Divisive cover (Q2319439)

The main contribution of the paper is to present a method for computing persistent homology that performs well at large filtration values. For this purpose the authors introduce the notion of filtered nerve of a filtered cover and construct a new approximation to the Čech complex computing persistent homology down to a predefined threshold that can be chosen arbitrarily. The top-down approach proposed is fundamentally different from existing algorithms which are fundamentally bottom-up.