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Documents authored by Radermacher, Marcel

Document
DOI: 10.4230/LIPIcs.ESA.2019.76
Geometric Crossing-Minimization - A Scalable Randomized Approach

Authors: Marcel Radermacher and Ignaz Rutter

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

Abstract
We consider the minimization of edge-crossings in geometric drawings of graphs G=(V, E), i.e., in drawings where each edge is depicted as a line segment. The respective decision problem is NP-hard [Daniel Bienstock, 1991]. Crossing-minimization, in general, is a popular theoretical research topic; see Vrt'o [Imrich Vrt'o, 2014]. In contrast to theory and the topological setting, the geometric setting did not receive a lot of attention in practice. Prior work [Marcel Radermacher et al., 2018] is limited to the crossing-minimization in geometric graphs with less than 200 edges. The described heuristics base on the primitive operation of moving a single vertex v to its crossing-minimal position, i.e., the position in R^2 that minimizes the number of crossings on edges incident to v. In this paper, we introduce a technique to speed-up the computation by a factor of 20. This is necessary but not sufficient to cope with graphs with a few thousand edges. In order to handle larger graphs, we drop the condition that each vertex v has to be moved to its crossing-minimal position and compute a position that is only optimal with respect to a small random subset of the edges. In our theoretical contribution, we consider drawings that contain for each edge uv in E and each position p in R^2 for v o(|E|) crossings. In this case, we prove that with a random subset of the edges of size Theta(k log k) the co-crossing number of a degree-k vertex v, i.e., the number of edge pairs uv in E, e in E that do not cross, can be approximated by an arbitrary but fixed factor delta with high probability. In our experimental evaluation, we show that the randomized approach reduces the number of crossings in graphs with up to 13 000 edges considerably. The evaluation suggests that depending on the degree-distribution different strategies result in the fewest number of crossings.
Cite as

Marcel Radermacher and Ignaz Rutter. Geometric Crossing-Minimization - A Scalable Randomized Approach. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 76:1-76:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{radermacher_et_al:LIPIcs.ESA.2019.76,
  author =	{Radermacher, Marcel and Rutter, Ignaz},
  title =	{{Geometric Crossing-Minimization - A Scalable Randomized Approach}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{76:1--76:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola 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.2019.76},
  URN =		{urn:nbn:de:0030-drops-111977},
  doi =		{10.4230/LIPIcs.ESA.2019.76},
  annote =	{Keywords: Geometric Crossing Minimization, Randomization, Approximation, VC-Dimension, Experiments}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2013.94
Evolution and Evaluation of the Penalty Method for Alternative Graphs

Authors: Moritz Kobitzsch, Marcel Radermacher, and Dennis Schieferdecker

Published in: OASIcs, Volume 33, 13th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (2013)

Abstract
Computing meaningful alternative routes in a road network is a complex problem -- already giving a clear definition of a best alternative seems to be impossible. Still, multiple methods describe how to compute reasonable alternative routes, each according to their own quality criteria. Among these methods, the penalty method has received much less attention than the via-node or plateaux based approaches. A mayor cause for the lack of interest might be the unavailability of an efficient implementation. In this paper, we take a closer look at the penalty method and extend upon its ideas. We provide the first viable implementation --suitable for interactive use-- using dynamic runtime adjustments to perform up to multiple orders of magnitude faster queries than previous implementations. Using our new implementation, we thoroughly evaluate the penalty method for its flaws and benefits.
Cite as

Moritz Kobitzsch, Marcel Radermacher, and Dennis Schieferdecker. Evolution and Evaluation of the Penalty Method for Alternative Graphs. In 13th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems. Open Access Series in Informatics (OASIcs), Volume 33, pp. 94-107, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{kobitzsch_et_al:OASIcs.ATMOS.2013.94,
  author =	{Kobitzsch, Moritz and Radermacher, Marcel and Schieferdecker, Dennis},
  title =	{{Evolution and Evaluation of the Penalty Method for Alternative Graphs}},
  booktitle =	{13th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems},
  pages =	{94--107},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-58-3},
  ISSN =	{2190-6807},
  year =	{2013},
  volume =	{33},
  editor =	{Frigioni, Daniele and Stiller, Sebastian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2013.94},
  URN =		{urn:nbn:de:0030-drops-42474},
  doi =		{10.4230/OASIcs.ATMOS.2013.94},
  annote =	{Keywords: Alternatives, Routing, Shortest Paths, Penalties, Parallelization}
}
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