Solving Some Instances of the 2-Color Problem

  • S. Brocchi
  • A. Frosini
  • S. Rinaldi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5810)

Abstract

In the field of Discrete Tomography, the 2-color problem consists in determining a matrix whose elements are of two different types, starting from its horizontal and vertical projections. It is known that the one color problem has a polynomial time reconstruction algorithm, while, with k ≥ 2, the k-color problem is NP-complete. Thus, the 2-color problem constitutes an interesting example of a problem just in the frontier between hard and easy problems.

In this paper we define a linear time algorithm to solve a set of its instances, where some values of the horizontal and vertical projections are constant, while the others are upper bounded by a positive number proportional to the dimension of the problem. Our algorithm relies on classical studies for the solution of the one color problem.

Keywords

Discrete tomography polynomial time algorithm k-color problem 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • S. Brocchi
    • 1
  • A. Frosini
    • 1
  • S. Rinaldi
    • 2
  1. 1.Dipartimento di Sistemi e InformaticaUniversità di FirenzeFirenzeItaly
  2. 2.Dipartimento di Scienze Matematiche ed InformaticheUniversità di SienaSienaItaly

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