Tile-Packing Tomography Is NP-hard
Chrobak, Marek; Dürr, Christoph; Guinez, Flavio; Lozano, Antoni; Thang, Nguyen Kim (2012), Tile-Packing Tomography Is NP-hard, Algorithmica, 64, 2, p. 267-278. http://dx.doi.org/10.1007/s00453-011-9498-1
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Abstract (EN)Discrete tomography deals with reconstructing finite spatial objects from their projections. The objects we study in this paper are called tilings or tile-packings, and they consist of a number of disjoint copies of a fixed tile, where a tile is defined as a connected set of grid points. A row projection specifies how many grid points are covered by tiles in a given row; column projections are defined analogously. For a fixed tile, is it possible to reconstruct its tilings from their projections in polynomial time? It is known that the answer to this question is affirmative if the tile is a bar (its width or height is 1), while for some other types of tiles NP -hardness results have been shown in the literature. In this paper we present a complete solution to this question by showing that the problem remains NP-hard for all tiles other than bars.
Subjects / KeywordsTilings; Discrete tomography; NP-hardness; Affine independence
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