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. © 2010 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Chrobak, M., Dürr, C., Guíñez, F., Lozano, A., & Thang, N. K. (2010). Tile-packing tomography is ℕℙ-hard. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6196 LNCS, pp. 254–263). https://doi.org/10.1007/978-3-642-14031-0_29
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