# Ripser: efficient computation of Vietoris-Rips persistence barcodes

## TL;DR

Ripser introduces an efficient algorithm for computing Vietoris-Rips persistence barcodes that significantly reduces time and memory usage through innovative implicit representations and the use of apparent pairs.

## Contribution

The paper presents a novel algorithm and implementation for Vietoris-Rips persistence computation that improves efficiency by avoiding explicit matrix construction and leveraging apparent pairs.

## Key findings

- Substantial improvements in computation time over previous software
- Reduced memory usage during persistence barcode calculations
- Effective use of apparent pairs for discrete gradient construction

## Abstract

We present an algorithm for the computation of Vietoris-Rips persistence barcodes and describe its implementation in the software Ripser. The method relies on implicit representations of the coboundary operator and the filtration order of the simplices, avoiding the explicit construction and storage of the filtration coboundary matrix. Moreover, it makes use of apparent pairs, a simple but powerful method for constructing a discrete gradient field from a total order on the simplices of a simplicial complex, which is also of independent interest. Our implementation shows substantial improvements over previous software both in time and memory usage.