4 Search Results for "Devadoss, Satyan L."

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.63
Computing Distances on Graph Associahedra Is Fixed-Parameter Tractable

Authors: Luís Felipe I. Cunha, Ignasi Sau, Uéverton S. Souza, and Mario Valencia-Pabon

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
An elimination tree of a connected graph G is a rooted tree on the vertices of G obtained by choosing a root v and recursing on the connected components of G-v to obtain the subtrees of v. The graph associahedron of G is a polytope whose vertices correspond to elimination trees of G and whose edges correspond to tree rotations, a natural operation between elimination trees. These objects generalize associahedra, which correspond to the case where G is a path. Ito et al. [ICALP 2023] recently proved that the problem of computing distances on graph associahedra is NP-hard. In this paper we prove that the problem, for a general graph G, is fixed-parameter tractable parameterized by the distance k. Prior to our work, only the case where G is a path was known to be fixed-parameter tractable. To prove our result, we use a novel approach based on a marking scheme that restricts the search to a set of vertices whose size is bounded by a (large) function of k.
Cite as

Luís Felipe I. Cunha, Ignasi Sau, Uéverton S. Souza, and Mario Valencia-Pabon. Computing Distances on Graph Associahedra Is Fixed-Parameter Tractable. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 63:1-63:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cunha_et_al:LIPIcs.ICALP.2025.63,
  author =	{Cunha, Lu{\'\i}s Felipe I. and Sau, Ignasi and Souza, U\'{e}verton S. and Valencia-Pabon, Mario},
  title =	{{Computing Distances on Graph Associahedra Is Fixed-Parameter Tractable}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{63:1--63:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.63},
  URN =		{urn:nbn:de:0030-drops-234408},
  doi =		{10.4230/LIPIcs.ICALP.2025.63},
  annote =	{Keywords: graph associahedra, elimination tree, rotation distance, parameterized complexity, fixed-parameter tractable algorithm, combinatorial shortest path, reconfiguration}
}
Document
Media Exposition
DOI: 10.4230/LIPIcs.SoCG.2022.67
Visualizing and Unfolding Nets of 4-Polytopes (Media Exposition)

Authors: Satyan L. Devadoss, Matthew S. Harvey, and Sam Zhang

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

Abstract
Over a decade ago, it was shown that every edge unfolding of the Platonic solids was without self-overlap, yielding a valid net. Recent work has extended this property to their higher-dimensional analogs: the 4-cube, 4-simplex, and 4-orthoplex. We present an interactive visualization that allows the user to unfold these polytopes by drawing on their dual 1-skeleton graph.
Cite as

Satyan L. Devadoss, Matthew S. Harvey, and Sam Zhang. Visualizing and Unfolding Nets of 4-Polytopes (Media Exposition). In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 67:1-67:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{devadoss_et_al:LIPIcs.SoCG.2022.67,
  author =	{Devadoss, Satyan L. and Harvey, Matthew S. and Zhang, Sam},
  title =	{{Visualizing and Unfolding Nets of 4-Polytopes}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{67:1--67:4},
  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.2022.67},
  URN =		{urn:nbn:de:0030-drops-160759},
  doi =		{10.4230/LIPIcs.SoCG.2022.67},
  annote =	{Keywords: unfoldings, nets, polytopes}
}
Document
Multimedia Exposition
DOI: 10.4230/LIPIcs.SoCG.2018.75
Geometric Realizations of the 3D Associahedron (Multimedia Exposition)

Authors: Satyan L. Devadoss, Daniel D. Johnson, Justin Lee, and Jackson Warley

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

Abstract
The associahedron is a convex polytope whose 1-skeleton is isomorphic to the flip graph of a convex polygon. There exists an elegant geometric realization of the associahedron, using the remarkable theory of secondary polytopes, based on the geometry of the underlying polygon. We present an interactive application that visualizes this correspondence in the 3D case.
Cite as

Satyan L. Devadoss, Daniel D. Johnson, Justin Lee, and Jackson Warley. Geometric Realizations of the 3D Associahedron (Multimedia Exposition). In 34th International Symposium on Computational Geometry (SoCG 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 99, pp. 75:1-75:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{devadoss_et_al:LIPIcs.SoCG.2018.75,
  author =	{Devadoss, Satyan L. and Johnson, Daniel D. and Lee, Justin and Warley, Jackson},
  title =	{{Geometric Realizations of the 3D Associahedron}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{75:1--75:4},
  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.2018.75},
  URN =		{urn:nbn:de:0030-drops-87886},
  doi =		{10.4230/LIPIcs.SoCG.2018.75},
  annote =	{Keywords: associahedron, secondary polytope, realization}
}
Document
Multimedia Exposition
DOI: 10.4230/LIPIcs.SoCG.2018.76
Star Unfolding of Boxes (Multimedia Exposition)

Authors: Dani Demas, Satyan L. Devadoss, and Yu Xuan Hong

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

Abstract
Given a convex polyhedron, the star unfolding of its surface is obtained by cutting along the shortest paths from a fixed source point to each of its vertices. We present an interactive application that visualizes the star unfolding of a box, such that its dimensions and source point locations can be continuously toggled by the user.
Cite as

Dani Demas, Satyan L. Devadoss, and Yu Xuan Hong. Star Unfolding of Boxes (Multimedia Exposition). In 34th International Symposium on Computational Geometry (SoCG 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 99, pp. 76:1-76:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{demas_et_al:LIPIcs.SoCG.2018.76,
  author =	{Demas, Dani and Devadoss, Satyan L. and Hong, Yu Xuan},
  title =	{{Star Unfolding of Boxes}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{76:1--76:4},
  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.2018.76},
  URN =		{urn:nbn:de:0030-drops-87890},
  doi =		{10.4230/LIPIcs.SoCG.2018.76},
  annote =	{Keywords: star unfolding, source unfolding, Voronoi diagram}
}
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