  Persistent homology is typically computed through persistent cohomology.
While this generally improves the running time significantly, it does not
facilitate extraction of homology representatives. The mentioned
representatives are geometric manifestations of the corresponding holes and
often carry desirable information.
  We propose a new method of extraction of persistent homology representatives
using cohomology. In a nutshell, we first compute persistent cohomology and use
the obtained information to significantly improve the running time of the
direct persistent homology computations. This algorithm applied to Rips
filtrations generally computes persistent homology representatives much faster
than the standard methods.
