On tiling under tomographic constraints

Authors:
Marek Chrobak;Peter Couperus;Christoph Dürr;Gerhard Woeginger
Affiliations:
Department of Computer Science, Unviersity of California, Riverside, CA;Department of Mathematics, University of Washington, Seattle, WA;LRI, Université Paris-Sud, Bätiment 490, F-91405 Orsay cédex, Paris, France;Department of Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, Netherlands
Venue:
Theoretical Computer Science
Year:
2003

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Abstract

Given a tiling of a 2D grid with several types of files, 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 files 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 reconstrction problems, by proving NP-completeness results for several sets of tiles.