# Delaunay-Rips filtration: a study and an algorithm

arXiv: https://arxiv.org/abs/2512.17382 · HTML: https://mlsanity.com/paper/2512.17382/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Dec 2025.

## Built on by (most cited first, 1 of 1)

- [The sublevel Flood bifiltration: towards scalable 2-parameter persistent homology](https://mlsanity.com/paper/2610.05441/) (2026)

## Abstract (arXiv)

The Delaunay-Rips filtration is a lighter and faster alternative to the well-known Rips filtration for low-dimensional Euclidean point clouds. Despite these advantages, it has seldom been studied. In this paper, we aim to bridge this gap by providing a thorough theoretical and empirical analysis of this construction. From a theoretical perspective, we show how the persistence diagrams associated with the Delaunay-Rips filtration approximate those obtained with the Rips filtration. Additionally, we describe the instabilities of the Delaunay-Rips persistence diagrams when the input point cloud is perturbed. Finally, we introduce an algorithm that computes persistence diagrams of Delaunay-Rips filtrations in any dimension. We show that our method is faster and has a lower memory footprint than traditional approaches in low dimensions. Our C++ implementation, which comes with Python bindings, is available at https://github.com/MClemot/GeoPH.