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Tile-Packing Tomography Is NP-hard

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Date
2012
Dewey
Recherche opérationnelle
Sujet
Tilings; Discrete tomography; NP-hardness; Affine independence
Journal issue
Algorithmica
Volume
64
Number
2
Publication date
2012
Article pages
267-278
Publisher
Springer
DOI
http://dx.doi.org/10.1007/s00453-011-9498-1
URI
https://basepub.dauphine.fr/handle/123456789/6051
Collections
  • LAMSADE : Publications
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Author
Chrobak, Marek
Dürr, Christoph
Guinez, Flavio
Lozano, Antoni
Thang, Nguyen Kim
Type
Article accepté pour publication ou publié
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.

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