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Reconstructing convex polyominoes from horizontal and vertical projections II

  • Elena Barcucci
  • Alberto Del Lungo
  • Maurice Nivat
  • Renzo Pinzani
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1176)

Abstract

In [1], we studied the problem of reconstructing a discrete set 5 from its horizontal and vertical projections. We defined an algorithm that establishes the existence of a convex polyomino Λ whose horizontal and vertical projections are equal to a pair of assigned vectors (H,V), with H m and V n . Its computational cost is O(n4m4). In this paper, we introduce some operations for recontructing convex polyominoes by means of vectors H's and V's partial sums. These operations allows us to define a new algorithm whose complexity is less than O(n2m2).

Keywords

Construction Procedure Vertical Projection Adjacent Column Filling Operation Good Expansion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    E. Barcucci, A. Del Lungo, M. Nivat and R. Pinzani, Reconstructing convex polyominoes from their horizontal and vertical projections, Theor. Comp. Sci. 155 (1996) 321–347.Google Scholar
  2. 2.
    M. R. Garey and D.S. Johnson, Computers and intractability: a guide to the theory of NP-completeness, Freeman, New York, (1979) 224.Google Scholar
  3. 3.
    G. J. Woeginger, The reconstruction of polyominoes from their orthogonal projections, (1996) Preprint.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Elena Barcucci
    • 1
  • Alberto Del Lungo
    • 1
  • Maurice Nivat
    • 2
  • Renzo Pinzani
    • 1
  1. 1.Dipartimento di Sistemi e InformaticaFirenzeItaly
  2. 2.LITP Institut Blaise PascalUniversité Paris 7 “Denis Diderot”Paris Cedex 05France

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