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.
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Malgouyres, R., Francés, A.R. (2008). Determining Whether a Simplicial 3-Complex Collapses to a 1-Complex Is NP-Complete. In: Coeurjolly, D., Sivignon, I., Tougne, L., Dupont, F. (eds) Discrete Geometry for Computer Imagery. DGCI 2008. Lecture Notes in Computer Science, vol 4992. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79126-3_17
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DOI: https://doi.org/10.1007/978-3-540-79126-3_17
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