2 Search Results for "Sedgwick, Eric"

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DOI: 10.4230/LIPIcs.SEA.2024.23

Engineering A* Search for the Flip Distance of Plane Triangulations

Authors: Philip Mayer and Petra Mutzel

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract

The flip distance for two triangulations of a point set is defined as the smallest number of edge flips needed to transform one triangulation into another, where an edge flip is the act of replacing an edge of a triangulation by a different edge such that the result remains a triangulation. We adapt and engineer a sophisticated A* search algorithm acting on the so-called flip graph. In particular, we prove that previously proposed lower bounds for the flip distance form consistent heuristics for A* and show that they can be computed efficiently using dynamic algorithms. As an alternative approach, we present an integer linear program (ILP) for the flip distance problem. We experimentally evaluate our approaches on a new real-world benchmark data set based on an application in geodesy, namely sea surface reconstruction. Our evaluation reveals that A* search consistently outperforms our ILP formulation as well as a naive baseline, which is bidirectional breadth-first search. In particular, the runtime of our approach improves upon the baseline by more than two orders of magnitude. Furthermore, our A* search successfully solves most of the considered sea surface instances with up to 41 points. This is a substantial improvement compared to the baseline, which struggles with subsets of the real-world data of size 25. Lastly, to allow the consideration of global sea level data, we developed a decomposition-based heuristic for the flip distance. In our experiments it yields optimal flip distance values for most of the considered sea level data and it can be applied to large data sets due to its fast runtime.

Cite as

Philip Mayer and Petra Mutzel. Engineering A* Search for the Flip Distance of Plane Triangulations. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 23:1-23:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{mayer_et_al:LIPIcs.SEA.2024.23,
  author =	{Mayer, Philip and Mutzel, Petra},
  title =	{{Engineering A* Search for the Flip Distance of Plane Triangulations}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{23:1--23:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.23},
  URN =		{urn:nbn:de:0030-drops-203887},
  doi =		{10.4230/LIPIcs.SEA.2024.23},
  annote =	{Keywords: Computational Geometry, Triangulations, Flip Distance, A-star Search, Integer Linear Programming}
}

Document

DOI: 10.4230/LIPIcs.SoCG.2019.49

The Unbearable Hardness of Unknotting

Authors: Arnaud de Mesmay, Yo'av Rieck, Eric Sedgwick, and Martin Tancer

Published in: LIPIcs, Volume 129, 35th International Symposium on Computational Geometry (SoCG 2019)

Abstract

We prove that deciding if a diagram of the unknot can be untangled using at most k Reidemeister moves (where k is part of the input) is NP-hard. We also prove that several natural questions regarding links in the 3-sphere are NP-hard, including detecting whether a link contains a trivial sublink with n components, computing the unlinking number of a link, and computing a variety of link invariants related to four-dimensional topology (such as the 4-ball Euler characteristic, the slicing number, and the 4-dimensional clasp number).

Cite as

Arnaud de Mesmay, Yo'av Rieck, Eric Sedgwick, and Martin Tancer. The Unbearable Hardness of Unknotting. In 35th International Symposium on Computational Geometry (SoCG 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 129, pp. 49:1-49:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{demesmay_et_al:LIPIcs.SoCG.2019.49,
  author =	{de Mesmay, Arnaud and Rieck, Yo'av and Sedgwick, Eric and Tancer, Martin},
  title =	{{The Unbearable Hardness of Unknotting}},
  booktitle =	{35th International Symposium on Computational Geometry (SoCG 2019)},
  pages =	{49:1--49:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-104-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{129},
  editor =	{Barequet, Gill and Wang, Yusu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2019.49},
  URN =		{urn:nbn:de:0030-drops-104530},
  doi =		{10.4230/LIPIcs.SoCG.2019.49},
  annote =	{Keywords: Knot, Link, NP-hard, Reidemeister move, Unknot recognition, Unlinking number, intermediate invariants}
}

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1 Theory of computation → Computational geometry
1 Theory of computation → Problems, reductions and completeness

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