Swap, Shift and Trim to Edge Collapse a Filtration
Computational Geometry
2022-03-15 v1 Algebraic Topology
Abstract
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.
Cite
@article{arxiv.2203.07022,
title = {Swap, Shift and Trim to Edge Collapse a Filtration},
author = {Marc Glisse and Siddharth Pritam},
journal= {arXiv preprint arXiv:2203.07022},
year = {2022}
}