Abstract
We challenge the problem of the reconstruction of a bicolored domino tiling of a rectangle from its horizontal and vertical projections. We give two NP-completeness results after having defined two non equivalent and very natural notions of projections on a generic bicolored domino tiling. The more general problem of the reconstruction of monochromatic domino tilings is still left open.
Chapter PDF
Similar content being viewed by others
References
M. Chrobak, C. Durr, Reconstructing Polyatomic Structures from Discrete X-Rays: NP-Completeness Proof for Three Atoms, Theoretical Computer Science, 259:81–98, (2001)
H. Ryser, Combinatorial Mathematics, Mathematical Association of America and Quinn & Boden, Rahway, New Jersey, (1963)
M.R. Garey, D.S. Johnson, Computers and intractability: A guide to the theory of NP-completeness, Freeman, New York, (1979)
C. Dürr, E. Goles, I. Rapaport, E. Rémila, Tiling withbars under tomographic constraints Theoretical Computer Science to appear.
C. Picouleau, Reconstruction of domino tiling from its two orthogonal projections Theoretical Computer Science, 255, pgg.437–447 (2001).
C. Picouleau, Reconstruction of a coloured domino tiling from its projections Theoretical Computer Science submitted.
G. J. Woeginger, The reconstruction of polyominoes from their orthogonal projections, Inf. Proc. Letters 77 pagg.225–229 (2001).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Frosini, A., Simi, G. (2002). The Reconstruction of a Bicolored Domino Tiling from Two Projections. In: Braquelaire, A., Lachaud, JO., Vialard, A. (eds) Discrete Geometry for Computer Imagery. DGCI 2002. Lecture Notes in Computer Science, vol 2301. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45986-3_12
Download citation
DOI: https://doi.org/10.1007/3-540-45986-3_12
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43380-4
Online ISBN: 978-3-540-45986-6
eBook Packages: Springer Book Archive