Minimal Decomposition of a Digital Surface into Digital Plane Segments Is NP-Hard

  • Isabelle Sivignon
  • David Coeurjolly
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4245)


This paper deals with the complexity of the decomposition of a digital surface into digital plane segments (DPS for short). We prove that the decision problem (does there exist a decomposition with less than k DPS?) is NP-complete, and thus that the optimisation problem (finding the minimal number of DPS) is NP-hard. The proof is based on a polynomial reduction of any instance of the well-known 3-SAT problem to an instance of the digital surface decomposition problem. A geometric model for the 3-SAT problem is proposed.


Active Part Truth Assignment Variable Object Boolean Expression Variable Instance 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Isabelle Sivignon
    • 1
  • David Coeurjolly
    • 1
  1. 1.Laboratoire LIRIS – Université Claude Bernard Lyon 1VilleurbanneFrance

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