Approximability of Latin square completion-type puzzles

Kazuya Haraguchi; Hirotaka Ono

doi:10.1007/978-3-319-07890-8_19

Approximability of Latin square completion-type puzzles

Kazuya Haraguchi, Hirotaka Ono

mathematics and information

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

4 Citations (Scopus)

Abstract

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.

Original language	English
Title of host publication	Fun with Algorithms - 7th International Conference, FUN 2014, Proceedings
Publisher	Springer Verlag
Pages	218-229
Number of pages	12
ISBN (Print)	9783319078892
DOIs	https://doi.org/10.1007/978-3-319-07890-8_19
Publication status	Published - 2014
Event	7th International Conference on Fun with Algorithms, FUN 2014 - Sicily, Italy Duration: Jul 1 2014 → Jul 3 2014

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	8496 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	7th International Conference on Fun with Algorithms, FUN 2014
Country/Territory	Italy
City	Sicily
Period	7/1/14 → 7/3/14

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-319-07890-8_19

Cite this

Haraguchi, K., & Ono, H. (2014). Approximability of Latin square completion-type puzzles. In Fun with Algorithms - 7th International Conference, FUN 2014, Proceedings (pp. 218-229). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8496 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-07890-8_19

Approximability of Latin square completion-type puzzles. / Haraguchi, Kazuya; Ono, Hirotaka.
Fun with Algorithms - 7th International Conference, FUN 2014, Proceedings. Springer Verlag, 2014. p. 218-229 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8496 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Haraguchi, K & Ono, H 2014, Approximability of Latin square completion-type puzzles. in Fun with Algorithms - 7th International Conference, FUN 2014, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8496 LNCS, Springer Verlag, pp. 218-229, 7th International Conference on Fun with Algorithms, FUN 2014, Sicily, Italy, 7/1/14. https://doi.org/10.1007/978-3-319-07890-8_19

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author = "Kazuya Haraguchi and Hirotaka Ono",

note = "Funding Information: This work is partially supported by JSPS KAKENHI Grant Number 24106004, 25104521 and 25870661.; 7th International Conference on Fun with Algorithms, FUN 2014 ; Conference date: 01-07-2014 Through 03-07-2014",

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Approximability of Latin square completion-type puzzles

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