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On tiling under tomographic constraints |
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| Authors: | Marek Chrobak, Peter Couperus, Christoph Dü rr,Gerhard Woeginger, |
| Affiliation: | a Department of Computer Science, University of California, Riverside, CA 92521, USA b Department of Mathematics, University of Washington, Seattle, WA 98195-4350, USA c LRI, Université Paris-Sud, Bâtiment 490, F-91405 Orsay cédex, Paris, France d Department of Mathematics, University of Twente, P.O. Box 217, 7500 AE, Enschede, Netherlands |
| Abstract: | Given a tiling of a 2D grid with several types of tiles, we can count for every row and column how many tiles of each type it intersects. These numbers are called the projections. We are interested in the problem of reconstructing a tiling which has given projections. Some simple variants of this problem, involving tiles that are 1×1 or 1×2 rectangles, have been studied in the past, and were proved to be either solvable in polynomial time or -complete. In this note, we make progress toward a comprehensive classification of various tiling reconstruction problems, by proving -completeness results for several sets of tiles. |
| Keywords: | Discrete tomography Tiling |
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