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Please use this identifier to cite or link to this item: http://hdl.handle.net/10119/15100

Title: Complexity of Tiling a Polygon with Trominoes or Bars
Authors: Horiyama, Takashi
Ito, Takehiro
Nakatsuka, Keita
Suzuki, Akira
Uehara, Ryuhei
Keywords: tiling problem
Issue Date: 2017-03-17
Publisher: Springer
Magazine name: Discrete and Computational Geometry
Volume: 58
Number: 3
Start page: 686
End page: 704
DOI: 10.1007/s00454-017-9884-9
Abstract: We study the computational hardness of the tiling puzzle with polyominoes, where a polyomino is a rectilinear polygon (i.e., a polygon made by connecting unit squares.) In the tiling problem, we are given a rectilinear polygon P and a set S of polyominoes, and asked whether P can be covered without any overlap using translated copies of polyominoes in S. In this paper, we focus on trominoes and bars as polyominoes; a tromino is a polyomino consisting of three unit squares, and a bar is a rectangle of either height one or width one. Notice that there are essentially two shapes of trominoes, that is, I-shape (i.e., a bar) and L-shape. We consider the tiling problem when restricted to only L-shape trominoes, only I-shape trominoes, both L-shape and I-shape trominoes, or only two bars. In this paper, we prove that the tiling problem remains NP-complete even for such restricted sets of polyominoes. All reductions are carefully designed so that we can also prove the #P-completeness and ASP-completeness of the counting and the another-solution-problem variants, respectively.Our results answer two open questions proposed by Moore and Robson (2001) and Pak and Yang (2013).
Rights: This is the author-created version of Springer, Takashi Horiyama, Takehiro Ito, Keita Nakatsuka, Akira Suzuki, and Ryuhei Uehara, Discrete and Computational Geometry, 58(3), 2017, 686-704. The original publication is available at www.springerlink.com, http://dx.doi.org/10.1007/s00454-017-9884-9
URI: http://hdl.handle.net/10119/15100
Material Type: author
Appears in Collections:b10-1. 雑誌掲載論文 (Journal Articles)

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