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Determining Whether a Simplicial 3-Complex Collapses to a 1-Complex Is NP-Complete

  • Rémy Malgouyres
  • Angel R. Francés
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4992)

Abstract

We show that determining whether or not a simplicial 2 − complex collapses to a point is deterministic polynomial time decidable. We do this by solving the problem of constructively deciding whether a simplicial 2 −complex collapses to a 1 −complex. We show that this proof cannot be extended to the 3D case, by proving that deciding whether a simplicial 3 −complex collapses to a 1 −complex is an NP −complete problem.

Keywords

Simplicial Topology Collapsing Computational Complexity NP −completeness 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Rémy Malgouyres
    • 1
  • Angel R. Francés
    • 2
  1. 1.Laboratoire d’Algorithmique et Image (LAIC, EA2146), IUT département informatiqueUniv. Clermont 1Aubière cedexFrance
  2. 2.Dpto. Informática e Ingeniería de Sistemas, Facultad de CienciasUniversidad de ZaragozaZaragozaSpain

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