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Documents authored by Vågset, Erlend Raa

Document
DOI: 10.4230/LIPIcs.SoCG.2026.85
ETH-Tight Complexity of Optimal Morse Matching on Bounded-Treewidth Complexes

Authors: Geevarghese Philip and Erlend Raa Vågset

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

Abstract
The Optimal Morse Matching (OMM) problem asks for a discrete gradient vector field on a simplicial complex that minimizes the number of critical simplices. It is NP-hard and has been studied extensively in heuristic, approximation, and parameterized complexity settings. Parameterized by treewidth k, OMM has long been known to be solvable on triangulations of 3-manifolds in 2^O(k²) n^O(1) time and in FPT time for triangulations of arbitrary manifolds, but the exact dependence on k has remained an open question. We resolve this by giving a new 2^O(k log k) n-time algorithm for any finite regular CW complex, and show that no 2^o(k log k) n^O(1)-time algorithm exists unless the Exponential Time Hypothesis (ETH) fails.
Cite as

Geevarghese Philip and Erlend Raa Vågset. ETH-Tight Complexity of Optimal Morse Matching on Bounded-Treewidth Complexes. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 85:1-85:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{philip_et_al:LIPIcs.SoCG.2026.85,
  author =	{Philip, Geevarghese and V\r{a}gset, Erlend Raa},
  title =	{{ETH-Tight Complexity of Optimal Morse Matching on Bounded-Treewidth Complexes}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{85:1--85:19},
  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.2026.85},
  URN =		{urn:nbn:de:0030-drops-258926},
  doi =		{10.4230/LIPIcs.SoCG.2026.85},
  annote =	{Keywords: Discrete Morse Theory, Simplicial Complexes, Optimal Morse Matching, Treewidth, Parameterized Algorithms, Computational Topology, Dynamic Programming, Exponential Time Hypothesis, Topological Data Analysis}
}
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}
}
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