The Reconstruction of a Bicolored Domino Tiling from Two Projections

  • A. Frosini
  • G. Simi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2301)


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.


Domino tiling Reconstruction Problem NP-completeness 


  1. 1.
    M. Chrobak, C. Durr, Reconstructing Polyatomic Structures from Discrete X-Rays: NP-Completeness Proof for Three Atoms, Theoretical Computer Science, 259:81–98, (2001)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    H. Ryser, Combinatorial Mathematics, Mathematical Association of America and Quinn & Boden, Rahway, New Jersey, (1963)Google Scholar
  3. 3.
    M.R. Garey, D.S. Johnson, Computers and intractability: A guide to the theory of NP-completeness, Freeman, New York, (1979)Google Scholar
  4. 4.
    C. Dürr, E. Goles, I. Rapaport, E. Rémila, Tiling withbars under tomographic constraints Theoretical Computer Science to appear.Google Scholar
  5. 5.
    C. Picouleau, Reconstruction of domino tiling from its two orthogonal projections Theoretical Computer Science, 255, pgg.437–447 (2001).MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    C. Picouleau, Reconstruction of a coloured domino tiling from its projections Theoretical Computer Science submitted.Google Scholar
  7. 7.
    G. J. Woeginger, The reconstruction of polyominoes from their orthogonal projections, Inf. Proc. Letters 77 pagg.225–229 (2001).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • A. Frosini
    • 1
  • G. Simi
    • 1
  1. 1.Dipartimento di MatematicaUniversità degli Studi di SienaSienaItaly

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