4 Search Results for "Schleimer, Saul"

Document
DOI: 10.4230/LIPIcs.SoCG.2023.50
A Structural Approach to Tree Decompositions of Knots and Spatial Graphs

Authors: Corentin Lunel and Arnaud de Mesmay

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

Abstract
Knots are commonly represented and manipulated via diagrams, which are decorated planar graphs. When such a knot diagram has low treewidth, parameterized graph algorithms can be leveraged to ensure the fast computation of many invariants and properties of the knot. It was recently proved that there exist knots which do not admit any diagram of low treewidth, and the proof relied on intricate low-dimensional topology techniques. In this work, we initiate a thorough investigation of tree decompositions of knot diagrams (or more generally, diagrams of spatial graphs) using ideas from structural graph theory. We define an obstruction on spatial embeddings that forbids low tree width diagrams, and we prove that it is optimal with respect to a related width invariant. We then show the existence of this obstruction for knots of high representativity, which include for example torus knots, providing a new and self-contained proof that those do not admit diagrams of low treewidth. This last step is inspired by a result of Pardon on knot distortion.
Cite as

Corentin Lunel and Arnaud de Mesmay. A Structural Approach to Tree Decompositions of Knots and Spatial Graphs. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 50:1-50:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{lunel_et_al:LIPIcs.SoCG.2023.50,
  author =	{Lunel, Corentin and de Mesmay, Arnaud},
  title =	{{A Structural Approach to Tree Decompositions of Knots and Spatial Graphs}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{50:1--50:16},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.50},
  URN =		{urn:nbn:de:0030-drops-179002},
  doi =		{10.4230/LIPIcs.SoCG.2023.50},
  annote =	{Keywords: Knots, Spatial Graphs, Tree Decompositions, Tangle, Representativity}
}
Document
DOI: 10.4230/DagRep.12.2.17
Computation and Reconfiguration in Low-Dimensional Topological Spaces (Dagstuhl Seminar 22062)

Authors: Maike Buchin, Anna Lubiw, Arnaud de Mesmay, Saul Schleimer, and Florestan Brunck

Published in: Dagstuhl Reports, Volume 12, Issue 2 (2022)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 22062 "Computation and Reconfiguration in Low-Dimensional Topological Spaces". The seminar consisted of a small collection of introductory talks, an open problem session, and then the seminar participants worked in small groups on problems on reconfiguration within the context of objects as diverse as elimination trees, morphings, curves on surfaces, translation surfaces and Delaunay triangulations.
Cite as

Maike Buchin, Anna Lubiw, Arnaud de Mesmay, Saul Schleimer, and Florestan Brunck. Computation and Reconfiguration in Low-Dimensional Topological Spaces (Dagstuhl Seminar 22062). In Dagstuhl Reports, Volume 12, Issue 2, pp. 17-66, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@Article{buchin_et_al:DagRep.12.2.17,
  author =	{Buchin, Maike and Lubiw, Anna and de Mesmay, Arnaud and Schleimer, Saul and Brunck, Florestan},
  title =	{{Computation and Reconfiguration in Low-Dimensional Topological Spaces (Dagstuhl Seminar 22062)}},
  pages =	{17--66},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2022},
  volume =	{12},
  number =	{2},
  editor =	{Buchin, Maike and Lubiw, Anna and de Mesmay, Arnaud and Schleimer, Saul and Brunck, Florestan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.12.2.17},
  URN =		{urn:nbn:de:0030-drops-169305},
  doi =		{10.4230/DagRep.12.2.17},
  annote =	{Keywords: Geometric Topology, Computational Geometry, Graph Drawing, Reconfiguration, Dagstuhl Seminar}
}
Document
DOI: 10.4230/DagRep.9.8.84
Computation in Low-Dimensional Geometry and Topology (Dagstuhl Seminar 19352)

Authors: Maarten Löffler, Anna Lubiw, Saul Schleimer, and Erin Moriarty Wolf Chambers

Published in: Dagstuhl Reports, Volume 9, Issue 8 (2020)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 19352 ``Computation in Low-Dimensional Geometry and Topology''. The seminar participants investigated problems in: knot theory, trajectory analysis, algorithmic topology, computational geometry of curves, and graph drawing, with an emphasis on how low-dimensional structures change over time.
Cite as

Maarten Löffler, Anna Lubiw, Saul Schleimer, and Erin Moriarty Wolf Chambers. Computation in Low-Dimensional Geometry and Topology (Dagstuhl Seminar 19352). In Dagstuhl Reports, Volume 9, Issue 8, pp. 84-112, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@Article{loffler_et_al:DagRep.9.8.84,
  author =	{L\"{o}ffler, Maarten and Lubiw, Anna and Schleimer, Saul and Wolf Chambers, Erin Moriarty},
  title =	{{Computation in Low-Dimensional Geometry and Topology (Dagstuhl Seminar 19352)}},
  pages =	{84--112},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2019},
  volume =	{9},
  number =	{8},
  editor =	{L\"{o}ffler, Maarten and Lubiw, Anna and Schleimer, Saul and Wolf Chambers, Erin Moriarty},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.9.8.84},
  URN =		{urn:nbn:de:0030-drops-117734},
  doi =		{10.4230/DagRep.9.8.84},
  annote =	{Keywords: Geometric topology, Graph Drawing, Computational Geometry}
}
Document
DOI: 10.4230/LIPIcs.STACS.2019.37
Compressed Decision Problems in Hyperbolic Groups

Authors: Derek Holt, Markus Lohrey, and Saul Schleimer

Published in: LIPIcs, Volume 126, 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)

Abstract
We prove that the compressed word problem and the compressed simultaneous conjugacy problem are solvable in polynomial time in hyperbolic groups. In such problems, group elements are input as words defined by straight-line programs defined over a finite generating set for the group. We prove also that, for any infinite hyperbolic group G, the compressed knapsack problem in G is NP-complete.
Cite as

Derek Holt, Markus Lohrey, and Saul Schleimer. Compressed Decision Problems in Hyperbolic Groups. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 37:1-37:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{holt_et_al:LIPIcs.STACS.2019.37,
  author =	{Holt, Derek and Lohrey, Markus and Schleimer, Saul},
  title =	{{Compressed Decision Problems in Hyperbolic Groups}},
  booktitle =	{36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
  pages =	{37:1--37:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-100-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{126},
  editor =	{Niedermeier, Rolf and Paul, Christophe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.37},
  URN =		{urn:nbn:de:0030-drops-102766},
  doi =		{10.4230/LIPIcs.STACS.2019.37},
  annote =	{Keywords: hyperbolic groups, algorithms for compressed words, circuit evaluation problems}
}
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