An Incremental Algorithm for Betti Numbers of Simplicial Complexes

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 S© this method has implementations that run in time O(n ̄(n)) and O(n), where n is the number of simplicesin the triangulation. If applied to the family of ̄-shapes of a finite point set in R© it takes time O(n ̄(n)) to compute the betti numbers of all ̄-shapes."