Reconstructing Binary Matrices with Neighborhood Constraints: An NP-hard Problem

  • A. Frosini
  • C. Picouleau
  • S. Rinaldi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4992)

Abstract

This paper deals with the reconstruction of binary matrices having exactly − 1 − 4 − adjacency constraints from the horizontal and vertical projections. Such a problem is shown to be non polynomial by means of a reduction which involves the classic NP-complete problem 3-color. The result is reached by bijectively mapping all the four different cells involved in 3-color into maximal configurations of 0s and 1s which show the adjacency constraint, and which can be merged into a single binary matrix.

Keywords

Discrete Tomography polynomial time reduction NP- complete Problem 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • A. Frosini
    • 1
  • C. Picouleau
    • 2
  • S. Rinaldi
    • 3
  1. 1.Dipartimento di Sistemi e InformaticaUniversità di Firenze(Firenze)(Italy)
  2. 2.Laboratoire CEDRIC CNAM(Paris)(France)
  3. 3.Dipartimento di Scienze Matematiche ed InformaticheUniversità di Siena(Siena)(Italy)

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