Computing persistent homology of directed flag complexes

TL;DR

This paper introduces Flagser, a new software package for efficiently computing persistent homology of directed flag complexes, optimized for large graphs and capable of parallel processing and approximate calculations.

Contribution

Flagser is a novel computational tool that constructs directed flag complexes and computes their persistent homology with optimizations for large-scale data and parallelization, including an approximate method for faster results.

Findings

Successfully applied to brain microcircuit reconstructions.

Achieved significant speedups with approximate homology computation.

Demonstrated scalability and efficiency on large datasets.

Abstract

We present a new computing package Flagser, designed to construct the directed flag complex of a finite directed graph, and compute persistent homology for flexibly defined filtrations on the graph and the resulting complex. The persistent homology computation part of Flagser is based on the program Ripser [Bau18a], but is optimized specifically for large computations. The construction of the directed flag complex is done in a way that allows easy parallelization by arbitrarily many cores. Flagser also has the option of working with undirected graphs. For homology computations Flagser has an Approximate option, which shortens compute time with remarkable accuracy. We demonstrate the power of Flagser by applying it to the construction of the directed flag complex of digital reconstructions of brain microcircuitry by the Blue Brain Project and several other examples. In some instances we perform computation of homology. For a more complete performance analysis, we also apply Flagser to some other data collections. In all cases the hardware used in the computation, the use of memory and the compute time are recorded.