Topological inference via meshing

We apply ideas from mesh generation to improve the time and space complexities of computing the full persistent homological information associated with a point cloud P in Eu- clidean space Rd. Classical approaches rely on the Cech, Rips, -complex, or witness complex ltrations of P , whose complexities scale up very badly with d. For instance, the -complex ltration incurs the n( d) size of the Delaunay triangulation, where n is the size of P. The