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Documents authored by van Dijk, Thomas C.

Document
DOI: 10.4230/LIPIcs.GIScience.2023.5
Visualizing Geophylogenies - Internal and External Labeling with Phylogenetic Tree Constraints

Authors: Jonathan Klawitter, Felix Klesen, Joris Y. Scholl, Thomas C. van Dijk, and Alexander Zaft

Published in: LIPIcs, Volume 277, 12th International Conference on Geographic Information Science (GIScience 2023)

Abstract
A geophylogeny is a phylogenetic tree where each leaf (biological taxon) has an associated geographic location (site). To clearly visualize a geophylogeny, the tree is typically represented as a crossing-free drawing next to a map. The correspondence between the taxa and the sites is either shown with matching labels on the map (internal labeling) or with leaders that connect each site to the corresponding leaf of the tree (external labeling). In both cases, a good order of the leaves is paramount for understanding the association between sites and taxa. We define several quality measures for internal labeling and give an efficient algorithm for optimizing them. In contrast, minimizing the number of leader crossings in an external labeling is NP-hard. We show nonetheless that optimal solutions can be found in a matter of seconds on realistic instances using integer linear programming. Finally, we provide several efficient heuristic algorithms and experimentally show them to be near optimal on real-world and synthetic instances.
Cite as

Jonathan Klawitter, Felix Klesen, Joris Y. Scholl, Thomas C. van Dijk, and Alexander Zaft. Visualizing Geophylogenies - Internal and External Labeling with Phylogenetic Tree Constraints. In 12th International Conference on Geographic Information Science (GIScience 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 277, pp. 5:1-5:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{klawitter_et_al:LIPIcs.GIScience.2023.5,
  author =	{Klawitter, Jonathan and Klesen, Felix and Scholl, Joris Y. and van Dijk, Thomas C. and Zaft, Alexander},
  title =	{{Visualizing Geophylogenies - Internal and External Labeling with Phylogenetic Tree Constraints}},
  booktitle =	{12th International Conference on Geographic Information Science (GIScience 2023)},
  pages =	{5:1--5:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-288-4},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{277},
  editor =	{Beecham, Roger and Long, Jed A. and Smith, Dianna and Zhao, Qunshan and Wise, Sarah},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GIScience.2023.5},
  URN =		{urn:nbn:de:0030-drops-189004},
  doi =		{10.4230/LIPIcs.GIScience.2023.5},
  annote =	{Keywords: geophylogeny, boundary labeling, external labeling, algorithms}
}
Document
DOI: 10.4230/LIPIcs.GIScience.2021.II.12
Map Matching for Semi-Restricted Trajectories

Authors: Timon Behr, Thomas C. van Dijk, Axel Forsch, Jan-Henrik Haunert, and Sabine Storandt

Published in: LIPIcs, Volume 208, 11th International Conference on Geographic Information Science (GIScience 2021) - Part II

Abstract
We consider the problem of matching trajectories to a road map, giving particular consideration to trajectories that do not exclusively follow the underlying network. Such trajectories arise, for example, when a person walks through the inner part of a city, crossing market squares or parking lots. We call such trajectories semi-restricted. Sensible map matching of semi-restricted trajectories requires the ability to differentiate between restricted and unrestricted movement. We develop in this paper an approach that efficiently and reliably computes concise representations of such trajectories that maintain their semantic characteristics. Our approach utilizes OpenStreetMap data to not only extract the network but also areas that allow for free movement (as e.g. parks) as well as obstacles (as e.g. buildings). We discuss in detail how to incorporate this information in the map matching process, and demonstrate the applicability of our method in an experimental evaluation on real pedestrian and bicycle trajectories.
Cite as

Timon Behr, Thomas C. van Dijk, Axel Forsch, Jan-Henrik Haunert, and Sabine Storandt. Map Matching for Semi-Restricted Trajectories. In 11th International Conference on Geographic Information Science (GIScience 2021) - Part II. Leibniz International Proceedings in Informatics (LIPIcs), Volume 208, pp. 12:1-12:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{behr_et_al:LIPIcs.GIScience.2021.II.12,
  author =	{Behr, Timon and van Dijk, Thomas C. and Forsch, Axel and Haunert, Jan-Henrik and Storandt, Sabine},
  title =	{{Map Matching for Semi-Restricted Trajectories}},
  booktitle =	{11th International Conference on Geographic Information Science (GIScience 2021) - Part II},
  pages =	{12:1--12:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-208-2},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{208},
  editor =	{Janowicz, Krzysztof and Verstegen, Judith A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GIScience.2021.II.12},
  URN =		{urn:nbn:de:0030-drops-147717},
  doi =		{10.4230/LIPIcs.GIScience.2021.II.12},
  annote =	{Keywords: map matching, OpenStreetMap, GPS, trajectory, road network}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2018.61
Stabbing Rectangles by Line Segments - How Decomposition Reduces the Shallow-Cell Complexity

Authors: Timothy M. Chan, Thomas C. van Dijk, Krzysztof Fleszar, Joachim Spoerhase, and Alexander Wolff

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
We initiate the study of the following natural geometric optimization problem. The input is a set of axis-aligned rectangles in the plane. The objective is to find a set of horizontal line segments of minimum total length so that every rectangle is stabbed by some line segment. A line segment stabs a rectangle if it intersects its left and its right boundary. The problem, which we call Stabbing, can be motivated by a resource allocation problem and has applications in geometric network design. To the best of our knowledge, only special cases of this problem have been considered so far. Stabbing is a weighted geometric set cover problem, which we show to be NP-hard. While for general set cover the best possible approximation ratio is Theta(log n), it is an important field in geometric approximation algorithms to obtain better ratios for geometric set cover problems. Chan et al. [SODA'12] generalize earlier results by Varadarajan [STOC'10] to obtain sub-logarithmic performances for a broad class of weighted geometric set cover instances that are characterized by having low shallow-cell complexity. The shallow-cell complexity of Stabbing instances, however, can be high so that a direct application of the framework of Chan et al. gives only logarithmic bounds. We still achieve a constant-factor approximation by decomposing general instances into what we call laminar instances that have low enough complexity. Our decomposition technique yields constant-factor approximations also for the variant where rectangles can be stabbed by horizontal and vertical segments and for two further geometric set cover problems.
Cite as

Timothy M. Chan, Thomas C. van Dijk, Krzysztof Fleszar, Joachim Spoerhase, and Alexander Wolff. Stabbing Rectangles by Line Segments - How Decomposition Reduces the Shallow-Cell Complexity. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 61:1-61:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{chan_et_al:LIPIcs.ISAAC.2018.61,
  author =	{Chan, Timothy M. and van Dijk, Thomas C. and Fleszar, Krzysztof and Spoerhase, Joachim and Wolff, Alexander},
  title =	{{Stabbing Rectangles by Line Segments - How Decomposition Reduces the Shallow-Cell Complexity}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{61:1--61:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.61},
  URN =		{urn:nbn:de:0030-drops-100094},
  doi =		{10.4230/LIPIcs.ISAAC.2018.61},
  annote =	{Keywords: Geometric optimization, NP-hard, approximation, shallow-cell complexity, line stabbing}
}
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