP-complete to determine whether a given puzzle instance has a proper solution. In this paper, we investigate the approximability of three LSCPs: Sudoku, Futoshiki and KenKen. We formulate each LSCP as a maximization problem that asks to fill as many cells as possible, under the Latin square condition and the inherent condition. We then propose simple generic approximation algorithms for them and analyze their approximation ratios.

Original languageEnglish
Pages (from-to)276-283
Number of pages8
JournalJournal of information processing
Issue number3
Publication statusPublished - 2015

All Science Journal Classification (ASJC) codes

  • General Computer Science


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