Determining whether a simplicial 3-complex collapses to a 1-complex is NP-complete

Authors:
Rémy Malgouyres;Angel R. Francés
Affiliations:
Univ. Clermont 1, Laboratoire d'Algorithmique et Image, IUT, Dpartement informatique, Aubière cedex, France;Dpto. Informática e Ingeniería de Sistemas, Facultad de Ciencias, Universidad de Zaragoza, Zaragoza, Spain
Venue:
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Year:
2008

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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.