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Article Dans Une Revue Algorithmica Année : 2012

Tile Packing Tomography is {NP}-hard

Marek Chrobak
  • Fonction : Auteur
Christoph Dürr
Flavio Guíñez
  • Fonction : Auteur
Antoni Lozano
  • Fonction : Auteur
Nguyen Kim Thang
  • Fonction : Auteur

Résumé

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.

Dates et versions

hal-01185268 , version 1 (19-08-2015)

Identifiants

Citer

Marek Chrobak, Christoph Dürr, Flavio Guíñez, Antoni Lozano, Nguyen Kim Thang. Tile Packing Tomography is {NP}-hard. Algorithmica, 2012, 64 (2), pp.267-278. ⟨10.1007/s00453-011-9498-1⟩. ⟨hal-01185268⟩
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