Stronger hardness results on the computational complexity of picross 3D

研究成果: Contribution to journalArticle査読

1 被引用数 (Scopus)

抄録

Picross 3D is a popular single-player puzzle video game for the Nintendo DS. It presents a rectangular parallelepiped (i.e., rectangular box) made of unit cubes, some of which must be removed to construct an object in three dimensions. Each row or column has at most one integer on it, and the integer indicates how many cubes in the corresponding 1D slice remain when the object is complete. Kusano et al. showed that Picross 3D is NP-complete and Kimura et al. showed that the counting version, the another solution problem, and the fewest clues problem of Picross 3D are #P-complete, NP-complete, and ΣP 2-complete, respectively, where those results are shown for the restricted input that the rectangular parallelepiped is of height four. On the other hand, Igarashi showed that Picross 3D is NPcomplete even if the height of the input rectangular parallelepiped is one. Extending the result by Igarashi, we in this paper show that the counting version, the another solution problem, and the fewest clues problem of Picross 3D are #P-complete, NP-complete, and ΣP 2 complete, respectively, even if the height of the input rectangular parallelepiped is one. Since the height of the rectangular parallelepiped of any instance of Picross 3D is at least one, our hardness results are best in terms of height.

本文言語英語
ページ(範囲)668-676
ページ数9
ジャーナルIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
E103A
4
DOI
出版ステータス出版済み - 2020
外部発表はい

All Science Journal Classification (ASJC) codes

  • 信号処理
  • コンピュータ グラフィックスおよびコンピュータ支援設計
  • 電子工学および電気工学
  • 応用数学

フィンガープリント

「Stronger hardness results on the computational complexity of picross 3D」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル