Journal of Information Processing
Online ISSN : 1882-6652
ISSN-L : 1882-6652
How Simple Algorithms Can Solve Latin Square Completion-Type Puzzles Approximately
Kazuya HaraguchiHirotaka Ono
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2015 Volume 23 Issue 3 Pages 276-283


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.

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© 2015 by the Information Processing Society of Japan
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