2 Search Results for "Fusy, Éric"

Document
DOI: 10.4230/LIPIcs.AofA.2020.9
Polyharmonic Functions And Random Processes in Cones

Authors: François Chapon, Éric Fusy, and Kilian Raschel

Published in: LIPIcs, Volume 159, 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020)

Abstract
We investigate polyharmonic functions associated to Brownian motions and random walks in cones. These are functions which cancel some power of the usual Laplacian in the continuous setting and of the discrete Laplacian in the discrete setting. We show that polyharmonic functions naturally appear while considering asymptotic expansions of the heat kernel in the Brownian case and in lattice walk enumeration problems. We provide a method to construct general polyharmonic functions through Laplace transforms and generating functions in the continuous and discrete cases, respectively. This is done by using a functional equation approach.
Cite as

François Chapon, Éric Fusy, and Kilian Raschel. Polyharmonic Functions And Random Processes in Cones. In 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 159, pp. 9:1-9:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{chapon_et_al:LIPIcs.AofA.2020.9,
  author =	{Chapon, Fran\c{c}ois and Fusy, \'{E}ric and Raschel, Kilian},
  title =	{{Polyharmonic Functions And Random Processes in Cones}},
  booktitle =	{31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020)},
  pages =	{9:1--9:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-147-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{159},
  editor =	{Drmota, Michael and Heuberger, Clemens},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2020.9},
  URN =		{urn:nbn:de:0030-drops-120390},
  doi =		{10.4230/LIPIcs.AofA.2020.9},
  annote =	{Keywords: Brownian motion in cones, Heat kernel, Random walks in cones, Harmonic functions, Polyharmonic functions, Complete asymptotic expansions, Functional equations}
}
Document
DOI: 10.4230/LIPIcs.SEA.2018.24
Fast Spherical Drawing of Triangulations: An Experimental Study of Graph Drawing Tools

Authors: Luca Castelli Aleardi, Gaspard Denis, and Éric Fusy

Published in: LIPIcs, Volume 103, 17th International Symposium on Experimental Algorithms (SEA 2018)

Abstract
We consider the problem of computing a spherical crossing-free geodesic drawing of a planar graph: this problem, as well as the closely related spherical parameterization problem, has attracted a lot of attention in the last two decades both in theory and in practice, motivated by a number of applications ranging from texture mapping to mesh remeshing and morphing. Our main concern is to design and implement a linear time algorithm for the computation of spherical drawings provided with theoretical guarantees. While not being aesthetically pleasing, our method is extremely fast and can be used as initial placer for spherical iterative methods and spring embedders. We provide experimental comparison with initial placers based on planar Tutte parameterization. Finally we explore the use of spherical drawings as initial layouts for (Euclidean) spring embedders: experimental evidence shows that this greatly helps to untangle the layout and to reach better local minima.
Cite as

Luca Castelli Aleardi, Gaspard Denis, and Éric Fusy. Fast Spherical Drawing of Triangulations: An Experimental Study of Graph Drawing Tools. In 17th International Symposium on Experimental Algorithms (SEA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 103, pp. 24:1-24:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

Copy BibTex To Clipboard

@InProceedings{aleardi_et_al:LIPIcs.SEA.2018.24,
  author =	{Aleardi, Luca Castelli and Denis, Gaspard and Fusy, \'{E}ric},
  title =	{{Fast Spherical Drawing of Triangulations: An Experimental Study of Graph Drawing Tools}},
  booktitle =	{17th International Symposium on Experimental Algorithms (SEA 2018)},
  pages =	{24:1--24:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-070-5},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{103},
  editor =	{D'Angelo, Gianlorenzo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2018.24},
  URN =		{urn:nbn:de:0030-drops-89597},
  doi =		{10.4230/LIPIcs.SEA.2018.24},
  annote =	{Keywords: Graph drawing, planar triangulations, spherical parameterizations}
}
  • Refine by Author
  • 2 Fusy, Éric
  • 1 Aleardi, Luca Castelli
  • 1 Chapon, François
  • 1 Denis, Gaspard
  • 1 Raschel, Kilian

  • Refine by Classification
  • 1 Mathematics of computing → Enumeration
  • 1 Mathematics of computing → Generating functions
  • 1 Mathematics of computing → Graph theory
  • 1 Mathematics of computing → Markov processes
  • 1 Theory of computation → Random walks and Markov chains

  • Refine by Keyword
  • 1 Brownian motion in cones
  • 1 Complete asymptotic expansions
  • 1 Functional equations
  • 1 Graph drawing
  • 1 Harmonic functions
  • Show More...

  • Refine by Type
  • 2 document

  • Refine by Publication Year
  • 1 2018
  • 1 2020

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact