Faster computation of degree-1 persistent homology using the reduced Vietoris-Rips filtration

TL;DR

This paper introduces an efficient algorithm for computing degree-1 persistent homology of large point clouds in low-dimensional Euclidean spaces, addressing a key computational bottleneck.

Contribution

The authors develop a novel algorithm that significantly speeds up the computation of degree-1 Vietoris-Rips persistent homology for large datasets.

Findings

Enables analysis of larger point clouds than previously possible

Reduces computational time for persistent homology calculations

Improves scalability of persistent homology methods

Abstract

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 degree-1 Vietoris-Rips Persistent Homology of point clouds in low dimensional Euclidean Space for larger point clouds.