4 Search Results for "Schrezenmaier, Hendrik"

Document
DOI: 10.4230/LIPIcs.GD.2025.35
A Walk on the Wild Side: A Shape-First Methodology for Orthogonal Drawings

Authors: Giordano Andreola, Susanna Caroppo, Giuseppe Di Battista, Fabrizio Grosso, Maurizio Patrignani, and Allegra Strippoli

Published in: LIPIcs, Volume 357, 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)

Abstract
Several algorithms for the construction of orthogonal drawings of graphs, including those based on the Topology-Shape-Metrics (TSM) paradigm, tend to prioritize the minimization of crossings. This emphasis has two notable side effects: some edges are drawn with unnecessarily long sequences of segments and bends, and the overall drawing area may become excessively large. As a result, the produced drawings often lack geometric uniformity. Moreover, orthogonal crossings are known to have a limited impact on readability, suggesting that crossing minimization may not always be the optimal goal. In this paper, we introduce a methodology that "subverts" the traditional TSM pipeline by focusing on minimizing bends. Given a graph G, we ideally seek to construct a rectilinear drawing of G, that is, an orthogonal drawing with no bends. When not possible, we incrementally subdivide the edges of G by introducing dummy vertices that will (possibly) correspond to bends in the final drawing. This process continues until a rectilinear drawing of a subdivision of the graph is found, after which the final coordinates are computed. We tackle the (NP-complete) rectilinear drawability problem by encoding it as a SAT formula and solving it with state-of-the-art SAT solvers. If the SAT formula is unsatisfiable, we use the solver’s proof to determine which edge to subdivide. Our implementation, domus, which is fairly simple, is evaluated through extensive experiments on small- to medium-sized graphs. The results show that it consistently outperforms ogdf’s TSM-based approach across most standard graph drawing metrics.
Cite as

Giordano Andreola, Susanna Caroppo, Giuseppe Di Battista, Fabrizio Grosso, Maurizio Patrignani, and Allegra Strippoli. A Walk on the Wild Side: A Shape-First Methodology for Orthogonal Drawings. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 35:1-35:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{andreola_et_al:LIPIcs.GD.2025.35,
  author =	{Andreola, Giordano and Caroppo, Susanna and Di Battista, Giuseppe and Grosso, Fabrizio and Patrignani, Maurizio and Strippoli, Allegra},
  title =	{{A Walk on the Wild Side: A Shape-First Methodology for Orthogonal Drawings}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{35:1--35:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.35},
  URN =		{urn:nbn:de:0030-drops-250218},
  doi =		{10.4230/LIPIcs.GD.2025.35},
  annote =	{Keywords: Non-planar Orthogonal Drawings, SAT Solver, Experimental Comparison}
}
Document
DOI: 10.4230/LIPIcs.GD.2025.29
Stabbing Faces by a Convex Curve

Authors: David Eppstein

Published in: LIPIcs, Volume 357, 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)

Abstract
We prove that, for every plane graph G and every smooth convex curve C not on a single line, there exists a straight-line drawing of G for which every face is crossed by C.
Cite as

David Eppstein. Stabbing Faces by a Convex Curve. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 29:1-29:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{eppstein:LIPIcs.GD.2025.29,
  author =	{Eppstein, David},
  title =	{{Stabbing Faces by a Convex Curve}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{29:1--29:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.29},
  URN =		{urn:nbn:de:0030-drops-250155},
  doi =		{10.4230/LIPIcs.GD.2025.29},
  annote =	{Keywords: planar graphs, convex curves, stabbing, transversal}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2023.31
Linear Size Universal Point Sets for Classes of Planar Graphs

Authors: Stefan Felsner, Hendrik Schrezenmaier, Felix Schröder, and Raphael Steiner

Published in: LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023)

Abstract
A finite set P of points in the plane is n-universal with respect to a class 𝒞 of planar graphs if every n-vertex graph in 𝒞 admits a crossing-free straight-line drawing with vertices at points of P. For the class of all planar graphs the best known upper bound on the size of a universal point set is quadratic and the best known lower bound is linear in n. Some classes of planar graphs are known to admit universal point sets of near linear size, however, there are no truly linear bounds for interesting classes beyond outerplanar graphs. In this paper, we show that there is a universal point set of size 2n-2 for the class of bipartite planar graphs with n vertices. The same point set is also universal for the class of n-vertex planar graphs of maximum degree 3. The point set used for the results is what we call an exploding double chain, and we prove that this point set allows planar straight-line embeddings of many more planar graphs, namely of all subgraphs of planar graphs admitting a one-sided Hamiltonian cycle. The result for bipartite graphs also implies that every n-vertex plane graph has a 1-bend drawing all whose bends and vertices are contained in a specific point set of size 4n-6, this improves a bound of 6n-10 for the same problem by Löffler and Tóth.
Cite as

Stefan Felsner, Hendrik Schrezenmaier, Felix Schröder, and Raphael Steiner. Linear Size Universal Point Sets for Classes of Planar Graphs. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 31:1-31:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{felsner_et_al:LIPIcs.SoCG.2023.31,
  author =	{Felsner, Stefan and Schrezenmaier, Hendrik and Schr\"{o}der, Felix and Steiner, Raphael},
  title =	{{Linear Size Universal Point Sets for Classes of Planar Graphs}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{31:1--31:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-273-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{258},
  editor =	{Chambers, Erin W. and Gudmundsson, Joachim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.31},
  URN =		{urn:nbn:de:0030-drops-178814},
  doi =		{10.4230/LIPIcs.SoCG.2023.31},
  annote =	{Keywords: Graph drawing, Universal point set, One-sided Hamiltonian, 2-page book embedding, Separating decomposition, Quadrangulation, 2-tree, Subcubic planar graph}
}
Document
DOI: 10.4230/LIPIcs.ESA.2021.5
The Voronoi Diagram of Rotating Rays With applications to Floodlight Illumination

Authors: Carlos Alegría, Ioannis Mantas, Evanthia Papadopoulou, Marko Savić, Hendrik Schrezenmaier, Carlos Seara, and Martin Suderland

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract
We introduce the Voronoi Diagram of Rotating Rays, a Voronoi structure where the input sites are rays, and the distance function is the counterclockwise angular distance between a point and a ray-site. This novel Voronoi diagram is motivated by illumination and coverage problems, where a domain has to be covered by floodlights (wedges) of uniform angle, and the goal is to find the minimum angle necessary to cover the domain. We study the diagram in the plane, and we present structural properties, combinatorial complexity bounds, and a construction algorithm. If the rays are induced by a convex polygon, we show how to construct the ray Voronoi diagram within this polygon in linear time. Using this information, we can find in optimal linear time the Brocard angle, the minimum angle required to illuminate a convex polygon with floodlights of uniform angle. This last algorithm improves upon previous results, settling an interesting open problem.
Cite as

Carlos Alegría, Ioannis Mantas, Evanthia Papadopoulou, Marko Savić, Hendrik Schrezenmaier, Carlos Seara, and Martin Suderland. The Voronoi Diagram of Rotating Rays With applications to Floodlight Illumination. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 5:1-5:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{alegria_et_al:LIPIcs.ESA.2021.5,
  author =	{Alegr{\'\i}a, Carlos and Mantas, Ioannis and Papadopoulou, Evanthia and Savi\'{c}, Marko and Schrezenmaier, Hendrik and Seara, Carlos and Suderland, Martin},
  title =	{{The Voronoi Diagram of Rotating Rays With applications to Floodlight Illumination}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{5:1--5:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus 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.2021.5},
  URN =		{urn:nbn:de:0030-drops-145865},
  doi =		{10.4230/LIPIcs.ESA.2021.5},
  annote =	{Keywords: rotating rays, Voronoi diagram, oriented angular distance, Brocard angle, floodlight illumination, coverage problems, art gallery problems}
}
  • Refine by Type
  • 4 Document/PDF
  • 2 Document/HTML

  • Refine by Publication Year
  • 2 2025
  • 1 2023
  • 1 2021

  • Refine by Author
  • 2 Schrezenmaier, Hendrik
  • 1 Alegría, Carlos
  • 1 Andreola, Giordano
  • 1 Caroppo, Susanna
  • 1 Di Battista, Giuseppe
  • Show More...

  • Refine by Series/Journal
  • 4 LIPIcs

  • Refine by Classification
  • 4 Theory of computation → Computational geometry
  • 1 Human-centered computing → Graph drawings
  • 1 Mathematics of computing → Graph algorithms
  • 1 Mathematics of computing → Graph theory
  • 1 Mathematics of computing → Graphs and surfaces
  • Show More...

  • Refine by Keyword
  • 1 2-page book embedding
  • 1 2-tree
  • 1 Brocard angle
  • 1 Experimental Comparison
  • 1 Graph drawing
  • Show More...

Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact