On tiling under tomographic constraints


Chrobak, Marek and Couperus, Peter and Dürr, Christoph and Woeginger, Gerhard (2003) On tiling under tomographic constraints. Theoretical Computer Science, 290 (3). pp. 2125-2136. ISSN 0304-3975

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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 NP-complete. In this note, we make progress toward a comprehensive classification of various tiling reconstruction problems, by proving NP-completeness results for several sets of tiles.
Item Type:Article
Copyright:© 2003 Elsevier
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/75176
Official URL:https://doi.org/10.1016/S0304-3975(02)00542-X
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