  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.
