  Boissonnat and Pritam introduced an algorithm to reduce a filtration of flag
(or clique) complexes, which can in particular speed up the computation of its
persistent homology. They used so-called edge collapse to reduce the input flag
filtration and their reduction method required only the 1-skeleton of the
filtration. In this paper we revisit the usage of edge collapse for efficient
computation of persistence homology. We first give a simple and intuitive
explanation of the principles underlying that algorithm. This in turn allows us
to propose various extensions including a zigzag filtration simplification
algorithm. We finally show some experiments to better understand how it
behaves.
