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Strong Collapse for Persistence

Authors Jean-Daniel Boissonnat, Siddharth Pritam, Divyansh Pareek



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Author Details

Jean-Daniel Boissonnat
  • Université Côte d'Azur, INRIA, France
Siddharth Pritam
  • Université Côte d'Azur, INRIA, France
Divyansh Pareek
  • Indian Institute of Technology Bombay, India

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Jean-Daniel Boissonnat, Siddharth Pritam, and Divyansh Pareek. Strong Collapse for Persistence. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 67:1-67:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.ESA.2018.67

Abstract

We introduce a fast and memory efficient approach to compute the persistent homology (PH) of a sequence of simplicial complexes. The basic idea is to simplify the complexes of the input sequence by using strong collapses, as introduced by J. Barmak and E. Miniam [DCG (2012)], and to compute the PH of an induced sequence of reduced simplicial complexes that has the same PH as the initial one. Our approach has several salient features that distinguishes it from previous work. It is not limited to filtrations (i.e. sequences of nested simplicial subcomplexes) but works for other types of sequences like towers and zigzags. To strong collapse a simplicial complex, we only need to store the maximal simplices of the complex, not the full set of all its simplices, which saves a lot of space and time. Moreover, the complexes in the sequence can be strong collapsed independently and in parallel. As a result and as demonstrated by numerous experiments on publicly available data sets, our approach is extremely fast and memory efficient in practice.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Algebraic topology
Keywords
  • Computational Topology
  • Topological Data Analysis
  • Strong Collapse
  • Persistent homology

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