Approximability of Latin Square Completion-Type Puzzles

  • Kazuya Haraguchi
  • Hirotaka Ono
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8496)


Among many variations of pencil puzzles, Latin square Completion-Type puzzles (LSCP), such as Sudoku, Futoshiki and BlockSum, 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 LSCP. We formulate LSCP as the 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 LSCP and analyze their approximation ratios.


Latin square Completion-Type puzzles approximation algorithms Sudoku Futoshiki BlockSum 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Kazuya Haraguchi
    • 1
  • Hirotaka Ono
    • 2
  1. 1.Faculty of CommerceOtaru University of CommerceJapan
  2. 2.Faculty of EconomicsKyushu UniversityJapan

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