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DOI: 10.4230/LIPIcs.ESA.2016.76

Sampling-Based Bottleneck Pathfinding with Applications to Fréchet Matching

Authors: Kiril Solovey and Dan Halperin

Published in: LIPIcs, Volume 57, 24th Annual European Symposium on Algorithms (ESA 2016)

Abstract

We describe a general probabilistic framework to address a variety of Fréchet-distance optimization problems. Specifically, we are interested in finding minimal bottleneck-paths in d-dimensional Euclidean space between given start and goal points, namely paths that minimize the maximal value over a continuous cost map. We present an efficient and simple sampling-based framework for this problem, which is inspired by, and draws ideas from, techniques for robot motion planning. We extend the framework to handle not only standard bottleneck pathfinding, but also the more demanding case, where the path needs to be monotone in all dimensions. Finally, we provide experimental results of the framework on several types of problems.

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Kiril Solovey and Dan Halperin. Sampling-Based Bottleneck Pathfinding with Applications to Fréchet Matching. In 24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 57, pp. 76:1-76:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{solovey_et_al:LIPIcs.ESA.2016.76,
  author =	{Solovey, Kiril and Halperin, Dan},
  title =	{{Sampling-Based Bottleneck Pathfinding with Applications to Fr\'{e}chet Matching}},
  booktitle =	{24th Annual European Symposium on Algorithms (ESA 2016)},
  pages =	{76:1--76:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-015-6},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{57},
  editor =	{Sankowski, Piotr and Zaroliagis, Christos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2016.76},
  URN =		{urn:nbn:de:0030-drops-64179},
  doi =		{10.4230/LIPIcs.ESA.2016.76},
  annote =	{Keywords: Computational geometry, Fr\'{e}chet distances, sampling-based algorithms, random geometric graphs, bottleneck pathfinding}
}

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Sampling-Based Bottleneck Pathfinding with Applications to Fréchet Matching

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