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Documents authored by Wolf, Matthias

Document
DOI: 10.4230/LIPIcs.ESA.2019.55
Engineering Negative Cycle Canceling for Wind Farm Cabling

Authors: Sascha Gritzbach, Torsten Ueckerdt, Dorothea Wagner, Franziska Wegner, and Matthias Wolf

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

Abstract
In a wind farm turbines convert wind energy into electrical energy. The generation of each turbine is transmitted, possibly via other turbines, to a substation that is connected to the power grid. On every possible interconnection there can be at most one of various different cable types. Each cable type comes with a cost per unit length and with a capacity. Designing a cost-minimal cable layout for a wind farm to feed all turbine production into the power grid is called the Wind Farm Cabling Problem (WCP). We consider a formulation of WCP as a flow problem on a graph where the cost of a flow on an edge is modeled by a step function originating from the cable types. Recently, we presented a proof-of-concept for a negative cycle canceling-based algorithm for WCP [Sascha Gritzbach et al., 2018]. We extend key steps of that heuristic and build a theoretical foundation that explains how this heuristic tackles the problems arising from the special structure of WCP. A thorough experimental evaluation identifies the best setup of the algorithm and compares it to existing methods from the literature such as Mixed-integer Linear Programming (MILP) and Simulated Annealing (SA). The heuristic runs in a range of half a millisecond to under two minutes on instances with up to 500 turbines. It provides solutions of similar quality compared to both competitors with running times of one hour and one day. When comparing the solution quality after a running time of two seconds, our algorithm outperforms the MILP- and SA-approaches, which allows it to be applied in interactive wind farm planning.
Cite as

Sascha Gritzbach, Torsten Ueckerdt, Dorothea Wagner, Franziska Wegner, and Matthias Wolf. Engineering Negative Cycle Canceling for Wind Farm Cabling. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 55:1-55:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{gritzbach_et_al:LIPIcs.ESA.2019.55,
  author =	{Gritzbach, Sascha and Ueckerdt, Torsten and Wagner, Dorothea and Wegner, Franziska and Wolf, Matthias},
  title =	{{Engineering Negative Cycle Canceling for Wind Farm Cabling}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{55:1--55:16},
  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.2019.55},
  URN =		{urn:nbn:de:0030-drops-111766},
  doi =		{10.4230/LIPIcs.ESA.2019.55},
  annote =	{Keywords: Negative Cycle Canceling, Step Cost Function, Wind Farm Planning}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2019.53
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
DOI: 10.4230/LIPIcs.SoCG.2017.14
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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