3 Search Results for "Niedermann, Benjamin"


Document
Efficient Algorithms for Ortho-Radial Graph Drawing

Authors: Benjamin Niedermann, Ignaz Rutter, and Matthias Wolf

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


Abstract
Orthogonal drawings, i.e., embeddings of graphs into grids, are a classic topic in Graph Drawing. Often the goal is to find a drawing that minimizes the number of bends on the edges. A key ingredient for bend minimization algorithms is the existence of an orthogonal representation that allows to describe such drawings purely combinatorially by only listing the angles between the edges around each vertex and the directions of bends on the edges, but neglecting any kind of geometric information such as vertex coordinates or edge lengths. Barth et al. [2017] have established the existence of an analogous ortho-radial representation for ortho-radial drawings, which are embeddings into an ortho-radial grid, whose gridlines are concentric circles around the origin and straight-line spokes emanating from the origin but excluding the origin itself. While any orthogonal representation admits an orthogonal drawing, it is the circularity of the ortho-radial grid that makes the problem of characterizing valid ortho-radial representations all the more complex and interesting. Barth et al. prove such a characterization. However, the proof is existential and does not provide an efficient algorithm for testing whether a given ortho-radial representation is valid, let alone actually obtaining a drawing from an ortho-radial representation. In this paper we give quadratic-time algorithms for both of these tasks. They are based on a suitably constrained left-first DFS in planar graphs and several new insights on ortho-radial representations. Our validity check requires quadratic time, and a naive application of it would yield a quartic algorithm for constructing a drawing from a valid ortho-radial representation. Using further structural insights we speed up the drawing algorithm to quadratic running time.

Cite as

Benjamin Niedermann, Ignaz Rutter, and Matthias Wolf. Efficient Algorithms for Ortho-Radial Graph Drawing. In 35th International Symposium on Computational Geometry (SoCG 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 129, pp. 53:1-53:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{niedermann_et_al:LIPIcs.SoCG.2019.53,
  author =	{Niedermann, Benjamin and Rutter, Ignaz and Wolf, Matthias},
  title =	{{Efficient Algorithms for Ortho-Radial Graph Drawing}},
  booktitle =	{35th International Symposium on Computational Geometry (SoCG 2019)},
  pages =	{53:1--53:14},
  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.2019.53},
  URN =		{urn:nbn:de:0030-drops-104572},
  doi =		{10.4230/LIPIcs.SoCG.2019.53},
  annote =	{Keywords: Graph Drawing, Ortho-Radial Graph Drawing, Ortho-Radial Representation, Topology-Shape-Metrics, Efficient Algorithms}
}
Document
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}
}
Document
Towards a Topology-Shape-Metrics Framework for Ortho-Radial Drawings

Authors: Lukas Barth, Benjamin Niedermann, Ignaz Rutter, and Matthias Wolf

Published in: LIPIcs, Volume 77, 33rd International Symposium on Computational Geometry (SoCG 2017)


Abstract
Ortho-Radial drawings are a generalization of orthogonal drawings to grids that are formed by concentric circles and straight-line spokes emanating from the circles' center. Such drawings have applications in schematic graph layouts, e.g., for metro maps and destination maps. A plane graph is a planar graph with a fixed planar embedding. We give a combinatorial characterization of the plane graphs that admit a planar ortho-radial drawing without bends. Previously, such a characterization was only known for paths, cycles, and theta graphs, and in the special case of rectangular drawings for cubic graphs, where the contour of each face is required to be a rectangle. The characterization is expressed in terms of an ortho-radial representation that, similar to Tamassia's orthogonal representations for orthogonal drawings describes such a drawing combinatorially in terms of angles around vertices and bends on the edges. In this sense our characterization can be seen as a first step towards generalizing the Topology-Shape-Metrics framework of Tamassia to ortho-radial drawings.

Cite as

Lukas Barth, Benjamin Niedermann, Ignaz Rutter, and Matthias Wolf. Towards a Topology-Shape-Metrics Framework for Ortho-Radial Drawings. In 33rd International Symposium on Computational Geometry (SoCG 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 77, pp. 14:1-14:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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@InProceedings{barth_et_al:LIPIcs.SoCG.2017.14,
  author =	{Barth, Lukas and Niedermann, Benjamin and Rutter, Ignaz and Wolf, Matthias},
  title =	{{Towards a Topology-Shape-Metrics Framework for Ortho-Radial Drawings}},
  booktitle =	{33rd International Symposium on Computational Geometry (SoCG 2017)},
  pages =	{14:1--14:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-038-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{77},
  editor =	{Aronov, Boris and Katz, Matthew J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2017.14},
  URN =		{urn:nbn:de:0030-drops-72234},
  doi =		{10.4230/LIPIcs.SoCG.2017.14},
  annote =	{Keywords: Graph Drawing, Ortho-Radial Drawings, Combinatorial Characterization, Bend Minimization, Topology-Shape-Metrics}
}
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