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Documents authored by Haunert, Jan-Henrik

Document
DOI: 10.4230/LIPIcs.ESA.2024.90
Many-To-Many Polygon Matching à La Jaccard

Authors: Alexander Naumann, Annika Bonerath, and Jan-Henrik Haunert

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
Integration of spatial data is a major field of research. An important task of data integration is finding correspondences between entities. Here, we focus on combining building footprint data from cadastre and from volunteered geographic information, in particular OpenStreetMap. Previous research on this topic has led to exact 1:1 matching approaches and heuristic m:n matching approaches, most of which are lacking a mathematical problem definition. We introduce a model for many-to-many polygon matching based on the well-established Jaccard index. This is a natural extension to the existing 1:1 matching approaches. We show that the problem is NP-complete and a naive approach via integer programming fails easily. By analyzing the structure of the problem in detail, we can reduce the number of variables significantly. This approach yields an optimal m:n matching even for large real-world instances with appropriate running time. In particular, for the set of all building footprints of the city of Bonn (119,300 / 97,284 polygons) it yielded an optimal solution in approximately 1 hour.
Cite as

Alexander Naumann, Annika Bonerath, and Jan-Henrik Haunert. Many-To-Many Polygon Matching à La Jaccard. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 90:1-90:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{naumann_et_al:LIPIcs.ESA.2024.90,
  author =	{Naumann, Alexander and Bonerath, Annika and Haunert, Jan-Henrik},
  title =	{{Many-To-Many Polygon Matching \`{a} La Jaccard}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{90:1--90:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.90},
  URN =		{urn:nbn:de:0030-drops-211614},
  doi =		{10.4230/LIPIcs.ESA.2024.90},
  annote =	{Keywords: polygon matching, exact algorithm, Jaccard index}
}
Document
DOI: 10.4230/DagRep.12.11.66
Set Visualization and Uncertainty (Dagstuhl Seminar 22462)

Authors: Susanne Bleisch, Steven Chaplick, Jan-Henrik Haunert, Eva Mayr, Marc van Kreveld, and Annika Bonerath

Published in: Dagstuhl Reports, Volume 12, Issue 11 (2023)

Abstract
The Dagstuhl Seminar on Set Visualization and Uncertainty brought together a group of researchers from diverse disciplines, all of which are interested in various aspects of this type of visualization: the cognitive aspects, the modelling aspects, the algorithmic aspects, and the information visualization aspects. An important but difficult to handle problem is how one should visualize information with underlying uncertainty. The seminar focused on uncertainty in set systems. This report includes short abstracts of the talks given during the seminar as well as more extensive working group reports on the research done during the seminar.
Cite as

Susanne Bleisch, Steven Chaplick, Jan-Henrik Haunert, Eva Mayr, Marc van Kreveld, and Annika Bonerath. Set Visualization and Uncertainty (Dagstuhl Seminar 22462). In Dagstuhl Reports, Volume 12, Issue 11, pp. 66-95, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Article{bleisch_et_al:DagRep.12.11.66,
  author =	{Bleisch, Susanne and Chaplick, Steven and Haunert, Jan-Henrik and Mayr, Eva and van Kreveld, Marc and Bonerath, Annika},
  title =	{{Set Visualization and Uncertainty (Dagstuhl Seminar 22462)}},
  pages =	{66--95},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2023},
  volume =	{12},
  number =	{11},
  editor =	{Bleisch, Susanne and Chaplick, Steven and Haunert, Jan-Henrik and Mayr, Eva and van Kreveld, Marc and Bonerath, Annika},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.12.11.66},
  URN =		{urn:nbn:de:0030-drops-178360},
  doi =		{10.4230/DagRep.12.11.66},
  annote =	{Keywords: cartography, graph drawing, information visualization, set visualization, uncertainty}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2022.7
Minimum-Error Triangulations for Sea Surface Reconstruction

Authors: Anna Arutyunova, Anne Driemel, Jan-Henrik Haunert, Herman Haverkort, Jürgen Kusche, Elmar Langetepe, Philip Mayer, Petra Mutzel, and Heiko Röglin

Published in: LIPIcs, Volume 224, 38th International Symposium on Computational Geometry (SoCG 2022)

Abstract
We apply state-of-the-art computational geometry methods to the problem of reconstructing a time-varying sea surface from tide gauge records. Our work builds on a recent article by Nitzke et al. (Computers & Geosciences, 157:104920, 2021) who have suggested to learn a triangulation D of a given set of tide gauge stations. The objective is to minimize the misfit of the piecewise linear surface induced by D to a reference surface that has been acquired with satellite altimetry. The authors restricted their search to k-order Delaunay (k-OD) triangulations and used an integer linear program in order to solve the resulting optimization problem. In geometric terms, the input to our problem consists of two sets of points in ℝ² with elevations: a set 𝒮 that is to be triangulated, and a set ℛ of reference points. Intuitively, we define the error of a triangulation as the average vertical distance of a point in ℛ to the triangulated surface that is obtained by interpolating elevations of 𝒮 linearly in each triangle. Our goal is to find the triangulation of 𝒮 that has minimum error with respect to ℛ. In our work, we prove that the minimum-error triangulation problem is NP-hard and cannot be approximated within any multiplicative factor in polynomial time unless P = NP. At the same time we show that the problem instances that occur in our application (considering sea level data from several hundreds of tide gauge stations worldwide) can be solved relatively fast using dynamic programming when restricted to k-OD triangulations for k ≤ 7. In particular, instances for which the number of connected components of the so-called k-OD fixed-edge graph is small can be solved within few seconds.
Cite as

Anna Arutyunova, Anne Driemel, Jan-Henrik Haunert, Herman Haverkort, Jürgen Kusche, Elmar Langetepe, Philip Mayer, Petra Mutzel, and Heiko Röglin. Minimum-Error Triangulations for Sea Surface Reconstruction. In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{arutyunova_et_al:LIPIcs.SoCG.2022.7,
  author =	{Arutyunova, Anna and Driemel, Anne and Haunert, Jan-Henrik and Haverkort, Herman and Kusche, J\"{u}rgen and Langetepe, Elmar and Mayer, Philip and Mutzel, Petra and R\"{o}glin, Heiko},
  title =	{{Minimum-Error Triangulations for Sea Surface Reconstruction}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{7:1--7:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-227-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{224},
  editor =	{Goaoc, Xavier and Kerber, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.7},
  URN =		{urn:nbn:de:0030-drops-160155},
  doi =		{10.4230/LIPIcs.SoCG.2022.7},
  annote =	{Keywords: Minimum-Error Triangulation, k-Order Delaunay Triangulations, Data dependent Triangulations, Sea Surface Reconstruction, fixed-Edge Graph}
}
Document
DOI: 10.4230/LIPIcs.GIScience.2021.II.6
Bicriteria Aggregation of Polygons via Graph Cuts

Authors: Peter Rottmann, Anne Driemel, Herman Haverkort, Heiko Röglin, and Jan-Henrik Haunert

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

Abstract
We present a new method for the task of detecting groups of polygons in a given geographic data set and computing a representative polygon for each group. This task is relevant in map generalization where the aim is to derive a less detailed map from a given map. Following a classical approach, we define the output polygons by merging the input polygons with a set of triangles that we select from a constrained Delaunay triangulation of the input polygons' exterior. The innovation of our method is to compute the selection of triangles by solving a bicriteria optimization problem. While on the one hand we aim at minimizing the total area of the outputs polygons, we aim on the other hand at minimizing their total perimeter. We combine these two objectives in a weighted sum and study two computational problems that naturally arise. In the first problem, the parameter that balances the two objectives is fixed and the aim is to compute a single optimal solution. In the second problem, the aim is to compute a set containing an optimal solution for every possible value of the parameter. We present efficient algorithms for these problems based on computing a minimum cut in an appropriately defined graph. Moreover, we show how the result set of the second problem can be approximated with few solutions. In an experimental evaluation, we finally show that the method is able to derive settlement areas from building footprints that are similar to reference solutions.
Cite as

Peter Rottmann, Anne Driemel, Herman Haverkort, Heiko Röglin, and Jan-Henrik Haunert. Bicriteria Aggregation of Polygons via Graph Cuts. In 11th International Conference on Geographic Information Science (GIScience 2021) - Part II. Leibniz International Proceedings in Informatics (LIPIcs), Volume 208, pp. 6:1-6:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{rottmann_et_al:LIPIcs.GIScience.2021.II.6,
  author =	{Rottmann, Peter and Driemel, Anne and Haverkort, Herman and R\"{o}glin, Heiko and Haunert, Jan-Henrik},
  title =	{{Bicriteria Aggregation of Polygons via Graph Cuts}},
  booktitle =	{11th International Conference on Geographic Information Science (GIScience 2021) - Part II},
  pages =	{6:1--6:16},
  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.6},
  URN =		{urn:nbn:de:0030-drops-147658},
  doi =		{10.4230/LIPIcs.GIScience.2021.II.6},
  annote =	{Keywords: map generalization, aggregation, graph cuts, bicriteria optimization}
}
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.GISCIENCE.2018.13
A Network Flow Model for the Analysis of Green Spaces in Urban Areas

Authors: Benjamin Niedermann, Johannes Oehrlein, Sven Lautenbach, and Jan-Henrik Haunert

Published in: LIPIcs, Volume 114, 10th International Conference on Geographic Information Science (GIScience 2018)

Abstract
Green spaces in urban areas offer great possibilities of recreation, provided that they are easily accessible. Therefore, an ideal city should offer large green spaces close to where its residents live. Although there are several measures for the assessment of urban green spaces, the existing measures usually focus either on the total size of green spaces or on their accessibility. Hence, in this paper, we present a new methodology for assessing green-space provision and accessibility in an integrated way. The core of our methodology is an algorithm based on linear programming that computes an optimal assignment between residential areas and green spaces. In a basic setting, it assigns a green space of a prescribed size exclusively to each resident such that the average distance between residents and assigned green spaces is minimized. We contribute a detailed presentation on how to engineer an assignment-based method such that it yields reasonable results (e.g., by considering distances in the road network) and becomes efficient enough for the analysis of large metropolitan areas (e.g., we were able to process an instance of Berlin with about 130000 polygons representing green spaces, 18000 polygons representing residential areas, and 6 million road segments). Furthermore, we show that the optimal assignments resulting from our method enable a subsequent analysis that reveals both interesting global properties of a city as well as spatial patterns. For example, our method allows us to identify neighborhoods with a shortage of green spaces, which will help spatial planners in their decision making.
Cite as

Benjamin Niedermann, Johannes Oehrlein, Sven Lautenbach, and Jan-Henrik Haunert. A Network Flow Model for the Analysis of Green Spaces in Urban Areas. In 10th International Conference on Geographic Information Science (GIScience 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 114, pp. 13:1-13:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{niedermann_et_al:LIPIcs.GISCIENCE.2018.13,
  author =	{Niedermann, Benjamin and Oehrlein, Johannes and Lautenbach, Sven and Haunert, Jan-Henrik},
  title =	{{A Network Flow Model for the Analysis of Green Spaces in Urban Areas}},
  booktitle =	{10th International Conference on Geographic Information Science (GIScience 2018)},
  pages =	{13:1--13:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-083-5},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{114},
  editor =	{Winter, Stephan and Griffin, Amy and Sester, Monika},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GISCIENCE.2018.13},
  URN =		{urn:nbn:de:0030-drops-93412},
  doi =		{10.4230/LIPIcs.GISCIENCE.2018.13},
  annote =	{Keywords: urban green, transportation problem, maximum flow, linear program}
}
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