  We introduce a fast and memory efficient approach to compute the persistent
homology (PH) of a sequence of simplicial complexes. The basic idea is to
simplify the complexes of the input sequence by using strong collapses, as
introduced by J. Barmak and E. Miniam [DCG (2012)], and to compute the PH of an
induced sequence of reduced simplicial complexes that has the same PH as the
initial one. Our approach has several salient features that distinguishes it
from previous work. It is not limited to filtrations (i.e. sequences of nested
simplicial subcomplexes) but works for other types of sequences like towers and
zigzags. To strong collapse a simplicial complex, we only need to store the
maximal simplices of the complex, not the full set of all its simplices, which
saves a lot of space and time. Moreover, the complexes in the sequence can be
strong collapsed independently and in parallel. Finally, we can compromize
between precision and time by choosing the number of simplicial complexes of
the sequence we strong collapse. As a result and as demonstrated by numerous
experiments on publicly available data sets, our approach is extremely fast and
memory efficient in practice.
