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Persistent Homology on GPU for 1d and 2d Cubical Filtrations

Author Marc Glisse

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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Algebraic topology
  • Theory of computation → Computational geometry
  • Computing methodologies → Parallel algorithms
Keywords
  • Persistent homology
  • cubical complex
  • parallelism
  • GPU

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Abstract

This paper describes the algorithmic choices made in a pure GPU implementation to compute persistent homology for cubical complexes in dimension 1 or 2. The main ingredients are the parallel detection of apparent pairs, the simple reduction of the remaining complex when we only consider H₀, and the possibility to iterate those two steps. The result can be 200 times faster than a sequential CPU implementation.

Cite As Get BibTex

Marc Glisse. Persistent Homology on GPU for 1d and 2d Cubical Filtrations. In 34th Annual European Symposium on Algorithms (ESA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 388, pp. 5:1-5:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ESA.2026.5

Author Details

Marc Glisse
  • Université Paris-Saclay, CNRS, Inria, Laboratoire de Mathématiques d'Orsay, 91405, Orsay, France

Funding

  • Glisse, Marc: ANR TopAI chair in Artificial Intelligence (ANR–19–CHIA–0001).

Supplementary Materials

References

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