  Forman-Ricci curvature (FRC) is a potent and powerful tool for analysing
empirical networks, as the distribution of the curvature values can identify
structural information that is not readily detected by other geometrical
methods. Crucially, FRC captures higher-order structural information of clique
complexes of a graph or Vietoris-Rips complexes, which is not readily
accessible to alternative methods. However, existing FRC platforms are
prohibitively computationally expensive. Therefore, herein we develop an
efficient set-theoretic formulation for computing such high-order FRC in
simplicial complexes. Significantly, our set theory representation reveals
previous computational bottlenecks and also accelerates the computation of FRC.
Finally, We provide a pseudo-code, a software implementation coined FastForman,
as well as a benchmark comparison with alternative implementations. We envisage
that FastForman will be used in Topological and Geometrical Data analysis for
high-dimensional complex data sets. Moreover, our development paves the way for
future generalisations towards efficient computations of FRC on cell complexes.
