2 Search Results for "J�ttler, Bert"


Document
Counting and Sampling Labeled Chordal Graphs in Polynomial Time

Authors: Úrsula Hébert-Johnson, Daniel Lokshtanov, and Eric Vigoda

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)


Abstract
We present the first polynomial-time algorithm to exactly compute the number of labeled chordal graphs on n vertices. Our algorithm solves a more general problem: given n and ω as input, it computes the number of ω-colorable labeled chordal graphs on n vertices, using O(n⁷) arithmetic operations. A standard sampling-to-counting reduction then yields a polynomial-time exact sampler that generates an ω-colorable labeled chordal graph on n vertices uniformly at random. Our counting algorithm improves upon the previous best result by Wormald (1985), which computes the number of labeled chordal graphs on n vertices in time exponential in n. An implementation of the polynomial-time counting algorithm gives the number of labeled chordal graphs on up to 30 vertices in less than three minutes on a standard desktop computer. Previously, the number of labeled chordal graphs was only known for graphs on up to 15 vertices.

Cite as

Úrsula Hébert-Johnson, Daniel Lokshtanov, and Eric Vigoda. Counting and Sampling Labeled Chordal Graphs in Polynomial Time. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 58:1-58:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{hebertjohnson_et_al:LIPIcs.ESA.2023.58,
  author =	{H\'{e}bert-Johnson, \'{U}rsula and Lokshtanov, Daniel and Vigoda, Eric},
  title =	{{Counting and Sampling Labeled Chordal Graphs in Polynomial Time}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{58:1--58:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.58},
  URN =		{urn:nbn:de:0030-drops-187119},
  doi =		{10.4230/LIPIcs.ESA.2023.58},
  annote =	{Keywords: Counting algorithms, graph sampling, chordal graphs}
}
Document
Voronoi Diagrams for Parallel Halflines and Line Segments in Space

Authors: Franz Aurenhammer, Bert Jüttler, and Günter Paulini

Published in: LIPIcs, Volume 92, 28th International Symposium on Algorithms and Computation (ISAAC 2017)


Abstract
We consider the Euclidean Voronoi diagram for a set of $n$ parallel halflines in 3-space. A relation of this diagram to planar power diagrams is shown, and is used to analyze its geometric and topological properties. Moreover, an easy-to-implement space sweep algorithm is proposed that computes the Voronoi diagram for parallel halflines at logarithmic cost per face. Previously only an approximation algorithm for this problem was known. Our method of construction generalizes to Voronoi diagrams for parallel line segments, and to higher dimensions.

Cite as

Franz Aurenhammer, Bert Jüttler, and Günter Paulini. Voronoi Diagrams for Parallel Halflines and Line Segments in Space. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 7:1-7:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


Copy BibTex To Clipboard

@InProceedings{aurenhammer_et_al:LIPIcs.ISAAC.2017.7,
  author =	{Aurenhammer, Franz and J\"{u}ttler, Bert and Paulini, G\"{u}nter},
  title =	{{Voronoi Diagrams for Parallel Halflines and Line Segments in Space}},
  booktitle =	{28th International Symposium on Algorithms and Computation (ISAAC 2017)},
  pages =	{7:1--7:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-054-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{92},
  editor =	{Okamoto, Yoshio and Tokuyama, Takeshi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.7},
  URN =		{urn:nbn:de:0030-drops-82157},
  doi =		{10.4230/LIPIcs.ISAAC.2017.7},
  annote =	{Keywords: Voronoi diagram, line segments, space-sweep algorithm}
}
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