Search Results

Documents authored by Samaga, Shreyas N.

Document
DOI: 10.4230/LIPIcs.SoCG.2024.51
Efficient Algorithms for Complexes of Persistence Modules with Applications

Authors: Tamal K. Dey, Florian Russold, and Shreyas N. Samaga

Published in: LIPIcs, Volume 293, 40th International Symposium on Computational Geometry (SoCG 2024)

Abstract
We extend the persistence algorithm, viewed as an algorithm computing the homology of a complex of free persistence or graded modules, to complexes of modules that are not free. We replace persistence modules by their presentations and develop an efficient algorithm to compute the homology of a complex of presentations. To deal with inputs that are not given in terms of presentations, we give an efficient algorithm to compute a presentation of a morphism of persistence modules. This allows us to compute persistent (co)homology of instances giving rise to complexes of non-free modules. Our methods lead to a new efficient algorithm for computing the persistent homology of simplicial towers and they enable efficient algorithms to compute the persistent homology of cosheaves over simplicial towers and cohomology of persistent sheaves on simplicial complexes. We also show that we can compute the cohomology of persistent sheaves over arbitrary finite posets by reducing the computation to a computation over simplicial complexes.
Cite as

Tamal K. Dey, Florian Russold, and Shreyas N. Samaga. Efficient Algorithms for Complexes of Persistence Modules with Applications. In 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 293, pp. 51:1-51:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{dey_et_al:LIPIcs.SoCG.2024.51,
  author =	{Dey, Tamal K. and Russold, Florian and Samaga, Shreyas N.},
  title =	{{Efficient Algorithms for Complexes of Persistence Modules with Applications}},
  booktitle =	{40th International Symposium on Computational Geometry (SoCG 2024)},
  pages =	{51:1--51:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-316-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{293},
  editor =	{Mulzer, Wolfgang and Phillips, Jeff M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2024.51},
  URN =		{urn:nbn:de:0030-drops-199969},
  doi =		{10.4230/LIPIcs.SoCG.2024.51},
  annote =	{Keywords: Persistent (co)homology, Persistence modules, Sheaves, Presentations}
}
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact