1993•Unpublished venueOpen access

An incremental algorithm for Betti numbers of simplicial complexes

Cecil Jose A. Delfinado, Herbert Edelsbrunner

Abstract

A general and direct method for computing the betti numbers of the homology groups of a finite simplicial complex is given. For subcomplexes of a triangulation of S3 this method has implementations that run in time O(nα(n)) and O(n), where n is the number of simplices in the triangulation. If applied to the family of α-shapes of a finite point set in ℝ3 it takes time O(nℝ(n)) to compute the betti numbers of all α-shapes.

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Key concepts: Betti number, Simplicial complex, Triangulation, Mathematics, Simplicial homology, Combinatorics, Simplicial approximation theorem, Persistent homology