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Conference Papers Year : 2022

Swap, Shift and Trim to Edge Collapse a Filtration

Marc Glisse
Siddharth Pritam
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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 use of edge collapse for efficient computation of persistent 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.
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Dates and versions

hal-03791448 , version 1 (29-09-2022)

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Marc Glisse, Siddharth Pritam. Swap, Shift and Trim to Edge Collapse a Filtration. SoCG 2022 - 38th International Symposium on Computational Geometry, Jun 2022, Berlin, Germany. ⟨10.4230/LIPIcs.SoCG.2022.44⟩. ⟨hal-03791448⟩
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