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How to Decompose a Binary Matrix into Three hv-convex Polyominoes

  • Andrea Frosini
  • Christophe Picouleau
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7749)

Abstract

Given a binary matrix, deciding wether it can be decomposed into three hv-convex matrices is an \(\cal NP\)-complete problem, whereas its decomposition into two hv-convex matrices or two hv-polyominoes can be performed in polynomial time. In this paper we give a polynomial time algorithm that decomposes a binary matrix into three hv-polyominoes, if such a decomposition exists. These problems are motivated by the Intensity Modulated Radiation Therapy (IMRT).

Keywords

computational complexity matrix decomposition convex polyomino 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Andrea Frosini
    • 1
  • Christophe Picouleau
    • 2
  1. 1.Dipartimento di Sistemi e InformaticaUniversitá di FirenzeFirenzeItaly
  2. 2.Laboratoire CEDRICCNAMParisFrance

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