Ripser: efficient computation of Vietoris–Rips persistence barcodes

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