Reduced Vietoris-Rips Complexes: New methods to compute Vietoris-Rips Persistent Homology

Computing Persistent Homology for large point clouds remains a bottleneck for the wider adoption of persistent homology by the scientific community. We present an algorithm which can compute the one-dimensional Vietoris-Rips Persistent Homology of point clouds in low dimensional Euclidean Space for point clouds of the the order $10^5$.