7 Search Results for "Huszár, Kristóf"

Document
DOI: 10.4230/LIPIcs.SoCG.2026.58
On Sparse Representations of 3‑Manifolds

Authors: Kristóf Huszár and Clément Maria

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

Abstract
3-manifolds are commonly represented as triangulations, consisting of abstract tetrahedra whose triangular faces are identified in pairs. The combinatorial sparsity of a triangulation, as measured by the treewidth of its dual graph, plays a fundamental role in the design of parameterized algorithms. In this work, we investigate algorithmic procedures that transform or modify a given triangulation while controlling specific sparsity parameters. First, we revisit a standard, linear-time algorithm that converts a given triangulation into a Heegaard diagram of the underlying 3-manifold, showing that the construction preserves treewidth. We apply this construction to exhibit a fixed-parameter tractable framework for computing Kuperberg’s quantum invariants of 3-manifolds. Second, we present a quasi-linear-time algorithm that retriangulates a given triangulation into one with maximum edge valence of at most nine, while only moderately increasing the treewidth of the dual graph. Combining these two algorithms yields a quasi-linear-time algorithm that produces, from a given triangulation, a Heegaard diagram in which every attaching curve intersects at most nine others.
Cite as

Kristóf Huszár and Clément Maria. On Sparse Representations of 3‑Manifolds. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 58:1-58:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{huszar_et_al:LIPIcs.SoCG.2026.58,
  author =	{Husz\'{a}r, Krist\'{o}f and Maria, Cl\'{e}ment},
  title =	{{On Sparse Representations of 3‑Manifolds}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{58:1--58:18},
  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.2026.58},
  URN =		{urn:nbn:de:0030-drops-258659},
  doi =		{10.4230/LIPIcs.SoCG.2026.58},
  annote =	{Keywords: computational 3-manifold topology, fixed-parameter tractability, Heegaard splittings and diagrams, triangulations, edge valence, treewidth, quantum invariants, tensor networks}
}
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.ESA.2025.37
Hardness of Computation of Quantum Invariants on 3-Manifolds with Restricted Topology

Authors: Henrique Ennes and Clément Maria

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
Quantum invariants in low-dimensional topology offer a wide variety of valuable invariants about knots and 3-manifolds, presented by explicit formulas that are readily computable. Their computational complexity has been actively studied and is tightly connected to topological quantum computing. In this article, we prove that for any 3-manifold quantum invariant in the Reshetikhin-Turaev model, there is a deterministic polynomial time algorithm that, given as input an arbitrary closed 3-manifold M, outputs a closed 3-manifold M' with the same quantum invariant, such that M' is hyperbolic, contains no low genus embedded incompressible surface, and is presented by a strongly irreducible Heegaard diagram. Our construction relies on properties of Heegaard splittings and the Hempel distance. At the level of computational complexity, this proves that the hardness of computing a given quantum invariant of 3-manifolds is preserved even when severely restricting the topology and the combinatorics of the input. This positively answers a question raised by Samperton [Samperton, 2023].
Cite as

Henrique Ennes and Clément Maria. Hardness of Computation of Quantum Invariants on 3-Manifolds with Restricted Topology. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 37:1-37:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ennes_et_al:LIPIcs.ESA.2025.37,
  author =	{Ennes, Henrique and Maria, Cl\'{e}ment},
  title =	{{Hardness of Computation of Quantum Invariants on 3-Manifolds with Restricted Topology}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{37:1--37:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.37},
  URN =		{urn:nbn:de:0030-drops-245057},
  doi =		{10.4230/LIPIcs.ESA.2025.37},
  annote =	{Keywords: 3-manifold, Heegaard splitting, Hempel distance, Quantum invariant, polynomial time reduction}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.23
On the Twin-Width of Smooth Manifolds

Authors: Édouard Bonnet and Kristóf Huszár

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

Abstract
Building on Whitney’s classical method of triangulating smooth manifolds, we show that every compact d-dimensional smooth manifold admits a triangulation with dual graph of twin-width at most d^O(d). In particular, it follows that every compact 3-manifold has a triangulation with dual graph of bounded twin-width. This is in sharp contrast to the case of treewidth, where for any natural number n there exists a closed 3-manifold such that every triangulation thereof has dual graph with treewidth at least n. To establish this result, we bound the twin-width of the dual graph of the d-skeleton of the second barycentric subdivision of the 2d-dimensional hypercubic honeycomb. We also show that every compact, piecewise-linear (hence smooth) d-dimensional manifold has triangulations where the dual graph has an arbitrarily large twin-width.
Cite as

Édouard Bonnet and Kristóf Huszár. On the Twin-Width of Smooth Manifolds. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 23:1-23:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bonnet_et_al:LIPIcs.SoCG.2025.23,
  author =	{Bonnet, \'{E}douard and Husz\'{a}r, Krist\'{o}f},
  title =	{{On the Twin-Width of Smooth Manifolds}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{23:1--23:16},
  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.2025.23},
  URN =		{urn:nbn:de:0030-drops-231752},
  doi =		{10.4230/LIPIcs.SoCG.2025.23},
  annote =	{Keywords: Smooth manifolds, triangulations, twin-width, Whitney embedding theorem, structural graph parameters, computational topology}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2023.42
On the Width of Complicated JSJ Decompositions

Authors: Kristóf Huszár and Jonathan Spreer

Published in: LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023)

Abstract
Motivated by the algorithmic study of 3-dimensional manifolds, we explore the structural relationship between the JSJ decomposition of a given 3-manifold and its triangulations. Building on work of Bachman, Derby-Talbot and Sedgwick, we show that a "sufficiently complicated" JSJ decomposition of a 3-manifold enforces a "complicated structure" for all of its triangulations. More concretely, we show that, under certain conditions, the treewidth (resp. pathwidth) of the graph that captures the incidences between the pieces of the JSJ decomposition of an irreducible, closed, orientable 3-manifold M yields a linear lower bound on its treewidth tw (M) (resp. pathwidth pw(M)), defined as the smallest treewidth (resp. pathwidth) of the dual graph of any triangulation of M. We present several applications of this result. We give the first example of an infinite family of bounded-treewidth 3-manifolds with unbounded pathwidth. We construct Haken 3-manifolds with arbitrarily large treewidth - previously the existence of such 3-manifolds was only known in the non-Haken case. We also show that the problem of providing a constant-factor approximation for the treewidth (resp. pathwidth) of bounded-degree graphs efficiently reduces to computing a constant-factor approximation for the treewidth (resp. pathwidth) of 3-manifolds.
Cite as

Kristóf Huszár and Jonathan Spreer. On the Width of Complicated JSJ Decompositions. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 42:1-42:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{huszar_et_al:LIPIcs.SoCG.2023.42,
  author =	{Husz\'{a}r, Krist\'{o}f and Spreer, Jonathan},
  title =	{{On the Width of Complicated JSJ Decompositions}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{42:1--42:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-273-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{258},
  editor =	{Chambers, Erin W. and Gudmundsson, Joachim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.42},
  URN =		{urn:nbn:de:0030-drops-178920},
  doi =		{10.4230/LIPIcs.SoCG.2023.42},
  annote =	{Keywords: computational 3-manifold topology, fixed-parameter tractability, generalized Heegaard splittings, JSJ decompositions, pathwidth, treewidth, triangulations}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2019.44
3-Manifold Triangulations with Small Treewidth

Authors: Kristóf Huszár and Jonathan Spreer

Published in: LIPIcs, Volume 129, 35th International Symposium on Computational Geometry (SoCG 2019)

Abstract
Motivated by fixed-parameter tractable (FPT) problems in computational topology, we consider the treewidth tw(M) of a compact, connected 3-manifold M, defined to be the minimum treewidth of the face pairing graph of any triangulation T of M. In this setting the relationship between the topology of a 3-manifold and its treewidth is of particular interest. First, as a corollary of work of Jaco and Rubinstein, we prove that for any closed, orientable 3-manifold M the treewidth tw(M) is at most 4g(M)-2, where g(M) denotes Heegaard genus of M. In combination with our earlier work with Wagner, this yields that for non-Haken manifolds the Heegaard genus and the treewidth are within a constant factor. Second, we characterize all 3-manifolds of treewidth one: These are precisely the lens spaces and a single other Seifert fibered space. Furthermore, we show that all remaining orientable Seifert fibered spaces over the 2-sphere or a non-orientable surface have treewidth two. In particular, for every spherical 3-manifold we exhibit a triangulation of treewidth at most two. Our results further validate the parameter of treewidth (and other related parameters such as cutwidth or congestion) to be useful for topological computing, and also shed more light on the scope of existing FPT-algorithms in the field.
Cite as

Kristóf Huszár and Jonathan Spreer. 3-Manifold Triangulations with Small Treewidth. In 35th International Symposium on Computational Geometry (SoCG 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 129, pp. 44:1-44:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{huszar_et_al:LIPIcs.SoCG.2019.44,
  author =	{Husz\'{a}r, Krist\'{o}f and Spreer, Jonathan},
  title =	{{3-Manifold Triangulations with Small Treewidth}},
  booktitle =	{35th International Symposium on Computational Geometry (SoCG 2019)},
  pages =	{44:1--44:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-104-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{129},
  editor =	{Barequet, Gill and Wang, Yusu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2019.44},
  URN =		{urn:nbn:de:0030-drops-104487},
  doi =		{10.4230/LIPIcs.SoCG.2019.44},
  annote =	{Keywords: computational 3-manifold topology, fixed-parameter tractability, layered triangulations, structural graph theory, treewidth, cutwidth, Heegaard genus, lens spaces, Seifert fibered spaces}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2018.46
On the Treewidth of Triangulated 3-Manifolds

Authors: Kristóf Huszár, Jonathan Spreer, and Uli Wagner

Published in: LIPIcs, Volume 99, 34th International Symposium on Computational Geometry (SoCG 2018)

Abstract
In graph theory, as well as in 3-manifold topology, there exist several width-type parameters to describe how "simple" or "thin" a given graph or 3-manifold is. These parameters, such as pathwidth or treewidth for graphs, or the concept of thin position for 3-manifolds, play an important role when studying algorithmic problems; in particular, there is a variety of problems in computational 3-manifold topology - some of them known to be computationally hard in general - that become solvable in polynomial time as soon as the dual graph of the input triangulation has bounded treewidth. In view of these algorithmic results, it is natural to ask whether every 3-manifold admits a triangulation of bounded treewidth. We show that this is not the case, i.e., that there exists an infinite family of closed 3-manifolds not admitting triangulations of bounded pathwidth or treewidth (the latter implies the former, but we present two separate proofs). We derive these results from work of Agol and of Scharlemann and Thompson, by exhibiting explicit connections between the topology of a 3-manifold M on the one hand and width-type parameters of the dual graphs of triangulations of M on the other hand, answering a question that had been raised repeatedly by researchers in computational 3-manifold topology. In particular, we show that if a closed, orientable, irreducible, non-Haken 3-manifold M has a triangulation of treewidth (resp. pathwidth) k then the Heegaard genus of M is at most 48(k+1) (resp. 4(3k+1)).
Cite as

Kristóf Huszár, Jonathan Spreer, and Uli Wagner. On the Treewidth of Triangulated 3-Manifolds. In 34th International Symposium on Computational Geometry (SoCG 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 99, pp. 46:1-46:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{huszar_et_al:LIPIcs.SoCG.2018.46,
  author =	{Husz\'{a}r, Krist\'{o}f and Spreer, Jonathan and Wagner, Uli},
  title =	{{On the Treewidth of Triangulated 3-Manifolds}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{46:1--46:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-066-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{99},
  editor =	{Speckmann, Bettina and T\'{o}th, Csaba D.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2018.46},
  URN =		{urn:nbn:de:0030-drops-87591},
  doi =		{10.4230/LIPIcs.SoCG.2018.46},
  annote =	{Keywords: computational topology, triangulations of 3-manifolds, thin position, fixed-parameter tractability, congestion, treewidth}
}
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