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Documents authored by Jendrysiak, Jan

Artifact
Software
DOI: 10.4230/artifacts.26094
Skyscraper Invariant and Filtered Multiparameter Landscapes

Authors: Jan Jendrysiak

Abstract
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Jan Jendrysiak. Skyscraper Invariant and Filtered Multiparameter Landscapes (Software, Source Code for computing the Skyscraper invariant). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@misc{dagstuhl-artifact-26094,
   title = {{Skyscraper Invariant and Filtered Multiparameter Landscapes}}, 
   author = {Jendrysiak, Jan},
   note = {Software, version 0.1., swhId: \href{https://archive.softwareheritage.org/swh:1:dir:8ed2562604075467f0b0014975100a2d26e434ba;origin=https://github.com/JanJend/Skyscraper-Invariant;visit=swh:1:snp:2df2fa4334a0a30eec73f451f9e4e76dde600987;anchor=swh:1:rev:9c484a798aca448f7c6a9305a249b57e9bb389c9}{\texttt{swh:1:dir:8ed2562604075467f0b0014975100a2d26e434ba}} (visited on 2026-05-27)},
   url = {https://github.com/JanJend/Skyscraper-Invariant},
   doi = {10.4230/artifacts.26094},
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.47
Computing the Skyscraper Invariant

Authors: Marc Fersztand and Jan Jendrysiak

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
We develop the first algorithms for computing the Skyscraper Invariant [FJNT24]. This is a filtration of the classical rank invariant for multiparameter persistence modules defined by the Harder-Narasimhan filtrations along every central charge supported at a single parameter value. Cheng’s algorithm [Cheng24] can be used to compute HN filtrations of arbitrary acyclic quiver representations in polynomial time in the total dimension, but in practice, the large dimension of persistence modules makes this direct approach infeasible. We show that by exploiting the additivity of the HN filtration and the special central charges, one can get away with a brute-force approach. For d-parameter modules, this produces an FPT ε-approximate algorithm with runtime dominated by 𝒪(1/ε^d ⋅ T_dec), where T_dec is the time for decomposition, which we compute with aida [DJK25]. We show that the wall-and-chamber structure of the module can be computed via lower envelopes of degree d - 1 polynomials. This allows for an exact computation of the Skyscraper Invariant roughly in 𝒪(n^d ⋅ T_dec) time for n the size of the presentation and enables a fast hybrid algorithm. For 2-parameter modules, we have implemented not only our algorithms but also, for the first time, Cheng’s algorithm. We compare all algorithms and, as a proof of concept for data analysis, compute a filtered version of the Multiparameter Landscape for biomedical data.
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Marc Fersztand and Jan Jendrysiak. Computing the Skyscraper Invariant. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 47:1-47:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{fersztand_et_al:LIPIcs.SoCG.2026.47,
  author =	{Fersztand, Marc and Jendrysiak, Jan},
  title =	{{Computing the Skyscraper Invariant}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{47:1--47:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.47},
  URN =		{urn:nbn:de:0030-drops-258535},
  doi =		{10.4230/LIPIcs.SoCG.2026.47},
  annote =	{Keywords: Topological Data Analysis, Multiparameter Persistence, Persistence, Harder-Narasimhan Filtration, Skyscraper Invariant}
}
Artifact
Software
DOI: 10.4230/artifacts.23282
AIDA

Authors: Jan Jendrysiak

Abstract
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Jan Jendrysiak. AIDA (Software, Algorithm). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@misc{dagstuhl-artifact-23282,
   title = {{AIDA}}, 
   author = {Jendrysiak, Jan},
   note = {Software, version 0.2., FWF P 33765-N, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:c339cb432335e83758b23a807641b9c6a43525c8;origin=https://github.com/JanJend/AIDA;visit=swh:1:snp:a1ca65299db1d0ad7dd5644ff52befd0ee9f8886;anchor=swh:1:rev:92bd309d5bf80860601482124ba9ad67cc204b47}{\texttt{swh:1:dir:c339cb432335e83758b23a807641b9c6a43525c8}} (visited on 2025-06-20)},
   url = {https://github.com/JanJend/AIDA},
   doi = {10.4230/artifacts.23282},
}
Artifact
Software
DOI: 10.4230/artifacts.23283
Persistence Algebra

Authors: Jan Jendrysiak

Abstract
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Jan Jendrysiak. Persistence Algebra (Software, Library). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@misc{dagstuhl-artifact-23283,
   title = {{Persistence Algebra}}, 
   author = {Jendrysiak, Jan},
   note = {Software, version 0.1., FWF P 33765-N, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:e41d23c6d743921e03d8a54e45ea3a4d36f7718b;origin=https://github.com/JanJend/Persistence-Algebra;visit=swh:1:snp:3a0bdc3f338aebcbea46c12944a4a330f010dec4;anchor=swh:1:rev:1e64b4eb18e6cb1de21b5e66d540bb974f6cac38}{\texttt{swh:1:dir:e41d23c6d743921e03d8a54e45ea3a4d36f7718b}} (visited on 2025-06-20)},
   url = {https://github.com/JanJend/Persistence-Algebra},
   doi = {10.4230/artifacts.23283},
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.41
Decomposing Multiparameter Persistence Modules

Authors: Tamal K. Dey, Jan Jendrysiak, and Michael Kerber

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
Dey and Xin (J.Appl.Comput.Top., 2022) describe an algorithm to decompose finitely presented multiparameter persistence modules using a matrix reduction algorithm. Their algorithm only works for modules whose generators and relations are distinctly graded. We extend their approach to work on all finitely presented modules and introduce several improvements that lead to significant speed-ups in practice. Our algorithm is fixed-parameter tractable with respect to the maximal number of relations of the same degree and with further optimisation we obtain an O(n³) time algorithm for interval-decomposable modules. In particular, we can decide interval-decomposability in this time. As a by-product to the proofs of correctness we develop a theory of parameter restriction for persistence modules. Our algorithm is implemented as a software library aida, the first to enable the decomposition of large inputs. We show its capabilities via extensive experimental evaluation.
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Tamal K. Dey, Jan Jendrysiak, and Michael Kerber. Decomposing Multiparameter Persistence Modules. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 41:1-41:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dey_et_al:LIPIcs.SoCG.2025.41,
  author =	{Dey, Tamal K. and Jendrysiak, Jan and Kerber, Michael},
  title =	{{Decomposing Multiparameter Persistence Modules}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{41:1--41:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.41},
  URN =		{urn:nbn:de:0030-drops-231939},
  doi =		{10.4230/LIPIcs.SoCG.2025.41},
  annote =	{Keywords: Topological Data Analysis, Multiparameter Persistence Modules, Persistence, Decomposition}
}
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