Ripser: efficient computation of Vietoris-Rips persistence barcodes

Understand

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.