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Documents authored by Pfretzschner, Matthias

Document
DOI: 10.4230/LIPIcs.GD.2025.4
Heuristics for Exact 1-Planarity Testing

Authors: Simon D. Fink, Miriam Münch, Matthias Pfretzschner, and Ignaz Rutter

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

Abstract
Since many real-world graphs are nonplanar, the study of graphs that allow few crossings per edge has been an active subfield of graph theory in recent years. One of the most natural generalizations of planar graphs are the so-called 1-planar graphs that admit a drawing with at most one crossing per edge. Unfortunately, testing whether a graph is 1-planar is known to be NP-complete even for very restricted graph classes. On the positive side, Binucci, Didimo and Montecchiani [Binucci et al., 2023] presented the first practical algorithm for testing 1-planarity based on an easy-to-implement backtracking strategy. We build on this idea and systematically explore the design choices of such algorithms and propose several new ingredients, such as different branching strategies and multiple filter criteria that allow us to reject certain branches in the search tree early on. We conduct an extensive experimental evaluation that evaluates the efficiency and effectiveness of these ingredients. Given a time limit of three hours per instance, our best configuration is able to solve more than 95% of the non-planar instances from the well-known North and Rome graphs with up to 50 vertices. Notably, the median running time for solved instances is well below 4 seconds.
Cite as

Simon D. Fink, Miriam Münch, Matthias Pfretzschner, and Ignaz Rutter. Heuristics for Exact 1-Planarity Testing. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 4:1-4:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fink_et_al:LIPIcs.GD.2025.4,
  author =	{Fink, Simon D. and M\"{u}nch, Miriam and Pfretzschner, Matthias and Rutter, Ignaz},
  title =	{{Heuristics for Exact 1-Planarity Testing}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{4:1--4:19},
  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.2025.4},
  URN =		{urn:nbn:de:0030-drops-249909},
  doi =		{10.4230/LIPIcs.GD.2025.4},
  annote =	{Keywords: 1-Planarity, Experiments, Backtracking}
}
Document
Poster Abstract
DOI: 10.4230/LIPIcs.GD.2024.50
Level Planarity Is More Difficult Than We Thought (Poster Abstract)

Authors: Simon D. Fink, Matthias Pfretzschner, Ignaz Rutter, and Peter Stumpf

Published in: LIPIcs, Volume 320, 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)

Abstract
We consider three simple quadratic-time algorithms for Level Planarity and give a level-planar instance that they either falsely classify as negative or for which they output a non-planar drawing.
Cite as

Simon D. Fink, Matthias Pfretzschner, Ignaz Rutter, and Peter Stumpf. Level Planarity Is More Difficult Than We Thought (Poster Abstract). In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 50:1-50:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{fink_et_al:LIPIcs.GD.2024.50,
  author =	{Fink, Simon D. and Pfretzschner, Matthias and Rutter, Ignaz and Stumpf, Peter},
  title =	{{Level Planarity Is More Difficult Than We Thought}},
  booktitle =	{32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
  pages =	{50:1--50:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-343-0},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{320},
  editor =	{Felsner, Stefan and Klein, Karsten},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.50},
  URN =		{urn:nbn:de:0030-drops-213341},
  doi =		{10.4230/LIPIcs.GD.2024.50},
  annote =	{Keywords: level planarity, 2-SAT, simple algorithm, counterexample}
}
Document
DOI: 10.4230/LIPIcs.ESA.2021.43
Experimental Comparison of PC-Trees and PQ-Trees

Authors: Simon D. Fink, Matthias Pfretzschner, and Ignaz Rutter

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

Abstract
PQ-trees and PC-trees are data structures that represent sets of linear and circular orders, respectively, subject to constraints that specific subsets of elements have to be consecutive. While equivalent to each other, PC-trees are conceptually much simpler than PQ-trees; updating a PC-tree so that a set of elements becomes consecutive requires only a single operation, whereas PQ-trees use an update procedure that is described in terms of nine transformation templates that have to be recursively matched and applied. Despite these theoretical advantages, to date no practical PC-tree implementation is available. This might be due to the original description by Hsu and McConnell [Hsu et al., 2003] in some places only sketching the details of the implementation. In this paper, we describe two alternative implementations of PC-trees. For the first one, we follow the approach by Hsu and McConnell, filling in the necessary details and also proposing improvements on the original algorithm. For the second one, we use a different technique for efficiently representing the tree using a Union-Find data structure. In an extensive experimental evaluation we compare our implementations to a variety of other implementations of PQ-trees that are available on the web as part of academic and other software libraries. Our results show that both PC-tree implementations beat their closest fully correct competitor, the PQ-tree implementation from the OGDF library [Markus Chimani et al., 2014; Leipert, 1997], by a factor of 2 to 4, showing that PC-trees are not only conceptually simpler but also fast in practice. Moreover, we find the Union-Find-based implementation, while having a slightly worse asymptotic runtime, to be twice as fast as the one based on the description by Hsu and McConnell.
Cite as

Simon D. Fink, Matthias Pfretzschner, and Ignaz Rutter. Experimental Comparison of PC-Trees and PQ-Trees. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 43:1-43:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{fink_et_al:LIPIcs.ESA.2021.43,
  author =	{Fink, Simon D. and Pfretzschner, Matthias and Rutter, Ignaz},
  title =	{{Experimental Comparison of PC-Trees and PQ-Trees}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{43:1--43:13},
  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.2021.43},
  URN =		{urn:nbn:de:0030-drops-146245},
  doi =		{10.4230/LIPIcs.ESA.2021.43},
  annote =	{Keywords: PQ-Tree, PC-Tree, circular consecutive ones, implementation, experimental evaluation}
}
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