2 Search Results for "Heidemann, Gunther"

Document
DOI: 10.4230/LIPIcs.SoCG.2025.48
Exact Algorithms for Minimum Dilation Triangulation

Authors: Sándor P. Fekete, Phillip Keldenich, and Michael Perk

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

Abstract
We provide a spectrum of new theoretical insights and practical results for finding a Minimum Dilation Triangulation (MDT), a natural geometric optimization problem of considerable previous attention: Given a set P of n points in the plane, find a triangulation T, such that a shortest Euclidean path in T between any pair of points increases by the smallest possible factor compared to their straight-line distance. No polynomial-time algorithm is known for the problem; moreover, evaluating the objective function involves computing the sum of (possibly many) square roots. On the other hand, the problem is not known to be NP-hard. (1) We provide practically robust methods and implementations for computing an MDT for benchmark sets with up to 30,000 points in reasonable time on commodity hardware, based on new geometric insights into the structure of optimal edge sets. Previous methods only achieved results for up to 200 points, so we extend the range of optimally solvable instances by a factor of 150. (2) We develop scalable techniques for accurately evaluating many shortest-path queries that arise as large-scale sums of square roots, allowing us to certify exact optimal solutions, with previous work relying on (possibly inaccurate) floating-point computations. (3) We resolve an open problem by establishing a lower bound of 1.44116 on the dilation of the regular 84-gon (and thus for arbitrary point sets), improving the previous worst-case lower bound of 1.4308 and greatly reducing the remaining gap to the upper bound of 1.4482 from the literature. In the process, we provide optimal solutions for regular n-gons up to n = 100.
Cite as

Sándor P. Fekete, Phillip Keldenich, and Michael Perk. Exact Algorithms for Minimum Dilation Triangulation. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 48:1-48:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fekete_et_al:LIPIcs.SoCG.2025.48,
  author =	{Fekete, S\'{a}ndor P. and Keldenich, Phillip and Perk, Michael},
  title =	{{Exact Algorithms for Minimum Dilation Triangulation}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{48:1--48:18},
  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.2025.48},
  URN =		{urn:nbn:de:0030-drops-232006},
  doi =		{10.4230/LIPIcs.SoCG.2025.48},
  annote =	{Keywords: dilation, minimum dilation triangulation, exact algorithms, algorithm engineering, experimental evaluation}
}
Document
DOI: 10.4230/LIPIcs.TIME.2018.21
An Empirical Study on Bidirectional Recurrent Neural Networks for Human Motion Recognition

Authors: Pattreeya Tanisaro and Gunther Heidemann

Published in: LIPIcs, Volume 120, 25th International Symposium on Temporal Representation and Reasoning (TIME 2018)

Abstract
The deep recurrent neural networks (RNNs) and their associated gated neurons, such as Long Short-Term Memory (LSTM) have demonstrated a continued and growing success rates with researches in various sequential data processing applications, especially when applied to speech recognition and language modeling. Despite this, amongst current researches, there are limited studies on the deep RNNs architectures and their effects being applied to other application domains. In this paper, we evaluated the different strategies available to construct bidirectional recurrent neural networks (BRNNs) applying Gated Recurrent Units (GRUs), as well as investigating a reservoir computing RNNs, i.e., Echo state networks (ESN) and a few other conventional machine learning techniques for skeleton-based human motion recognition. The evaluation of tasks focuses on the generalization of different approaches by employing arbitrary untrained viewpoints, combined together with previously unseen subjects. Moreover, we extended the test by lowering the subsampling frame rates to examine the robustness of the algorithms being employed against the varying of movement speed.
Cite as

Pattreeya Tanisaro and Gunther Heidemann. An Empirical Study on Bidirectional Recurrent Neural Networks for Human Motion Recognition. In 25th International Symposium on Temporal Representation and Reasoning (TIME 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 120, pp. 21:1-21:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

Copy BibTex To Clipboard

@InProceedings{tanisaro_et_al:LIPIcs.TIME.2018.21,
  author =	{Tanisaro, Pattreeya and Heidemann, Gunther},
  title =	{{An Empirical Study on Bidirectional Recurrent Neural Networks for Human Motion Recognition}},
  booktitle =	{25th International Symposium on Temporal Representation and Reasoning (TIME 2018)},
  pages =	{21:1--21:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-089-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{120},
  editor =	{Alechina, Natasha and N{\o}rv\r{a}g, Kjetil and Penczek, Wojciech},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2018.21},
  URN =		{urn:nbn:de:0030-drops-97865},
  doi =		{10.4230/LIPIcs.TIME.2018.21},
  annote =	{Keywords: Recurrent Neural Networks, Human Motion Classification, Echo State Networks, Motion Capture, Bidirectional Recurrent Neural Networks}
}
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