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Documents authored by Blaser, Nello

Document
DOI: 10.4230/LIPIcs.SoCG.2022.17
ETH-Tight Algorithms for Finding Surfaces in Simplicial Complexes of Bounded Treewidth

Authors: Mitchell Black, Nello Blaser, Amir Nayyeri, and Erlend Raa Vågset

Published in: LIPIcs, Volume 224, 38th International Symposium on Computational Geometry (SoCG 2022)

Abstract
Given a simplicial complex with n simplices, we consider the Connected Subsurface Recognition (c-SR) problem of finding a subcomplex that is homeomorphic to a given connected surface with a fixed boundary. We also study the related Sum-of-Genus Subsurface Recognition (SoG) problem, where we instead search for a surface whose boundary, number of connected components, and total genus are given. For both of these problems, we give parameterized algorithms with respect to the treewidth k of the Hasse diagram that run in 2^{O(k log k)}n^{O(1)} time. For the SoG problem, we also prove that our algorithm is optimal assuming the exponential-time hypothesis. In fact, we prove the stronger result that our algorithm is ETH-tight even without restriction on the total genus.
Cite as

Mitchell Black, Nello Blaser, Amir Nayyeri, and Erlend Raa Vågset. ETH-Tight Algorithms for Finding Surfaces in Simplicial Complexes of Bounded Treewidth. In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 17:1-17:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{black_et_al:LIPIcs.SoCG.2022.17,
  author =	{Black, Mitchell and Blaser, Nello and Nayyeri, Amir and V\r{a}gset, Erlend Raa},
  title =	{{ETH-Tight Algorithms for Finding Surfaces in Simplicial Complexes of Bounded Treewidth}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{17:1--17:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-227-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{224},
  editor =	{Goaoc, Xavier and Kerber, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.17},
  URN =		{urn:nbn:de:0030-drops-160253},
  doi =		{10.4230/LIPIcs.SoCG.2022.17},
  annote =	{Keywords: Computational Geometry, Surface Recognition, Treewidth, Hasse Diagram, Simplicial Complexes, Low-Dimensional Topology, Parameterized Complexity, Computational Complexity}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2020.18
Relative Persistent Homology

Authors: Nello Blaser and Morten Brun

Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)

Abstract
The alpha complex efficiently computes persistent homology of a point cloud X in Euclidean space when the dimension d is low. Given a subset A of X, relative persistent homology can be computed as the persistent homology of the relative Čech complex Č(X, A). But this is not computationally feasible for larger point clouds X. The aim of this note is to present a method for efficient computation of relative persistent homology in low dimensional Euclidean space. We introduce the relative Delaunay-Čech complex DelČ(X, A) whose homology is the relative persistent homology. It is constructed from the Delaunay complex of an embedding of X in (d+1)-dimensional Euclidean space.
Cite as

Nello Blaser and Morten Brun. Relative Persistent Homology. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 18:1-18:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{blaser_et_al:LIPIcs.SoCG.2020.18,
  author =	{Blaser, Nello and Brun, Morten},
  title =	{{Relative Persistent Homology}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{18:1--18:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Cabello, Sergio and Chen, Danny Z.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.18},
  URN =		{urn:nbn:de:0030-drops-121762},
  doi =		{10.4230/LIPIcs.SoCG.2020.18},
  annote =	{Keywords: topological data analysis, relative homology, Delaunay-\v{C}ech complex, alpha complex}
}
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