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Recognizing Shrinkable Complexes Is NP-Complete

Dominique Attali 1 Olivier Devillers 2 Marc Glisse 3 Sylvain Lazard 2
1 GIPSA-AGPIG - GIPSA - Architecture, Géométrie, Perception, Images, Gestes
GIPSA-DIS - Département Images et Signal
2 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
3 DATASHAPE - Understanding the Shape of Data
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : We say that a simplicial complex is shrinkable if there exists a sequence of admissible edge contractions that reduces the complex to a single vertex. We prove that it is NP-complete to decide whether a (two-dimensional) simplicial complex is shrinkable. Along the way, we describe examples of contractible complexes that are not shrinkable.
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Dominique Attali, Olivier Devillers, Marc Glisse, Sylvain Lazard. Recognizing Shrinkable Complexes Is NP-Complete. Journal of Computational Geometry, Carleton University, Computational Geometry Laboratory, 2016, 7 (1), pp.430--443. ⟨10.20382/jocg.v7i1a18⟩. ⟨hal-01384396v2⟩

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