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Swap, Shift and Trim to Edge Collapse a Filtration

Authors Marc Glisse , Siddharth Pritam



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Author Details

Marc Glisse
  • Université Paris-Saclay, CNRS, Inria, Laboratoire de Mathématiques d'Orsay, 91405, Orsay, France
Siddharth Pritam
  • School of Engineering, Department of Computer Science, Shiv Nadar University, Delhi NCR, India

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Marc Glisse and Siddharth Pritam. Swap, Shift and Trim to Edge Collapse a Filtration. In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 44:1-44:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.SoCG.2022.44

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Mathematics of computing → Algebraic topology
Keywords
  • edge collapse
  • flag complex
  • graph
  • persistent homology

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