Strongly Proximal Edelsbrunner-Harer Nerves in Voronoi Tessellations

zbMath1360.54021arXiv1604.05249MaRDI QIDQ5506970

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Publication date: 16 December 2016

Abstract: This paper introduces Edelsbrunner-Harer nerve in collections of Voronoi regions (called nucleus clusters) endowed with one or more proximity relations. The main results in this paper are that a maximal nucleus cluster (MNC) in a Voronoi Tessellation is a strongly proximal Edelsbrunner-Harer nerve, each MNC nerve and the union of the sets in the MNC have the same homotopy type.

Full work available at URL: https://arxiv.org/abs/1604.05249

zbMATH Keywords

homotopy typestrong proximitynerveVoronoï tessellationnucleus clustering

Mathematics Subject Classification ID

Classification and discrimination; cluster analysis (statistical aspects) (62H30) Pattern recognition, speech recognition (68T10) Axiomatic and generalized convexity (52A01) Polyhedra and polytopes; regular figures, division of spaces (51M20) Proximity structures and generalizations (54E05) Combinatorial aspects of tessellation and tiling problems (05B45) Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc. (57Q10) Tilings in (2) dimensions (aspects of discrete geometry) (52C20)

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