Volume
LIPIcs, Volume 357
33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)
-
Part of:
Series:
Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Graph Drawing and Network Visualization (GD)
Event
Editors
Publication Details
- published at: 2025-11-26
- Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- ISBN: 978-3-95977-403-1
Access Numbers
- Detailed Access Statistics available here
-
Total Document Accesses (updated on a weekly basis):
0PDF Downloads
Documents
No documents found matching your filter selection.
Document
Complete Volume
LIPIcs, Volume 357, GD 2025, Complete Volume
Abstract
LIPIcs, Volume 357, GD 2025, Complete Volume
Cite as
33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 1-786, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@Proceedings{dujmovic_et_al:LIPIcs.GD.2025,
title = {{LIPIcs, Volume 357, GD 2025, Complete Volume}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {1--786},
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},
URN = {urn:nbn:de:0030-drops-250744},
doi = {10.4230/LIPIcs.GD.2025},
annote = {Keywords: LIPIcs, Volume 357, GD 2025, Complete Volume}
}
Document
Front Matter
Front Matter, Table of Contents, Preface, Conference Organization
Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as
33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 0:i-0:xviii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{dujmovic_et_al:LIPIcs.GD.2025.0,
author = {Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
title = {{Front Matter, Table of Contents, Preface, Conference Organization}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {0:i--0:xviii},
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.2025.0},
URN = {urn:nbn:de:0030-drops-250731},
doi = {10.4230/LIPIcs.GD.2025.0},
annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Invited Talk
A Sketch of Parameterized Complexity (Invited Talk)
Abstract
In the field of parameterized complexity, we study algorithms for and the complexity of problems where one part of the input is a parameter that is assumed to be small. In this talk, a survey will be given of several central notions from parameterized complexity, and discuss some recent developments, including the classes XNLP and XALP. These topics will be illustrated with examples from results on graph layout and graph drawing.
Cite as
Hans L. Bodlaender. A Sketch of Parameterized Complexity (Invited Talk). In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, p. 1:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{bodlaender:LIPIcs.GD.2025.1,
author = {Bodlaender, Hans L.},
title = {{A Sketch of Parameterized Complexity}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {1:1--1:1},
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.2025.1},
URN = {urn:nbn:de:0030-drops-249877},
doi = {10.4230/LIPIcs.GD.2025.1},
annote = {Keywords: Parameterized complexity, XNLP, XALP}
}
Document
Invited Talk
Transforming Graph Visualization through AI and Human-AI Collaboration (Invited Talk)
Abstract
In recent years, the intersection of artificial intelligence (AI) and graph visualization has led to advancements that enhance our ability to analyze and interpret complex data. In this talk, I will explore how AI and human-AI collaboration have transformed graph visualization, focusing on three key themes: efficiency in graph visualization, the integration of data storytelling, and the creative potential of human-AI partnerships.
In the first part of my talk, I will discuss how AI has been employed to create more efficient graph visualizations. I will highlight our innovative deep learning-based method for assessing the readability of graph layouts directly from images. This approach overcomes the limitations of traditional readability metrics, allowing for a more efficient evaluation of graph aesthetics, particularly in dense networks.
Next, I will delve into the application of graph visualization in data storytelling and virtual reality (VR) environments. I will present how tangible interactions can enhance live presentations of network visualizations, showcasing the effectiveness of intuitive physical interactions in engaging audiences. Additionally, I will discuss the development of semi-automatic data tours that guide users through complex networks, making exploration more intuitive and less time-consuming.
In the final section of my talk, I will focus on the creative aspects of human-AI collaboration in graph visualization. I will examine how generative AI techniques are reshaping the roles of humans and AI in the storytelling process, discussing the shift from human creators to AI-assisted storytelling. This evolution leads to innovative visualization techniques and highlights emerging collaboration patterns that enhance the storytelling experience.
By addressing these themes, my talk will illustrate the impact of AI and human-AI collaboration on graph visualization, highlighting both the opportunities and challenges that lie ahead in this rapidly evolving field.
Cite as
Huamin Qu. Transforming Graph Visualization through AI and Human-AI Collaboration (Invited Talk). In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{qu:LIPIcs.GD.2025.2,
author = {Qu, Huamin},
title = {{Transforming Graph Visualization through AI and Human-AI Collaboration}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {2:1--2:1},
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.2025.2},
URN = {urn:nbn:de:0030-drops-249882},
doi = {10.4230/LIPIcs.GD.2025.2},
annote = {Keywords: Graph Visualization, Virtual Reality, Human-AI Collaboration}
}
Document
On the Structure of Normalized Models of Circular-Arc Graphs I. Hsu’s Approach
Abstract
In the work [𝒪(m⋅ n) algorithms for the recognition and isomorphism problems on circular-arc graphs, SIAM J. Comput. 24(3), 411-439, (1995)], Wen-Lian Hsu claims three results concerning the class of circular-arc graphs:
- the design of so-called decomposition trees that represent the structure of all normalized intersection models of circular-arc graphs,
- an 𝒪(nm)-time recognition algorithm for circular-arc graphs,
- an 𝒪(nm)-time isomorphism algorithm for circular-arc graphs. In [Discrete Math. Theor. Comput. Sci., 15(1), 157-182, 2013] Curtis, Lin, McConnell, Nussbaum, Soulignac, Spinrad, and Szwarcfiter showed that Hsu’s isomorphism algorithm is incorrect. In this note, we show that the other two results - namely, the construction of decomposition trees and the recognition algorithm - are also flawed.
We also present the main ideas that made it possible to construct a data structure that maintains normalized models of circular-arc graphs.
Cite as
Tomasz Krawczyk. On the Structure of Normalized Models of Circular-Arc Graphs I. Hsu’s Approach. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 3:1-3:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{krawczyk:LIPIcs.GD.2025.3,
author = {Krawczyk, Tomasz},
title = {{On the Structure of Normalized Models of Circular-Arc Graphs I. Hsu’s Approach}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {3:1--3:15},
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.2025.3},
URN = {urn:nbn:de:0030-drops-249892},
doi = {10.4230/LIPIcs.GD.2025.3},
annote = {Keywords: intersection graphs and models, circular-arc graphs and circular-arc intersection models}
}
Document
Heuristics for Exact 1-Planarity Testing
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)
Copy BibTex To Clipboard
@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
Constrained Flips in Plane Spanning Trees
Abstract
A flip in a plane spanning tree T is the operation of removing one edge from T and adding another edge such that the resulting structure is again a plane spanning tree. For trees on a set of points in convex position we study two classic types of constrained flips: (1) Compatible flips are flips in which the removed and inserted edge do not cross each other. We relevantly improve the previous upper bound of 2n-O(√n) on the diameter of the compatible flip graph to (5n/3)-O(1), by this matching the upper bound for unrestricted flips by Bjerkevik, Kleist, Ueckerdt, and Vogtenhuber [SODA 2025] up to an additive constant of 1. We further show that no shortest compatible flip sequence removes an edge that is already in its target position. Using this so-called happy edge property, we derive a fixed-parameter tractable algorithm to compute the shortest compatible flip sequence between two given trees. (2) Rotations are flips in which the removed and inserted edge share a common vertex. Besides showing that the happy edge property does not hold for rotations, we improve the previous upper bound of 2n-O(1) for the diameter of the rotation graph to (7n/4)-O(1).
Cite as
Oswin Aichholzer, Joseph Dorfer, and Birgit Vogtenhuber. Constrained Flips in Plane Spanning Trees. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 5:1-5:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{aichholzer_et_al:LIPIcs.GD.2025.5,
author = {Aichholzer, Oswin and Dorfer, Joseph and Vogtenhuber, Birgit},
title = {{Constrained Flips in Plane Spanning Trees}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {5:1--5:18},
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.2025.5},
URN = {urn:nbn:de:0030-drops-249913},
doi = {10.4230/LIPIcs.GD.2025.5},
annote = {Keywords: Non-crossing spanning trees, Flip Graphs, Diameter, Complexity, Happy edges}
}
Document
Approximating Barnette’s Conjecture
Abstract
A well-known conjecture, named after David W. Barnette, asserts that every 3-regular, 3-connected, bipartite, planar graph (for short, Barnette graph) is Hamiltonian. As another step towards addressing Barnette’s conjecture positively, we show that every n-vertex Barnette graph admits a subhamiltonian cycle containing 5n/6 edges, improving upon the previous bound of 2n/3. Equivalently, every Barnette graph admits a 2-page book embedding in which at least 5n/6 consecutive vertex pairs along the spine are connected by edges. As a byproduct, we present a simple proof for a known result that guarantees the existence of Hamiltonian cycles in a certain subclass of Barnette graphs.
Cite as
Michael A. Bekos, Michael Kaufmann, and Maximilian Pfister. Approximating Barnette’s Conjecture. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 6:1-6:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{bekos_et_al:LIPIcs.GD.2025.6,
author = {Bekos, Michael A. and Kaufmann, Michael and Pfister, Maximilian},
title = {{Approximating Barnette’s Conjecture}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {6:1--6:7},
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.2025.6},
URN = {urn:nbn:de:0030-drops-249927},
doi = {10.4230/LIPIcs.GD.2025.6},
annote = {Keywords: Barnette’s Conjecture, Subhamiltonicity, Book embeddings}
}
Document
Same Quality Metrics, Different Graph Drawings
Abstract
Graph drawings are commonly used to visualize relational data. User understanding and performance are linked to the quality of such drawings, which is measured by quality metrics. The tacit knowledge in the graph drawing community about these quality metrics is that they are not always able to accurately capture the quality of graph drawings. In particular, such metrics may rate drawings with very poor quality as very good. In this work we make this tacit knowledge explicit by showing that we can modify existing graph drawings into arbitrary target shapes while keeping one or more quality metrics almost identical. This supports the claim that more advanced quality metrics are needed to capture the "goodness" of a graph drawing and that we cannot confidently rely on the value of a single (or several) certain quality metrics.
Cite as
Simon van Wageningen, Tamara Mchedlidze, and Alexandru C. Telea. Same Quality Metrics, Different Graph Drawings. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 7:1-7:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{vanwageningen_et_al:LIPIcs.GD.2025.7,
author = {van Wageningen, Simon and Mchedlidze, Tamara and Telea, Alexandru C.},
title = {{Same Quality Metrics, Different Graph Drawings}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {7:1--7:13},
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.2025.7},
URN = {urn:nbn:de:0030-drops-249935},
doi = {10.4230/LIPIcs.GD.2025.7},
annote = {Keywords: graph drawing, quality metrics, assumptions, fooling}
}
Document
Tangling and Untangling Trees on Point-Sets
Abstract
We study a question that lies at the intersection of classical research subjects in Topological Graph Theory and Graph Drawing: Computing a drawing of a graph with a prescribed number of crossings on a given set S of points, while ensuring that its curve complexity (i.e., maximum number of bends per edge) is bounded by a constant. We focus on trees: Let T be a tree, ϑ(T) be its thrackle number, and χ be any integer in the interval [0,ϑ(T)]. In the tangling phase we compute a topological linear embedding of T with ϑ(T) edge crossings and a constant number of spine traversals. In the untangling phase we remove edge crossings without increasing the spine traversals until we reach χ crossings. The computed linear embedding is used to construct a drawing of T on S with χ crossings and constant curve complexity. Our approach gives rise to an O(n²)-time algorithm for general trees and an O(n log n)-time algorithm for paths. We also adapt the approach to compute RAC drawings, i.e. drawings where the angles formed at edge crossings are π/2.
Cite as
Giuseppe Di Battista, Giuseppe Liotta, Maurizio Patrignani, Antonios Symvonis, and Ioannis G. Tollis. Tangling and Untangling Trees on Point-Sets. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{dibattista_et_al:LIPIcs.GD.2025.8,
author = {Di Battista, Giuseppe and Liotta, Giuseppe and Patrignani, Maurizio and Symvonis, Antonios and Tollis, Ioannis G.},
title = {{Tangling and Untangling Trees on Point-Sets}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {8:1--8:18},
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.2025.8},
URN = {urn:nbn:de:0030-drops-249947},
doi = {10.4230/LIPIcs.GD.2025.8},
annote = {Keywords: Tree drawings, Prescribed edge crossings, Thrackle, Curve complexity, Point-set embeddings, RAC drawings, Topological linear embeddings}
}
Document
The Page Number of Monotone Directed Acyclic Outerplanar Graphs Is Four or Five
Abstract
A k-page book embedding of a directed acyclic graph consists of a topological order of its vertices and a k-coloring of its edges, such that no two edges of the same color cross, that is, their endpoints do not alternate in the order. The minimum value of k for which such an embedding exists is referred to as the page number of the graph. In contrast to general directed acyclic planar graphs, which may have unbounded page number [SIAM J. Comput. 28(5), 1999], it was recently shown that directed acyclic outerplanar graphs have bounded page number. In particular, Jungeblut, Merker and Ueckerdt provided an upper bound of 24,776 on their page number [FOCS 2023: 1937-1952].
In this work, we focus on so-called monotone directed acyclic outerplanar graphs. Starting from a single edge, these graphs are constructed by iteratively connecting a new vertex to the endpoints of an existing edge on the outer face using either two incoming or two outgoing edges incident to it. These graphs have twist-number 4 [GD 2023: 135-151] (i.e., they admit a topological order in which no more than four edges pairwise cross), a property, which was leveraged by Jungeblut, Merker and Ueckerdt to show that their page number is at most 128. We lower this upper bound to 5 and we also provide a lower bound of 4. A notable consequence of our result is a significant improvement of the upper bound on the page number of general directed outerplanar graphs from 24,776 to 1,160.
Cite as
Jawaherul Md. Alam, Michael A. Bekos, Martin Gronemann, and Michael Kaufmann. The Page Number of Monotone Directed Acyclic Outerplanar Graphs Is Four or Five. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{alam_et_al:LIPIcs.GD.2025.9,
author = {Alam, Jawaherul Md. and Bekos, Michael A. and Gronemann, Martin and Kaufmann, Michael},
title = {{The Page Number of Monotone Directed Acyclic Outerplanar Graphs Is Four or Five}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {9:1--9:17},
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.2025.9},
URN = {urn:nbn:de:0030-drops-249952},
doi = {10.4230/LIPIcs.GD.2025.9},
annote = {Keywords: Book embeddings, page number, directed outerplanar graphs}
}
Document
The Bend Number of Cocomparability Graphs
Abstract
We introduce a new complexity measure for cocomparability graphs of posets or in other words, intersection graphs of piecewise linear functions, the bend number. We prove that cocomparability graphs of bounded bend number are not too plentiful and give two hierarchies of classes of cocomparability graphs, depending on whether the piecewise linear functions are restricted to slopes of ±1 (diagonal case) or not (general case). These hierarchies give a gradation between permutation graphs and cocomparability graphs.
Cite as
Todor Antić, Vit Jelínek, Martin Pergel, Felix Schröder, Peter Stumpf, and Pavel Valtr. The Bend Number of Cocomparability Graphs. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 10:1-10:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{antic_et_al:LIPIcs.GD.2025.10,
author = {Anti\'{c}, Todor and Jel{\'\i}nek, Vit and Pergel, Martin and Schr\"{o}der, Felix and Stumpf, Peter and Valtr, Pavel},
title = {{The Bend Number of Cocomparability Graphs}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {10:1--10:23},
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.2025.10},
URN = {urn:nbn:de:0030-drops-249963},
doi = {10.4230/LIPIcs.GD.2025.10},
annote = {Keywords: Intersection Graphs, Bend Number, Piecewise Linear Functions, Graph Class Hierarchy, Cocomparability Graphs, Permutation Graphs, Poset Dimension}
}
Document
Towards a Better Understanding of Graph Perception in Immersive Environments
Abstract
As Immersive Analytics (IA) increasingly uses Virtual Reality (VR) for stereoscopic 3D (S3D) graph visualisation, it is crucial to understand how users perceive network structures in these immersive environments. However, little is known about how humans read S3D graphs during task solving, and how gaze behaviour indicates task performance. To address this gap, we report a user study with 18 participants asked to perform three analytical tasks on S3D graph visualisations in a VR environment. Our findings reveal systematic relationships between network structural properties and gaze behaviour. Based on these insights, we contribute a comprehensive eye tracking methodology for analysing human perception in immersive environments and establish eye tracking as a valuable tool for objectively evaluating cognitive load in S3D graph visualisation.
Cite as
Lin Zhang, Yao Wang, Ying Zhang, Wilhelm Kerle-Malcharek, Karsten Klein, Falk Schreiber, and Andreas Bulling. Towards a Better Understanding of Graph Perception in Immersive Environments. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 11:1-11:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{zhang_et_al:LIPIcs.GD.2025.11,
author = {Zhang, Lin and Wang, Yao and Zhang, Ying and Kerle-Malcharek, Wilhelm and Klein, Karsten and Schreiber, Falk and Bulling, Andreas},
title = {{Towards a Better Understanding of Graph Perception in Immersive Environments}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {11:1--11:19},
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.2025.11},
URN = {urn:nbn:de:0030-drops-249976},
doi = {10.4230/LIPIcs.GD.2025.11},
annote = {Keywords: Stereoscopic 3D, Graph Visualisation, Eye Tracking, Graph Perception}
}
Document
Flipping Odd Matchings in Geometric and Combinatorial Settings
Abstract
We study the problem of reconfiguring odd matchings, that is, matchings that cover all but a single vertex. Our reconfiguration operation is a so-called flip where the unmatched vertex of the first matching gets matched, while consequently another vertex becomes unmatched. We consider two distinct settings: the geometric setting, in which the vertices are points embedded in the plane and all occurring odd matchings are crossing-free, and a combinatorial setting, in which we consider odd matchings in general graphs.
For the latter setting, we provide a complete polynomial time checkable characterization of graphs in which any two odd matchings can be reconfigured into each another. This complements the previously known result that the flip graph is always connected in the geometric setting [Oswin Aichholzer et al., 2025]. In the combinatorial setting, we prove that the diameter of the flip graph, if connected, is linear in the number of vertices. Furthermore, we establish that deciding whether there exists a flip sequence of length k transforming one given matching into another is NP-complete in both the combinatorial and the geometric settings. To prove the latter, we introduce a framework that allows us to transform partial order types into general position with only polynomial overhead. Finally, we demonstrate that when parameterized by the flip distance k, the problem is fixed-parameter tractable (FPT) in the geometric setting when restricted to convex point sets.
Cite as
Oswin Aichholzer, Sofia Brenner, Joseph Dorfer, Hung P. Hoang, Daniel Perz, Christian Rieck, and Francesco Verciani. Flipping Odd Matchings in Geometric and Combinatorial Settings. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 12:1-12:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{aichholzer_et_al:LIPIcs.GD.2025.12,
author = {Aichholzer, Oswin and Brenner, Sofia and Dorfer, Joseph and Hoang, Hung P. and Perz, Daniel and Rieck, Christian and Verciani, Francesco},
title = {{Flipping Odd Matchings in Geometric and Combinatorial Settings}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {12:1--12:18},
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.2025.12},
URN = {urn:nbn:de:0030-drops-249983},
doi = {10.4230/LIPIcs.GD.2025.12},
annote = {Keywords: Odd matchings, reconfiguration, flip graph, geometric, combinatorial, connectivity, NP-hardness, FPT}
}
Document
Separability of Witness Gabriel Drawings
Abstract
A witness Gabriel drawing Γ is a straight-line drawing of a graph in which any two vertices of Γ are adjacent if and only if the disk having these vertices as antipodal points contains no element of a special set of points called witnesses. A witness Gabriel drawing is linearly separable if the vertices and the witnesses lie in opposite half-planes. We prove that every outerplanar graph has a linearly separable witness Gabriel drawing by introducing and studying a new type of drawing that we call a border parabola drawing. We then use border parabola drawings to characterize those triangle-free graphs that admit a linearly separable witness Gabriel drawing. We also consider witness Gabriel drawings where no witness lies in the interior of the convex hull of the vertex set, which we call convexly separable drawings. We construct witness Gabriel drawable graphs for which any witness Gabriel drawing must be convexly separable and that do not admit any linearly separable witness Gabriel drawing.
Cite as
Carolina Haase, Philipp Kindermann, William Lenhart, and Giuseppe Liotta. Separability of Witness Gabriel Drawings. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 13:1-13:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{haase_et_al:LIPIcs.GD.2025.13,
author = {Haase, Carolina and Kindermann, Philipp and Lenhart, William and Liotta, Giuseppe},
title = {{Separability of Witness Gabriel Drawings}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {13:1--13:18},
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.2025.13},
URN = {urn:nbn:de:0030-drops-249998},
doi = {10.4230/LIPIcs.GD.2025.13},
annote = {Keywords: Proximity Drawings, Witness Gabriel Graphs, Geometric Graph Theory}
}
Document
OOPS: Optimized One-Planarity Solver via SAT
Abstract
We present OOPS (Optimized One-Planarity Solver), a practical heuristic for recognizing 1-planar graphs and several important subclasses. A graph is 1-planar if it can be drawn in the plane such that each edge is crossed at most once - a natural generalization of planar graphs that has received increasing attention in graph drawing and beyond-planar graph theory. Although testing planarity can be done in linear time, recognizing 1-planar graphs is NP-complete, making effective practical algorithms especially valuable.
The core idea of our approach is to reduce the recognition of 1-planarity to a propositional satisfiability (SAT) instance, enabling the use of modern SAT solvers to efficiently explore the search space. Despite the inherent complexity of the problem, our method is substantially faster in practice than naïve or brute-force algorithms. In addition to demonstrating the empirical performance of our solver on synthetic and real-world instances, we show how OOPS can be used as a discovery tool in theoretical graph theory. Specifically, we employ OOPS to investigate two research problems concerning 1-planarity of specific graph families. Our implementation of the algorithm is publicly available to support further exploration in the field.
Cite as
Sergey Pupyrev. OOPS: Optimized One-Planarity Solver via SAT. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 14:1-14:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{pupyrev:LIPIcs.GD.2025.14,
author = {Pupyrev, Sergey},
title = {{OOPS: Optimized One-Planarity Solver via SAT}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {14:1--14:19},
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.2025.14},
URN = {urn:nbn:de:0030-drops-250004},
doi = {10.4230/LIPIcs.GD.2025.14},
annote = {Keywords: beyond planarity, 1-planar graph, SAT, book embeddings, upward 1-planarity}
}
Document
Crossing Number of Simple 3-Plane Drawings
Abstract
We study 3-plane drawings, that is, drawings of graphs in which every edge has at most three crossings. We show how the recently developed Density Formula for topological drawings of graphs [Kaufmann et al., 2024] can be used to count the crossings in terms of the number n of vertices. As a main result, we show that every 3-plane drawing has at most 5.5(n-2) crossings, which is tight. In particular, it follows that every 3-planar graph on n vertices has crossing number at most 5.5n, which improves upon a recent bound [Bekos et al., 2024] of 6.6n. To apply the Density Formula, we carefully analyze the interplay between certain configurations of cells in a 3-plane drawing. As a by-product, we also obtain an alternative proof for the known statement that every 3-planar graph has at most 5.5(n-2) edges.
Cite as
Miriam Goetze, Michael Hoffmann, Ignaz Rutter, and Torsten Ueckerdt. Crossing Number of Simple 3-Plane Drawings. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 15:1-15:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{goetze_et_al:LIPIcs.GD.2025.15,
author = {Goetze, Miriam and Hoffmann, Michael and Rutter, Ignaz and Ueckerdt, Torsten},
title = {{Crossing Number of Simple 3-Plane Drawings}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {15:1--15:19},
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.2025.15},
URN = {urn:nbn:de:0030-drops-250014},
doi = {10.4230/LIPIcs.GD.2025.15},
annote = {Keywords: beyond planar graphs, edge density, crossing number, density formula}
}
Document
Structural Parameterizations of k-Planarity
Abstract
The concept of k-planarity is extensively studied in the context of Beyond Planarity. A graph is k-planar if it admits a drawing in the plane in which each edge is crossed at most k times. The local crossing number of a graph is the minimum integer k such that it is k-planar. The problem of determining whether an input graph is 1-planar is known to be NP-complete even for near-planar graphs [Cabello and Mohar, SIAM J. Comput. 2013], that is, the graphs obtained from planar graphs by adding a single edge. Moreover, the local crossing number is hard to approximate within a factor 2 - ε for any ε > 0 [Urschel and Wellens, IPL 2021]. To address this computational intractability, Bannister, Cabello, and Eppstein [JGAA 2018] investigated the parameterized complexity of the case of k = 1, particularly focusing on structural parameterizations on input graphs, such as treedepth, vertex cover number, and feedback edge number. In this paper, we extend their approach by considering the general case k ≥ 1 and give (tight) parameterized upper and lower bound results. In particular, we strengthen the aforementioned lower bound results to subclasses of constant-treewidth graphs: we show that testing 1-planarity is NP-complete even for near-planar graphs with feedback vertex set number at most 3 and pathwidth at most 4, and the local crossing number is hard to approximate within any constant factor for graphs with feedback vertex set number at most 2.
Cite as
Tatsuya Gima, Yasuaki Kobayashi, and Yuto Okada. Structural Parameterizations of k-Planarity. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 16:1-16:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{gima_et_al:LIPIcs.GD.2025.16,
author = {Gima, Tatsuya and Kobayashi, Yasuaki and Okada, Yuto},
title = {{Structural Parameterizations of k-Planarity}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {16:1--16:17},
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.2025.16},
URN = {urn:nbn:de:0030-drops-250021},
doi = {10.4230/LIPIcs.GD.2025.16},
annote = {Keywords: 1-planar graphs, local crossing number, beyond planarity, parameterized complexity, kernelization}
}
Document
Visualizing Treewidth
Abstract
A witness drawing of a graph is a visualization that clearly shows a given property of a graph. We study and implement various drawing paradigms for witness drawings to clearly show that graphs have bounded pathwidth or treewidth. Our approach draws the tree decomposition or path decomposition as a tree of bags, with induced subgraphs shown in each bag, and with "tracks" for each graph vertex connecting its copies in multiple bags. Within bags, we optimize the vertex layout to avoid crossings of edges and tracks. We implement a visualization prototype for crossing minimization using dynamic programming for graphs of small width and heuristic approaches for graphs of larger width. We introduce a taxonomy of drawing styles, which render the subgraph for each bag as an arc diagram with one or two pages or as a circular layout with straight-line edges, and we render tracks either with straight lines or with orbital-radial paths.
Cite as
Alvin Chiu, Thomas Depian, David Eppstein, Michael T. Goodrich, and Martin Nöllenburg. Visualizing Treewidth. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 17:1-17:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{chiu_et_al:LIPIcs.GD.2025.17,
author = {Chiu, Alvin and Depian, Thomas and Eppstein, David and Goodrich, Michael T. and N\"{o}llenburg, Martin},
title = {{Visualizing Treewidth}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {17:1--17:20},
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.2025.17},
URN = {urn:nbn:de:0030-drops-250034},
doi = {10.4230/LIPIcs.GD.2025.17},
annote = {Keywords: Graph drawing, witness drawings, pathwidth, treewidth}
}
Document
Internally-Convex Drawings of Outerplanar Graphs in Small Area
Abstract
A well-known result by Kant [Algorithmica, 1996] implies that n-vertex outerplane graphs admit embedding-preserving planar straight-line grid drawings where the internal faces are convex polygons in O(n²) area. In this paper, we present an algorithm to compute such drawings in O(n¹·⁵) area. We also consider outerplanar drawings in which the internal faces are required to be strictly-convex polygons. In this setting, we consider outerplanar graphs whose weak dual is a path and give a drawing algorithm that achieves Θ(nk²) area, where k is the maximum size of an internal facial cycle.
Cite as
Michael A. Bekos, Giordano Da Lozzo, Fabrizio Frati, Giuseppe Liotta, and Antonios Symvonis. Internally-Convex Drawings of Outerplanar Graphs in Small Area. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 18:1-18:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{bekos_et_al:LIPIcs.GD.2025.18,
author = {Bekos, Michael A. and Da Lozzo, Giordano and Frati, Fabrizio and Liotta, Giuseppe and Symvonis, Antonios},
title = {{Internally-Convex Drawings of Outerplanar Graphs in Small Area}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {18:1--18:17},
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.2025.18},
URN = {urn:nbn:de:0030-drops-250042},
doi = {10.4230/LIPIcs.GD.2025.18},
annote = {Keywords: Grid drawings, convexity, area bounds, outerplanar graphs}
}
Document
Crossing and Non-Crossing Families
Abstract
For a finite set P of points in the plane in general position, a crossing family of size k in P is a collection of k line segments with endpoints in P that are pairwise crossing. It is a long-standing open problem to determine the largest size of a crossing family in any set of n points in the plane in general position. It is widely believed that this size should be linear in n.
Motivated by results from the theory of partitioning complete geometric graphs, we study a variant of this problem for point sets P that do not contain a non-crossing family of size m, which is a collection of 4 disjoint subsets P₁, P₂, P₃, and P₄ of P, each containing m points of P, such that for every choice of 4 points p_i ∈ P_i, the set {p₁,p₂,p₃,p₄} is such that p₄ is in the interior of the triangle formed by p₁,p₂,p₃. We prove that, for every m ∈ ℕ, each set P of n points in the plane in general position contains either a crossing family of size n/2^{O(√{log{m}})} or a non-crossing family of size m, by this strengthening a recent breakthrough result by Pach, Rubin, and Tardos (2021). Our proof is constructive and we show that these families can be obtained in expected time O(nm^{1+o(1)}). We also prove that a crossing family of size Ω(n/m) or a non-crossing family of size m in P can be found in expected time O(n).
Cite as
Todor Antić, Martin Balko, and Birgit Vogtenhuber. Crossing and Non-Crossing Families. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 19:1-19:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{antic_et_al:LIPIcs.GD.2025.19,
author = {Anti\'{c}, Todor and Balko, Martin and Vogtenhuber, Birgit},
title = {{Crossing and Non-Crossing Families}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {19:1--19:15},
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.2025.19},
URN = {urn:nbn:de:0030-drops-250058},
doi = {10.4230/LIPIcs.GD.2025.19},
annote = {Keywords: crossing family, non-crossing family, geometric graph}
}
Document
A Systematic Approach to Crossing Numbers of Cartesian Products with Paths
Abstract
Determining the crossing numbers of Cartesian products of small graphs with arbitrarily large paths has been an ongoing topic of research since the 1970s. Doing so requires the establishment of coincident upper and lower bounds; the former is usually demonstrated by providing a suitable drawing procedure, while the latter often requires substantial theoretical arguments. Many such papers have been published, which typically focus on just one or two small graphs at a time, and use ad hoc arguments specific to those graphs. We propose a general approach which, when successful, establishes the required lower bound. This approach can be applied to the Cartesian product of any graph with arbitrarily large paths, and in each case involves solving a modified version of the crossing number problem on a finite number (typically only two or three) of small graphs. We demonstrate the potency of this approach by applying it to Cartesian products involving all 133 graphs of orders five or six, and show that it is successful in 128 cases. This includes 60 cases which a recent survey listed as either undetermined, or determined only in journals without adequate peer review.
Cite as
Zayed Asiri, Ryan Burdett, Markus Chimani, Michael Haythorpe, Alex Newcombe, and Mirko H. Wagner. A Systematic Approach to Crossing Numbers of Cartesian Products with Paths. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 20:1-20:32, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{asiri_et_al:LIPIcs.GD.2025.20,
author = {Asiri, Zayed and Burdett, Ryan and Chimani, Markus and Haythorpe, Michael and Newcombe, Alex and Wagner, Mirko H.},
title = {{A Systematic Approach to Crossing Numbers of Cartesian Products with Paths}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {20:1--20:32},
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.2025.20},
URN = {urn:nbn:de:0030-drops-250066},
doi = {10.4230/LIPIcs.GD.2025.20},
annote = {Keywords: Crossing number, Cartesian graph products, proof framework}
}
Document
On Geometric Bipartite Graphs with Asymptotically Smallest Zarankiewicz Numbers
Abstract
This paper considers the Zarankiewicz problem in bipartite graphs with low-dimensional geometric representation (i.e., low Ferrers dimension). Let Z(n;k) be the maximum number of edges in a bipartite graph with n nodes and is free of a k-by-k biclique. Note that Z(n;k) ∈ Ω(nk) for all "natural" graph classes. Our first result reveals a separation between bipartite graphs of Ferrers dimension three and four: while we show that Z(n;k) ≤ 9n(k-1) for graphs of Ferrers dimension three, Z(n;k) ∈ Ω(n k ⋅ (log n)/(log log n)) for Ferrers dimension four graphs (Chan & Har-Peled, 2023) (Chazelle, 1990). To complement this, we derive a tight upper bound of 2n(k-1) for chordal bipartite graphs and 54n(k-1) for grid intersection graphs (GIG), a prominent graph class residing in four Ferrers dimensions and capturing planar bipartite graphs as well as bipartite intersection graphs of rectangles. Previously, the best-known bound for GIG was Z(n;k) ∈ O(2^{O(k)} n), implied by the results of Fox & Pach (2006) and Mustafa & Pach (2016). Our results advance and offer new insights into the interplay between Ferrers dimensions and extremal combinatorics.
Cite as
Parinya Chalermsook, Ly Orgo, and Minoo Zarsav. On Geometric Bipartite Graphs with Asymptotically Smallest Zarankiewicz Numbers. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 21:1-21:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{chalermsook_et_al:LIPIcs.GD.2025.21,
author = {Chalermsook, Parinya and Orgo, Ly and Zarsav, Minoo},
title = {{On Geometric Bipartite Graphs with Asymptotically Smallest Zarankiewicz Numbers}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {21:1--21:24},
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.2025.21},
URN = {urn:nbn:de:0030-drops-250074},
doi = {10.4230/LIPIcs.GD.2025.21},
annote = {Keywords: Bipartite graph classes, extremal graph theory, geometric intersection graphs, Zarankiewicz problem, bicliques}
}
Document
NNP-NET: Accelerating t-SNE Graph Drawing for Very Large Graphs by Neural Networks
Abstract
tsNET is a recent graph drawing (GD) method that creates high quality layouts but suffers from a very high runtime. We present a new GD method, NNP-NET, which reduces tsNET’s time complexity to generate layouts for very large graphs in seconds. Additionally, we extend tsNET to support drawing graphs with edge weights. We accomplish this by replacing tsNET’s t-SNE projection with Neural Network Projection (NNP), a fast dimensionality reduction (DR) method that can imitate any given DR method. Our experiments show that NNP-NET gets good quality results when compared to other state-of-the art GD methods while yielding a better computational scalability.
Cite as
Ilan Hartskeerl, Tamara Mchedlidze, Simon van Wageningen, Peter Vangorp, and Alexandru Telea. NNP-NET: Accelerating t-SNE Graph Drawing for Very Large Graphs by Neural Networks. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 22:1-22:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{hartskeerl_et_al:LIPIcs.GD.2025.22,
author = {Hartskeerl, Ilan and Mchedlidze, Tamara and van Wageningen, Simon and Vangorp, Peter and Telea, Alexandru},
title = {{NNP-NET: Accelerating t-SNE Graph Drawing for Very Large Graphs by Neural Networks}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {22:1--22:22},
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.2025.22},
URN = {urn:nbn:de:0030-drops-250087},
doi = {10.4230/LIPIcs.GD.2025.22},
annote = {Keywords: supervised graph drawing, dimensionality reduction, t-SNE}
}
Document
The Price of Connectivity Augmentation on Planar Graphs
Abstract
Given two classes of graphs, 𝒢₁ ⊆ 𝒢₂, and a c-connected graph G ∈ 𝒢₁, we wish to augment G with a smallest cardinality set of new edges F to obtain a k-connected graph G' = (V,E∪ F) ∈ 𝒢₂. In general, this is the c → k connectivity augmentation problem. Previous research considered variants where 𝒢₁ = 𝒢₂ is the class of planar graphs, plane graphs, or planar straight-line graphs. In all three settings, we prove that the c → k augmentation problem is NP-complete when 2 ≤ c < k ≤ 5.
However, the connectivity of the augmented graph G' is at most 5 if 𝒢₂ is limited to planar graphs. We initiate the study of the c → k connectivity augmentation problem for arbitrary k ∈ ℕ, where 𝒢₁ is the class of planar graphs, plane graphs, or planar straight-line graphs, and 𝒢₂ is a beyond-planar class of graphs: 𝓁-planar, 𝓁-plane topological, or 𝓁-plane geometric graphs. We obtain tight bounds on the tradeoffs between the desired connectivity k and the local crossing number 𝓁 of the augmented graph G'. We also show that our hardness results apply to this setting.
The connectivity augmentation problem for triangulations is intimately related to edge flips; and the minimum augmentation problem to the flip distance between triangulations. We prove that it is NP-complete to find the minimum flip distance between a given triangulation and a 4-connected triangulation, settling an open problem posed in 2014, and present an EPTAS for this problem.
Cite as
Hugo A. Akitaya, Justin Dallant, Erik D. Demaine, Michael Kaufmann, Linda Kleist, Frederick Stock, Csaba D. Tóth, and Torsten Ueckerdt. The Price of Connectivity Augmentation on Planar Graphs. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 23:1-23:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{a.akitaya_et_al:LIPIcs.GD.2025.23,
author = {A. Akitaya, Hugo and Dallant, Justin and Demaine, Erik D. and Kaufmann, Michael and Kleist, Linda and Stock, Frederick and T\'{o}th, Csaba D. and Ueckerdt, Torsten},
title = {{The Price of Connectivity Augmentation on Planar Graphs}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {23:1--23:24},
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.2025.23},
URN = {urn:nbn:de:0030-drops-250095},
doi = {10.4230/LIPIcs.GD.2025.23},
annote = {Keywords: connectivity augmentation, local crossing number, flip distance}
}
Document
String Graph Obstacles of High Girth and of Bounded Degree
Abstract
A string graph is the intersection graph of curves in the plane. Kratochvíl previously showed the existence of infinitely many obstacles: graphs that are not string graphs but for which any edge contraction or vertex deletion produces a string graph. Kratochvíl’s obstacles contain arbitrarily large cliques, so they have girth three and unbounded degree. We extend this line of working by studying obstacles among graphs of restricted girth and/or degree. We construct an infinite family of obstacles of girth four; in addition, our construction is K_{2,3}-subgraph-free and near-planar (planar plus one edge). Furthermore, we prove that there is a subcubic obstacle of girth three, and that there are no subcubic obstacles of high girth. We characterize the subcubic string graphs as having a matching whose contraction yields a planar graph, and based on this characterization we find a linear-time algorithm for recognizing subcubic string graphs of bounded treewidth.
Cite as
Maria Chudnovsky, David Eppstein, and David Fischer. String Graph Obstacles of High Girth and of Bounded Degree. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 24:1-24:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{chudnovsky_et_al:LIPIcs.GD.2025.24,
author = {Chudnovsky, Maria and Eppstein, David and Fischer, David},
title = {{String Graph Obstacles of High Girth and of Bounded Degree}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {24:1--24:18},
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.2025.24},
URN = {urn:nbn:de:0030-drops-250108},
doi = {10.4230/LIPIcs.GD.2025.24},
annote = {Keywords: string graphs, induced minors, forbidden minors, sparsity, triangle-free graphs, near-planar graphs}
}
Document
Characterizing and Recognizing Twistedness
Abstract
In a simple drawing of a graph, any two edges intersect in at most one point (either a common endpoint or a proper crossing). A simple drawing is generalized twisted if it fulfills certain rather specific constraints on how the edges are drawn. An abstract rotation system of a graph assigns to each vertex a cyclic order of its incident edges. A realizable rotation system is one that admits a simple drawing such that at each vertex, the edges emanate in that cyclic order, and a generalized twisted rotation system can be realized as a generalized twisted drawing. Generalized twisted drawings have initially been introduced to obtain improved bounds on the size of plane substructures in any simple drawing of K_n. They have since gained independent interest due to their surprising properties. However, the definition of generalized twisted drawings is very geometric and drawing-specific.
In this paper, we develop characterizations of generalized twisted drawings that enable a purely combinatorial view on these drawings and lead to efficient recognition algorithms. Concretely, we show that for any n ≥ 7, an abstract rotation system of K_n is generalized twisted if and only if all subrotation systems induced by five vertices are generalized twisted. This implies a drawing-independent and concise characterization of generalized twistedness. Besides, the result yields a simple O(n⁵)-time algorithm to decide whether an abstract rotation system is generalized twisted and sheds new light on the structural features of simple drawings. We further develop a characterization via the rotations of a pair of vertices in a drawing, which we then use to derive an O(n²)-time algorithm to decide whether a realizable rotation system is generalized twisted.
Cite as
Oswin Aichholzer, Alfredo García, Javier Tejel, Birgit Vogtenhuber, and Alexandra Weinberger. Characterizing and Recognizing Twistedness. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 25:1-25:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{aichholzer_et_al:LIPIcs.GD.2025.25,
author = {Aichholzer, Oswin and Garc{\'\i}a, Alfredo and Tejel, Javier and Vogtenhuber, Birgit and Weinberger, Alexandra},
title = {{Characterizing and Recognizing Twistedness}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {25:1--25:17},
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.2025.25},
URN = {urn:nbn:de:0030-drops-250116},
doi = {10.4230/LIPIcs.GD.2025.25},
annote = {Keywords: generalized twisted drawings, simple drawings, rotation systems, recognition, combinatorial characterization, efficient algorithms}
}
Document
1-Planar Unit Distance Graphs with More Edges Than Matchstick Graphs
Abstract
Matchstick graphs are graphs that allow plane embedding with straight edges of equal length. One-planar unit distance graphs are graphs that allow a drawing in the plane in which all edges are straight-line segments of equal length and every edge crosses at most one other edge. The maximum number of edges of a matchstick graph (1-planar unit distance graph) of order n is denoted by u₀(n) (u₁(n), respectively). It is known that u₀(n) = ⌊ 3n-√{12n-3}⌋ holds for every n. At GD'24, Gehér and Tóth proved a slightly weaker upper bound on u₁(n), but noted that no 1-planar unit distance graph G with more than u₀(|V(G)|) vertices was known. They asked if u₁(n) = u₀(n) holds for every n. We give a negative answer to this question in a much stronger way. We show that u₁(n) > u₀(n) for every n ≥ 16135. Furthermore, we show that the gap between u₁(n) and u₀(n) can be arbitrarily large by proving that for n large enough with respect to a constant α < ∜{1/3}, u₁(n)-u₀(n) ≥ α∜{n}.
Cite as
Eliška Červenková and Jan Kratochvíl. 1-Planar Unit Distance Graphs with More Edges Than Matchstick Graphs. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 26:1-26:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{cervenkova_et_al:LIPIcs.GD.2025.26,
author = {\v{C}ervenkov\'{a}, Eli\v{s}ka and Kratochv{\'\i}l, Jan},
title = {{1-Planar Unit Distance Graphs with More Edges Than Matchstick Graphs}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {26:1--26:10},
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.2025.26},
URN = {urn:nbn:de:0030-drops-250126},
doi = {10.4230/LIPIcs.GD.2025.26},
annote = {Keywords: planar graph, unit distance graph, matchstick graph, 1-planar graph}
}
Document
Geometry Matters in Planar Storyplans
Abstract
A storyplan visualizes a graph G = (V,E) as a sequence of 𝓁 frames Γ₁, … , Γ_𝓁, each of which is a drawing of the induced subgraph G[V_i] of a vertex subset V_i ⊆ V. Moreover, each vertex v ∈ V is contained in a single consecutive sequence of frames Γ_i, … , Γ_j, all vertices and edges contained in consecutive frames are drawn identically, and the union of all frames is a drawing of G. In GD 2022, the concept of planar storyplans was introduced, in which each frame must be a planar (topological) drawing. Several (parameterized) complexity results for recognizing graphs that admit a planar storyplan were provided, including NP-hardness. In this paper, we investigate an open question posed in the GD paper and show that the geometric and topological settings of the planar storyplan problem differ: We provide an instance of a graph that admits a planar storyplan, but no planar geometric storyplan, in which each frame is a planar straight-line drawing. Still, by adapting the reduction proof from the topological to the geometric setting, we show that recognizing the graphs that admit planar geometric storyplans remains NP-hard.
Cite as
Alexander Dobler, Maximilian Holzmüller, and Martin Nöllenburg. Geometry Matters in Planar Storyplans. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 27:1-27:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{dobler_et_al:LIPIcs.GD.2025.27,
author = {Dobler, Alexander and Holzm\"{u}ller, Maximilian and N\"{o}llenburg, Martin},
title = {{Geometry Matters in Planar Storyplans}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {27:1--27:9},
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.2025.27},
URN = {urn:nbn:de:0030-drops-250135},
doi = {10.4230/LIPIcs.GD.2025.27},
annote = {Keywords: geometric storyplan, planarity, straight-line drawing, dynamic graph drawing}
}
Document
Treewidth of Outer k-Planar Graphs
Abstract
Treewidth is an important structural graph parameter that quantifies how closely a graph resembles a tree-like structure. It has applications in many algorithmic and combinatorial problems. In this paper, we study the treewidth of outer k-planar graphs, that is, graphs admitting a convex drawing (a straight-line drawing where all vertices lie on a circle) in which every edge crosses at most k other edges. We also consider the more general class of outer min-k-planar graphs, which are graphs admitting a convex drawing where for every crossing of two edges at least one of these edges is crossed at most k times.
Firman, Gutowski, Kryven, Okada and Wolff [GD 2024] proved that every outer k-planar graph has treewidth at most 1.5k+2 and provided a lower bound of k+2 for even k. We establish a lower bound of 1.5k+0.5 for every odd k. Additionally, they showed that every outer min-k-planar graph has treewidth at most 3k+1. We improve this upper bound to 3⋅⌊k/2⌋+4.
Our approach also allows us to upper bound the separation number, a parameter closely related to treewidth, of outer min-k-planar graphs by 2⋅⌊k/2⌋+4. This improves upon the previous bound of 2k+1 and achieves a bound with an optimal multiplicative constant.
Cite as
Rafał Pyzik. Treewidth of Outer k-Planar Graphs. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 28:1-28:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{pyzik:LIPIcs.GD.2025.28,
author = {Pyzik, Rafa{\l}},
title = {{Treewidth of Outer k-Planar Graphs}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {28:1--28:16},
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.2025.28},
URN = {urn:nbn:de:0030-drops-250141},
doi = {10.4230/LIPIcs.GD.2025.28},
annote = {Keywords: treewidth, outer k-planar graphs, outer min-k-planar graphs, separation number}
}
Document
Stabbing Faces by a Convex Curve
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
Universal Quality Metrics for Graph Drawings: Which Graphs Excite Us Most?
Abstract
Graphs are drawn for various purposes, and drawings are meant to display various features of a graph (such as planarity, Hamiltonicity). Still, there is a long history in measuring the quality of a graph drawing. Most of the metrics that have been implemented and used in large studies assume that graphs are drawn straight-line. Most of the studies use randomly generated graphs or one of very few existing benchmark sets that consist of graphs with a specific technical background (e.g., telecommunication networks).
In this paper, we extend ten commonly used metrics to node-link diagrams where edges can be curves or polygonal chains. We implement these measures and use them to evaluate a new collection of graph drawings that we have extracted from 27 proceedings of the Graph Drawing conference using an automated pipeline. We compare the "metrics landscape" of our new benchmark set, the GD-collection-v1, which seems to mostly contain manually drawn graphs, to the metric landscape of a benchmark set with randomly generated graphs and computer-generated straight-line drawings that has been used in a recent study [Mooney et al.; PacificVis 2024].
Comparing the GD-collection-v1 with the Mooney at al. dataset reveals a distinct metrics landscape: GD drawings come from much smaller graphs (median vertex number 11 vs. 48) and therefore attain higher medians on most readability metrics. For example, Neighbourhood Preservation (0.5 vs. 0.239) is markedly higher in the GD-collection-v1. We also find that a large proportion of extracted drawings contain curved and/or polygonal edges (57%), motivating the extended metric definitions.
Cite as
Gavin J. Mooney, Tim Hegemann, Alexander Wolff, Michael Wybrow, and Helen C. Purchase. Universal Quality Metrics for Graph Drawings: Which Graphs Excite Us Most?. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 30:1-30:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{mooney_et_al:LIPIcs.GD.2025.30,
author = {Mooney, Gavin J. and Hegemann, Tim and Wolff, Alexander and Wybrow, Michael and Purchase, Helen C.},
title = {{Universal Quality Metrics for Graph Drawings: Which Graphs Excite Us Most?}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {30:1--30:20},
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.2025.30},
URN = {urn:nbn:de:0030-drops-250162},
doi = {10.4230/LIPIcs.GD.2025.30},
annote = {Keywords: Graph drawing metrics, metric landscape, straight-line drawings, polyline drawings, curved drawings, automated extraction of graph drawings}
}
Document
From Local Pair-Crossing Number to Local Crossing Number
Abstract
We prove that if a graph can be drawn in the plane such that each edge crosses at most k other edges, then it can be redrawn so that each edge participates in at most k³+O(k²) crossings. This improves the previous exponential bound that follows from a result of Schaefer and Štefankovič and answers a question of Ackerman and Schaefer.
Cite as
Jacob Fox, János Pach, and Andrew Suk. From Local Pair-Crossing Number to Local Crossing Number. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 31:1-31:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{fox_et_al:LIPIcs.GD.2025.31,
author = {Fox, Jacob and Pach, J\'{a}nos and Suk, Andrew},
title = {{From Local Pair-Crossing Number to Local Crossing Number}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {31:1--31:6},
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.2025.31},
URN = {urn:nbn:de:0030-drops-250170},
doi = {10.4230/LIPIcs.GD.2025.31},
annote = {Keywords: Crossing numbers, pair crossing numbers}
}
Document
Planar Stories of Graph Drawings: Algorithms and Experiments
Abstract
We address the problem of computing a dynamic visualization of a geometric graph G as a sequence of frames. Each frame shows only a portion of the graph but their union covers G entirely. The two main requirements of our dynamic visualization are: (i) guaranteeing drawing stability, so to preserve the user’s mental map; (ii) keeping the visual complexity of each frame low. To satisfy the first requirement, we never change the position of the vertices. Regarding the second requirement, we avoid edge crossings in each frame. More precisely, in the first frame we visualize a suitable subset of non-crossing edges; in each subsequent frame, exactly one new edge enters the visualization and all the edges that cross with it are deleted. We call such a sequence of frames a planar story of G. Our goal is to find a planar story whose minimum number of edges contemporarily displayed is maximized (i.e., a planar story that maximizes the minimum frame size). Besides studying our model from a theoretical point of view, we also design and experimentally compare different algorithms, both exact techniques and heuristics. These algorithms provide an array of alternative trade-offs between efficiency and effectiveness, also depending on the structure of the input graph.
Cite as
Carla Binucci, Sabine Cornelsen, Walter Didimo, Seok-Hee Hong, Eleni Katsanou, Maurizio Patrignani, Antonios Symvonis, and Samuel Wolf. Planar Stories of Graph Drawings: Algorithms and Experiments. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 32:1-32:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{binucci_et_al:LIPIcs.GD.2025.32,
author = {Binucci, Carla and Cornelsen, Sabine and Didimo, Walter and Hong, Seok-Hee and Katsanou, Eleni and Patrignani, Maurizio and Symvonis, Antonios and Wolf, Samuel},
title = {{Planar Stories of Graph Drawings: Algorithms and Experiments}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {32:1--32:19},
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.2025.32},
URN = {urn:nbn:de:0030-drops-250182},
doi = {10.4230/LIPIcs.GD.2025.32},
annote = {Keywords: Graph Drawing, Dynamic Graphs, Graph Stories, Heuristics, ILP}
}
Document
Edge Densities of Drawings of Graphs with One Forbidden Cell
Abstract
A connected topological drawing of a graph divides the plane into a number of cells. The type of a cell c is the cyclic sequence of crossings and vertices along the boundary walk of c. For example, all triangular cells with three incident crossings and no incident vertex share the same cell type. When a non-homotopic drawing of an n-vertex multigraph G does not contain any such cells, Ackerman and Tardos [JCTA 2007] proved that G has at most 8n-20 edges, while Kaufmann, Klemz, Knorr, Reddy, Schröder, and Ueckerdt [GD 2024] showed that this bound is tight.
In this paper, we initiate the in-depth study of non-homotopic drawings that do not contain one fixed cell type 𝔠, and investigate the edge density of the corresponding multigraphs, i.e., the maximum possible number of edges. We consider non-homotopic as well as simple drawings, multigraphs as well as simple graphs, and every possible type of cell. For every combination of drawing style, graph type, and cell type, we give upper and lower bounds on the corresponding edge density. With the exception of the cell type with four incident crossings and no incident vertex, we show for every cell type 𝔠 that the edge density of n-vertex (multi)graphs with 𝔠-free drawings is either quadratic in n or linear in n. In most cases, our bounds are tight up to an additive constant.
Additionally, we improve the current lower bound on the edge density of simple graphs that admit a non-homotopic quasiplanar drawing from 7n-28 to 7.5n-28.
Cite as
Benedikt Hahn, Torsten Ueckerdt, and Birgit Vogtenhuber. Edge Densities of Drawings of Graphs with One Forbidden Cell. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 33:1-33:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{hahn_et_al:LIPIcs.GD.2025.33,
author = {Hahn, Benedikt and Ueckerdt, Torsten and Vogtenhuber, Birgit},
title = {{Edge Densities of Drawings of Graphs with One Forbidden Cell}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {33:1--33:17},
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.2025.33},
URN = {urn:nbn:de:0030-drops-250199},
doi = {10.4230/LIPIcs.GD.2025.33},
annote = {Keywords: Edge density, cell types, forbidden substructures, non-homotopic drawings, simple drawings}
}
Document
Layered Polyline Drawings of Planar Graphs
Abstract
A k-layer polyline drawing of a planar graph G is a planar drawing of G on a set L of k parallel lines such that each vertex is mapped to a point on L and each edge is mapped to a polygonal chain with the endpoints and bends lying on L. In the fixed embedding setting, the output drawing maintains the given planar embedding, whereas in the variable embedding setting, the embedding may change. Every n-vertex planar graph admits a polyline drawing on 2n/3 layers, which is the best known upper bound for both settings. We improve this bound in the variable embedding setting. We show that every planar graph can be drawn on 14n/27+O(√n) layers by choosing a proper planar embedding, breaking the long-standing 2n/3-layer barrier.
Cite as
Debajyoti Mondal. Layered Polyline Drawings of Planar Graphs. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 34:1-34:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{mondal:LIPIcs.GD.2025.34,
author = {Mondal, Debajyoti},
title = {{Layered Polyline Drawings of Planar Graphs}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {34:1--34:10},
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.2025.34},
URN = {urn:nbn:de:0030-drops-250202},
doi = {10.4230/LIPIcs.GD.2025.34},
annote = {Keywords: Layered Drawing, Variable Embedding, Polyline Drawing, Cycle Separator}
}
Document
A Walk on the Wild Side: A Shape-First Methodology for Orthogonal Drawings
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
Reconfiguration in Curve Arrangements to Reduce Self-Intersections and Popular Faces
Abstract
We study reconfiguration in curve arrangements, where a subset of the crossings are marked as switches which have three possible states, and the goal is to set the switches such that the resulting curve arrangement has few self-intersections, or few faces that are incident to the same curve multiple times (a.k.a. popular faces). Our results are that these problems are NP-hard, but FPT in the number of switches. Minimizing self-intersections is also FPT in the number of non-switchable crossings; for minimizing popular faces this problem remains open. Our results can be applied to generating curved nonograms, a type of logic puzzle that has received some attention lately. Specifically, our results make it possible to efficiently convert expert puzzles into advanced puzzles (or determine that this is impossible).
Cite as
Florestan Brunck, Hsien-Chih Chang, Maarten Löffler, Tim Ophelders, and Lena Schlipf. Reconfiguration in Curve Arrangements to Reduce Self-Intersections and Popular Faces. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 36:1-36:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{brunck_et_al:LIPIcs.GD.2025.36,
author = {Brunck, Florestan and Chang, Hsien-Chih and L\"{o}ffler, Maarten and Ophelders, Tim and Schlipf, Lena},
title = {{Reconfiguration in Curve Arrangements to Reduce Self-Intersections and Popular Faces}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {36:1--36:18},
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.2025.36},
URN = {urn:nbn:de:0030-drops-250220},
doi = {10.4230/LIPIcs.GD.2025.36},
annote = {Keywords: Curve Arrangements, Reconfiguration, Curve Arrangements, NP-hardness, Fixed-Parameter Tractability, Puzzle Generation}
}
Document
Show Me Your Best Side: Characteristics of User-Preferred Perspectives for 3D Graph Drawings
Abstract
The visual analysis of graphs in 3D has become increasingly popular, accelerated by the rise of immersive technology, such as augmented and virtual reality. Unlike 2D drawings, 3D graph layouts are highly viewpoint-dependent, making perspective selection critical for revealing structural and relational patterns. Despite its importance, there is limited empirical evidence guiding what constitutes an effective or preferred viewpoint from the user’s perspective. In this paper, we present a systematic investigation into user-preferred viewpoints in 3D graph visualisations. We conducted a controlled study with 23 participants in a virtual reality environment, where users selected their most and least preferred viewpoints for 36 different graphs varying in size and layout. From this data, enriched by qualitative feedback, we distil common strategies underlying viewpoint choice. We further analyse the alignment of user preferences with classical 2D aesthetic criteria (e.g., Crossings), 3D-specific measures (e.g., Node-Node Occlusion), and introduce a novel measure capturing the perceivability of a graph’s principal axes (Isometric Viewpoint Deviation). Our data-driven analysis indicates that Stress, Crossings, Gabriel Ratio, Edge-Node Overlap, and Isometric Viewpoint Deviation are key indicators of viewpoint preference. Beyond our findings, we contribute a publicly available dataset consisting of the graphs and computed aesthetic measures, supporting further research and the development of viewpoint evaluation measures for 3D graph drawing.
Cite as
Lucas Joos, Gavin J. Mooney, Maximilian T. Fischer, Daniel A. Keim, Falk Schreiber, Helen C. Purchase, and Karsten Klein. Show Me Your Best Side: Characteristics of User-Preferred Perspectives for 3D Graph Drawings. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 37:1-37:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{joos_et_al:LIPIcs.GD.2025.37,
author = {Joos, Lucas and Mooney, Gavin J. and Fischer, Maximilian T. and Keim, Daniel A. and Schreiber, Falk and Purchase, Helen C. and Klein, Karsten},
title = {{Show Me Your Best Side: Characteristics of User-Preferred Perspectives for 3D Graph Drawings}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {37:1--37:19},
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.2025.37},
URN = {urn:nbn:de:0030-drops-250236},
doi = {10.4230/LIPIcs.GD.2025.37},
annote = {Keywords: Graph Aesthetics, Immersive 3D, Node-Link Diagrams, Empirical Evaluation}
}
Document
Stress in Graph Drawings: Perception, Preference, and Performance
Abstract
Stress in a graph drawing has been a popular layout principle for more than two decades. Low stress drawings exhibit the property that the geometric distances between all pairs of nodes correlate with the shortest paths between them. The assumption has always been that low stress drawings are "nicer" and better support human perception and comprehension than high stress drawings. In this paper, we put these assumptions to the test. We use a normalised scale-independent and rotation-independent metric for stress; this is necessary to ensure strict controls on our experimental stimuli. We report on three experiments, exploring human perception of stress, preference for stress, and the effect of stress on a graph performance task. We conclude that people can see stress in a graph drawing, that they prefer low stress drawings, and that their performance in a shortest path task improves as stress decreases - thus empirically confirming long-standing assumptions.
Cite as
Gavin J. Mooney, Jacob Miller, Michael Wybrow, Stephen Kobourov, and Helen C. Purchase. Stress in Graph Drawings: Perception, Preference, and Performance. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 38:1-38:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{mooney_et_al:LIPIcs.GD.2025.38,
author = {Mooney, Gavin J. and Miller, Jacob and Wybrow, Michael and Kobourov, Stephen and Purchase, Helen C.},
title = {{Stress in Graph Drawings: Perception, Preference, and Performance}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {38:1--38:23},
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.2025.38},
URN = {urn:nbn:de:0030-drops-250240},
doi = {10.4230/LIPIcs.GD.2025.38},
annote = {Keywords: Graph Drawing, Graph Drawing Metrics, Stress, Visual Perception, User Study}
}
Document
Optimizing Wiggle in Storylines
Abstract
A storyline visualization shows interactions between characters over time. Each character is represented by an x-monotone curve. Time is mapped to the x-axis, and groups of characters that interact at a particular point t in time must be ordered consecutively in the y-dimension at x = t. The predominant objective in storyline optimization so far has been the minimization of crossings between (blocks of) characters. Building on this work, we investigate another important, but less studied quality criterion, namely the minimization of wiggle, i.e., the amount of vertical movement of the characters over time.
Given a storyline instance together with an ordering of the characters at any point in time, we show that wiggle count minimization is NP-complete. In contrast, we provide algorithms based on mathematical programming to solve linear wiggle height minimization and quadratic wiggle height minimization efficiently. Finally, we introduce a new method for routing character curves that focuses on keeping distances between neighboring curves constant as long as they run in parallel.
We have implemented our algorithms, and we conduct a case study that explores the differences between the three optimization objectives. We use existing benchmark data, but we also present a new use case for storylines, namely the visualization of rolling stock schedules in railway operation.
Cite as
Alexander Dobler, Tim Hegemann, Martin Nöllenburg, and Alexander Wolff. Optimizing Wiggle in Storylines. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 39:1-39:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{dobler_et_al:LIPIcs.GD.2025.39,
author = {Dobler, Alexander and Hegemann, Tim and N\"{o}llenburg, Martin and Wolff, Alexander},
title = {{Optimizing Wiggle in Storylines}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {39:1--39:17},
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.2025.39},
URN = {urn:nbn:de:0030-drops-250252},
doi = {10.4230/LIPIcs.GD.2025.39},
annote = {Keywords: Storyline visualization, wiggle minimization, NP-complete, linear programming, quadratic programming, experimental analysis}
}
Document
An Algorithm for Accurate and Simple-Looking Metaphorical Maps
Abstract
Metaphorical maps or contact representations are visual representations of vertex-weighted graphs that rely on the geographic map metaphor. The vertices are represented by countries, the weights by the areas of the countries, and the edges by contacts/boundaries among them. The accuracy with which the weights are mapped to areas and the simplicity of the polygons representing the countries are the two classical optimization goals for metaphorical maps. Mchedlidze & Schnorr [Mchedlidze and Schnorr, 2022] presented a force-based algorithm that creates metaphorical maps that balance between these two optimization goals. Their maps look visually simple, but the accuracy of the maps is far from optimal - the countries' areas can vary up to 30% compared to required. In this paper, we provide a multi-fold extension of the algorithm in [Mchedlidze and Schnorr, 2022]. More specifically:
1) Towards improving accuracy: We introduce the notion of region stiffness and suggest a technique for varying the stiffness based on the current pressure of map regions.
2) Towards maintaining simplicity: We introduce a weight coefficient to the pressure force exerted on each polygon point based on whether the corresponding point appears along a narrow passage.
3) Towards generality: We cover, in contrast to [Mchedlidze and Schnorr, 2022], non-triangulated graphs. This is done by either generating points where more than three regions meet or by introducing holes in the metaphorical map. We perform an extended experimental evaluation that, among other results, reveals that our algorithm is able to construct metaphorical maps with nearly perfect area accuracy with a little sacrifice in their simplicity.
Cite as
Eleni Katsanou, Tamara Mchedlidze, Antonios Symvonis, and Thanos Tolias. An Algorithm for Accurate and Simple-Looking Metaphorical Maps. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 40:1-40:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{katsanou_et_al:LIPIcs.GD.2025.40,
author = {Katsanou, Eleni and Mchedlidze, Tamara and Symvonis, Antonios and Tolias, Thanos},
title = {{An Algorithm for Accurate and Simple-Looking Metaphorical Maps}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {40:1--40:17},
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.2025.40},
URN = {urn:nbn:de:0030-drops-250268},
doi = {10.4230/LIPIcs.GD.2025.40},
annote = {Keywords: Metaphorical maps, contact representation, accuracy (cartographic error), simplicity (polygon complexity), force directed algorithm}
}
Document
Graph Drawing Contest Report
Graph Drawing Contest Report (Graph Drawing Contest Report)
Abstract
This report describes the 32nd Annual Graph Drawing Contest, held in conjunction with the 33rd International Symposium on Graph Drawing and Network Visualization (GD'25) at Linköping University, Norrköping, Sweden. The mission of the Graph Drawing Contest is to monitor and challenge the current state of the art in graph-drawing technology. This year’s edition featured two categories, a creative topic in which participants visualized a dataset based on the Netflix show Dark and a live challenge held at the conference where participants had to draw a graph on a grid, such that the drawing is k-planar for as low a k as possible. A special feature of this year’s contest is that the submissions to the creative topic were exhibited in the "Norrköping Decision Arena", a room with a circular annulus-shaped screen.
Cite as
Sara Di Bartolomeo, Fabian Klute, Debajyoti Mondal, and Jules Wulms. Graph Drawing Contest Report (Graph Drawing Contest Report). In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 41:1-41:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{dibartolomeo_et_al:LIPIcs.GD.2025.41,
author = {Di Bartolomeo, Sara and Klute, Fabian and Mondal, Debajyoti and Wulms, Jules},
title = {{Graph Drawing Contest Report}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {41:1--41:11},
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.2025.41},
URN = {urn:nbn:de:0030-drops-250275},
doi = {10.4230/LIPIcs.GD.2025.41},
annote = {Keywords: Graph Drawing, Information Visualization, Graph Drawing Contest}
}
Document
Graph Drawing Contest Abstract
Journey of a Time Machine (Graph Drawing Contest Abstract)
Abstract
What does the story of Netflix’s Dark look like from the perspective of the suitcase time machine? We visualized this perspective with our contribution to the Graph Drawing Contest Creative Topic. We outline the used ideas, concepts and give a high-level overview over the algorithmic implementations.
Cite as
Florian Sass, Jakob Speitkamp, and Guilherme Monteiro Oliveira. Journey of a Time Machine (Graph Drawing Contest Abstract). In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 42:1-42:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{sass_et_al:LIPIcs.GD.2025.42,
author = {Sass, Florian and Speitkamp, Jakob and Monteiro Oliveira, Guilherme},
title = {{Journey of a Time Machine}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {42:1--42:2},
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.2025.42},
URN = {urn:nbn:de:0030-drops-250286},
doi = {10.4230/LIPIcs.GD.2025.42},
annote = {Keywords: graph drawing, Dark, grid-based graph drawing, 360 degree visualization, cyclic graph drawing}
}
Document
Graph Drawing Contest Abstract
Winning the GD Challenge for the 4th Time: Our Approach (Graph Drawing Contest Abstract)
Abstract
We present the approach we designed to tackle and win the 2025 Graph Drawing Challenge on minimizing the k-planarity of graphs. Our method employs a multi-stage heuristic centered around two Simulated Annealing (SA) algorithms: the first aims to reduce the total number of crossings, while the second improves the k-value. To obtain a good initial solution, we first applied tools from the OGDF library, which helped reduce crossings. The challenge consisted of nine instances to optimize. Our approach achieved the best results on eight out of nine instances - sharing the top score twice with other teams and ranking first alone in six cases.
Cite as
Julien Bianchetti and Laurent Moalic. Winning the GD Challenge for the 4th Time: Our Approach (Graph Drawing Contest Abstract). In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 43:1-43:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{bianchetti_et_al:LIPIcs.GD.2025.43,
author = {Bianchetti, Julien and Moalic, Laurent},
title = {{Winning the GD Challenge for the 4th Time: Our Approach}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {43:1--43:4},
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.2025.43},
URN = {urn:nbn:de:0030-drops-250293},
doi = {10.4230/LIPIcs.GD.2025.43},
annote = {Keywords: Graph Drawing Contest, simulated annealing, k-planarity}
}
Document
Poster Abstract
Recovering Graphs from Their Witness Unit Square Representation (Poster Abstract)
Abstract
A wUSR of a graph G is a set of unit squares in the plane, one per vertex, if two vertices have an edge in G if their squares overlap and the overlap contains no witness. We present an output sensitive algorithm to compute a graph G based on its given witness unit square representation.
Cite as
Maarten Löffler, Frank Staals, and Soeren Terziadis. Recovering Graphs from Their Witness Unit Square Representation (Poster Abstract). In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 44:1-44:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{loffler_et_al:LIPIcs.GD.2025.44,
author = {L\"{o}ffler, Maarten and Staals, Frank and Terziadis, Soeren},
title = {{Recovering Graphs from Their Witness Unit Square Representation}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {44:1--44:4},
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.2025.44},
URN = {urn:nbn:de:0030-drops-250306},
doi = {10.4230/LIPIcs.GD.2025.44},
annote = {Keywords: proximity graphs, geometric intersection graphs, witness representation, unit square intersection graph, output sensitive algorithm, range searching}
}
Document
Poster Abstract
TReView: Visualizing the European Union Transparency Register (Poster Abstract)
Abstract
We present TReView, the first visual analytics system for the exploration of the European Union (EU) Transparency Register, a large repository that aims to enhance transparency around lobbying activities within the EU, by enabling public oversight of meetings between lobbyists and EU officials.
Cite as
Cristiano Bernardini, Davide Campanelli, Walter Didimo, Luca Grilli, Giuseppe Liotta, and Benedetto Ponti. TReView: Visualizing the European Union Transparency Register (Poster Abstract). In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 45:1-45:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{bernardini_et_al:LIPIcs.GD.2025.45,
author = {Bernardini, Cristiano and Campanelli, Davide and Didimo, Walter and Grilli, Luca and Liotta, Giuseppe and Ponti, Benedetto},
title = {{TReView: Visualizing the European Union Transparency Register}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {45:1--45:5},
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.2025.45},
URN = {urn:nbn:de:0030-drops-250310},
doi = {10.4230/LIPIcs.GD.2025.45},
annote = {Keywords: Transparency Registry, European Union, Graph Visualization, Interactive Visualization, Visual Analytics}
}
Document
Poster Abstract
Counting Triangulations of Fixed Cardinal Degrees (Poster Abstract)
Abstract
A fixed set of vertices in the plane may have multiple planar straight-line triangulations in which the degree of each vertex is the same. As such, the degree information does not completely determine the triangulation. We show that even if we know, for each vertex, the number of neighbors in each of the four cardinal directions, the triangulation is not completely determined. We show that counting such triangulations is #P-hard via a reduction from #3-regular bipartite planar vertex cover. pty
Cite as
Erin Chambers, Tim Ophelders, Anna Schenfisch, and Julia Sollberger. Counting Triangulations of Fixed Cardinal Degrees (Poster Abstract). In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 46:1-46:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{chambers_et_al:LIPIcs.GD.2025.46,
author = {Chambers, Erin and Ophelders, Tim and Schenfisch, Anna and Sollberger, Julia},
title = {{Counting Triangulations of Fixed Cardinal Degrees}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {46:1--46:4},
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.2025.46},
URN = {urn:nbn:de:0030-drops-250325},
doi = {10.4230/LIPIcs.GD.2025.46},
annote = {Keywords: Planar Triangulations, Degree Information, #P-Hardness}
}
Document
Poster Abstract
Reconfigurations of Plane Caterpillars and Paths (Poster Abstract)
Abstract
Let S be a point set in the plane, and let 𝒫(S) and 𝒞(S) be the sets of all plane spanning paths and caterpillars on S. We study reconfiguration operations on 𝒫(S) and 𝒞(S). In particular, we prove that all of the commonly studied reconfigurations on plane spanning trees still yield connected reconfiguration graphs for caterpillars when S is in convex position. If S is in general position, we show that the rotation, compatible flip and flip graphs of 𝒞(S) are connected while the slide graph is sometimes disconnected, but always has a component of size 1/4(3ⁿ-1). We then study sizes of connected components in reconfiguration graphs of plane spanning paths. In this direction, we show that no component of size at most 7 can exist in the flip graph on 𝒫(S).
Cite as
Todor Antić, Guillermo Gamboa Quintero, and Jelena Glišić. Reconfigurations of Plane Caterpillars and Paths (Poster Abstract). In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 47:1-47:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{antic_et_al:LIPIcs.GD.2025.47,
author = {Anti\'{c}, Todor and Gamboa Quintero, Guillermo and Gli\v{s}i\'{c}, Jelena},
title = {{Reconfigurations of Plane Caterpillars and Paths}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {47:1--47:5},
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.2025.47},
URN = {urn:nbn:de:0030-drops-250337},
doi = {10.4230/LIPIcs.GD.2025.47},
annote = {Keywords: reconfiguration graph, caterpillar, path, geometric graph}
}
Document
Poster Abstract
Drawing Trees and Cacti with Integer Edge Lengths on a Polynomial-Size Grid (Poster Abstract)
Abstract
A strengthened version of Harborth’s well-known conjecture - known as Kleber’s conjecture - states that every planar graph admits a planar straight-line drawing where every edge has integer length and each vertex is restricted to the integer grid. Positive results for Kleber’s conjecture are known for planar 3-regular graphs, for planar graphs that have maximum degree 4, and for planar 3-trees. However, all but one of the existing results are existential and do not provide bounds on the required grid size. We provide polynomial-time algorithms for computing crossing-free straight-line drawings of trees and cactus graphs with integer edge lengths and integer vertex position on polynomial-size integer grids. We also give an historic overview of planar straight-line graph drawing results.
Cite as
Henry Förster, Stephen Kobourov, Jacob Miller, and Johannes Zink. Drawing Trees and Cacti with Integer Edge Lengths on a Polynomial-Size Grid (Poster Abstract). In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 48:1-48:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{forster_et_al:LIPIcs.GD.2025.48,
author = {F\"{o}rster, Henry and Kobourov, Stephen and Miller, Jacob and Zink, Johannes},
title = {{Drawing Trees and Cacti with Integer Edge Lengths on a Polynomial-Size Grid}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {48:1--48:4},
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.2025.48},
URN = {urn:nbn:de:0030-drops-250349},
doi = {10.4230/LIPIcs.GD.2025.48},
annote = {Keywords: Harborth’s conjecture, tree drawings, cactus drawings, grid drawings}
}
Document
Poster Abstract
Defective Linear Layouts of Graphs (Poster Abstract)
Abstract
A linear layout of a graph defines a total order of the vertices and partitions the edges into either stacks or queues, i.e., crossing-free and non-nested sets of edges along the order, respectively. In this work, we study defective linear layouts that allow forbidden patterns among edges of the same set. Our focus is on k-defective stack layouts and k-defective queue layouts, in which the conflict graph representing the forbidden patterns among the edges of each stack or queue has maximum degree at most k.
Cite as
Michael A. Bekos, Carla Binucci, Emilio Di Giacomo, Walter Didimo, Luca Grilli, Maria Eleni Pavlidi, Alessandra Tappini, and Alexandra Weinberger. Defective Linear Layouts of Graphs (Poster Abstract). In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 49:1-49:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{bekos_et_al:LIPIcs.GD.2025.49,
author = {Bekos, Michael A. and Binucci, Carla and Di Giacomo, Emilio and Didimo, Walter and Grilli, Luca and Pavlidi, Maria Eleni and Tappini, Alessandra and Weinberger, Alexandra},
title = {{Defective Linear Layouts of Graphs}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {49:1--49:4},
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.2025.49},
URN = {urn:nbn:de:0030-drops-250350},
doi = {10.4230/LIPIcs.GD.2025.49},
annote = {Keywords: Linear layouts, stack layouts, queue layouts, defective layouts}
}
Document
Poster Abstract
Reeb Lobsters Are 1-Planar (Poster Abstract)
Abstract
Very recently, Chambers, Fasy, Hosseini Sereshgi and Löffler [Erin W. Chambers et al., 2025] showed that every Reeb caterpillar admits a crossing-free drawing. It turns out that this does not hold for Reeb lobsters but we show that these graphs admit drawings with at most one crossing per edge.
Cite as
Maarten Löffler, Miriam Münch, and Ignaz Rutter. Reeb Lobsters Are 1-Planar (Poster Abstract). In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 50:1-50:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{loffler_et_al:LIPIcs.GD.2025.50,
author = {L\"{o}ffler, Maarten and M\"{u}nch, Miriam and Rutter, Ignaz},
title = {{Reeb Lobsters Are 1-Planar}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {50:1--50:5},
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.2025.50},
URN = {urn:nbn:de:0030-drops-250365},
doi = {10.4230/LIPIcs.GD.2025.50},
annote = {Keywords: Reeb graphs, layered drawings, local crossing number}
}
Document
Poster Abstract
Graph Tiles (Poster Abstract)
Abstract
We define a graph tile to be a unit square (or more generally, a polygon) on which a piece of a graph has been drawn/embedded; in particular, it may have vertices in its interior, edges connecting those vertices, or half-edges that extend to the boundary of the tile. In a graph tiling problem, we are given as input a set of graph tiles, with multiplicities, and the output is an arrangement of those tiles forming a graph of larger area. We focus on a simple tile set: unit square tiles with a central vertex and either a half-edge or no half-edge on each side. Up to symmetry this gives us six different types. We characterize which multiplicities are compatible for sets of at most three different tiles.
Cite as
Oswin Aichholzer, Robert Ganian, Phillip Keldenich, Maarten Löffler, Gert Meijer, Alexandra Weinberger, and Carola Wenk. Graph Tiles (Poster Abstract). In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 51:1-51:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{aichholzer_et_al:LIPIcs.GD.2025.51,
author = {Aichholzer, Oswin and Ganian, Robert and Keldenich, Phillip and L\"{o}ffler, Maarten and Meijer, Gert and Weinberger, Alexandra and Wenk, Carola},
title = {{Graph Tiles}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {51:1--51:5},
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.2025.51},
URN = {urn:nbn:de:0030-drops-250371},
doi = {10.4230/LIPIcs.GD.2025.51},
annote = {Keywords: graph tiles}
}
Document
Poster Abstract
Investigating Crossing Perception in 3D Graph Visualisation (Poster Abstract)
Abstract
Human perception and understanding of graph drawings is influenced by a variety of impact factors for which quality measures such as the number of crossings are used as a proxy indicator. For the more and more common stereoscopic 3D (S3D) graph visualisations, evidence is required to better understand graph perception and its relation to quality measures. We investigate the perception of crossing configurations in S3D graph visualisations and present the results of a study.
Cite as
Ying Zhang, Niklas Gröne, Giuseppe Liotta, Falk Schreiber, and Karsten Klein. Investigating Crossing Perception in 3D Graph Visualisation (Poster Abstract). In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 52:1-52:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{zhang_et_al:LIPIcs.GD.2025.52,
author = {Zhang, Ying and Gr\"{o}ne, Niklas and Liotta, Giuseppe and Schreiber, Falk and Klein, Karsten},
title = {{Investigating Crossing Perception in 3D Graph Visualisation}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {52:1--52:5},
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.2025.52},
URN = {urn:nbn:de:0030-drops-250381},
doi = {10.4230/LIPIcs.GD.2025.52},
annote = {Keywords: Graph Perception, Stereoscopic 3D Graph Visualisation, Crossing Configurations}
}
Document
Poster Abstract
Edge Bundling as a Multi-Objective Optimization Problem (Poster Abstract)
Abstract
Edge bundling is a technique commonly used to reduce visual clutter and improve the comprehension of the drawings of large graphs. Here, we model edge bundling as a multi-objective optimization problem and employ clustering strategies, metaheuristic and Pareto analysis to identify non-dominated solutions for some classical graphs from the literature.
Cite as
Raissa dos Santos Vieira, Hugo A. D. do Nascimento, Joelma de Moura Ferreira, Les Foulds, Karsten Klein, and Falk Schreiber. Edge Bundling as a Multi-Objective Optimization Problem (Poster Abstract). In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 53:1-53:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{vieira_et_al:LIPIcs.GD.2025.53,
author = {Vieira, Raissa dos Santos and Nascimento, Hugo A. D. do and Ferreira, Joelma de Moura and Foulds, Les and Klein, Karsten and Schreiber, Falk},
title = {{Edge Bundling as a Multi-Objective Optimization Problem}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {53:1--53:5},
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.2025.53},
URN = {urn:nbn:de:0030-drops-250397},
doi = {10.4230/LIPIcs.GD.2025.53},
annote = {Keywords: Graph Drawing, Edge Bundling, Visual Clutter, Multi-objective Optimization}
}
Document
Poster Abstract
BH-tsNET, FIt-tsNET, L-tsNET: Fast tsNET Algorithms for Large Graph Drawing (Poster Abstract)
Abstract
The tsNET algorithm adapts the popular dimensional reduction method t-SNE for graph drawing to compute high-quality drawings, preserving the neighborhood and clustering structure. However, its O(nm) runtime results in poor scalability for large graphs. In this poster, we present three fast algorithms for reducing the time complexity of tsNET to O(n log n) time and O(n) time, by integrating new fast methods for computation of high-dimensional probabilities and entropy computation with fast t-SNE algorithms for computation of KL divergence gradient. Specifically, we present two O(n log n)-time algorithms BH-tsNET and FIt-tsNET, incorporating partial BFS-based high-dimensional probability computation and a new quadtree-based entropy computation with fast t-SNE algorithms, and O(n)-time algorithm L-tsNET, introducing a new fast interpolation-based entropy computation. Extensive experiments using benchmark data sets confirm that BH-tsNET, FIt-tsNET, and L-tsNET outperform tsNET, achieving 93.5%, 96%, and 98.6% faster runtime, respectively, while computing similar quality drawings in terms of quality metrics (neighborhood preservation, stress, shape-based metrics, and edge crossing) and visual comparison.
Cite as
Amyra Meidiana, Seok-Hee Hong, and Kwan-Liu Ma. BH-tsNET, FIt-tsNET, L-tsNET: Fast tsNET Algorithms for Large Graph Drawing (Poster Abstract). In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 54:1-54:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{meidiana_et_al:LIPIcs.GD.2025.54,
author = {Meidiana, Amyra and Hong, Seok-Hee and Ma, Kwan-Liu},
title = {{BH-tsNET, FIt-tsNET, L-tsNET: Fast tsNET Algorithms for Large Graph Drawing}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {54:1--54:5},
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.2025.54},
URN = {urn:nbn:de:0030-drops-250400},
doi = {10.4230/LIPIcs.GD.2025.54},
annote = {Keywords: tsNET, t-SNE, Large Graph Drawing}
}
Document
Poster Abstract
EnMRgy: Energy Network Analysis in Mixed Reality (Poster Abstract)
Abstract
The shifting and ever-growing demand for energy, for instance, driven by transformations towards new technologies such as electric vehicles, heat pumps, battery storage, or rooftop solar, requires urban infrastructure to adapt. Upgrading legacy infrastructure, such as undersized electric cables, is costly, time-consuming, and disruptive, and therefore requires a holistic perspective and thorough urban planning that considers multi energy systems and co-located utilities. We present EnMRgy, a mixed-reality decision-support system that enables experts and decision-makers to explore a city’s energy distribution networks, together with demand simulations and scenarios for infrastructure development. Within an immersive 3D city context, an energy network such as a power grid, modelled as a weighted graph, is visualised. Interactive functionalities allow users to adjust visual representations and compare scenarios across three different views. Our work enables evidence-based strategic planning for future-ready energy networks.
Cite as
Lucas Joos, Maximilian T. Fischer, Alexander Frings, and Daniel A. Keim. EnMRgy: Energy Network Analysis in Mixed Reality (Poster Abstract). In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 55:1-55:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{joos_et_al:LIPIcs.GD.2025.55,
author = {Joos, Lucas and Fischer, Maximilian T. and Frings, Alexander and Keim, Daniel A.},
title = {{EnMRgy: Energy Network Analysis in Mixed Reality}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {55:1--55:5},
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.2025.55},
URN = {urn:nbn:de:0030-drops-250412},
doi = {10.4230/LIPIcs.GD.2025.55},
annote = {Keywords: Energy, Node-Link Diagrams, Immersive Analytics, Mixed Reality}
}
Document
Poster Abstract
Using Reinforcement Learning to Optimize the Global and Local Crossing Number (Poster Abstract)
Abstract
We present a novel approach to graph drawing based on reinforcement learning for minimizing the global and the local crossing number, that is, the total number of edge crossings and the maximum number of crossings on any edge, respectively. An agent learns how to move a vertex based on a given observation vector. The agent receives feedback in the form of local reward signals tied to crossing reduction. To generate an initial layout, we use a stress-based graph-drawing algorithm. We compare our method against force- and stress-based baseline algorithms as well as three established algorithms for global crossing minimization on a suite of benchmark graphs. The experiments show mixed results: our current algorithm is mainly competitive for the local crossing number.
Cite as
Timo Brand, Henry Förster, Stephen Kobourov, Robin Schukrafft, Markus Wallinger, and Johannes Zink. Using Reinforcement Learning to Optimize the Global and Local Crossing Number (Poster Abstract). In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 56:1-56:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
Copy BibTex To Clipboard
@InProceedings{brand_et_al:LIPIcs.GD.2025.56,
author = {Brand, Timo and F\"{o}rster, Henry and Kobourov, Stephen and Schukrafft, Robin and Wallinger, Markus and Zink, Johannes},
title = {{Using Reinforcement Learning to Optimize the Global and Local Crossing Number}},
booktitle = {33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
pages = {56:1--56:4},
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.2025.56},
URN = {urn:nbn:de:0030-drops-250420},
doi = {10.4230/LIPIcs.GD.2025.56},
annote = {Keywords: Reinforcement Learning, Crossing Minimization, Local Crossing Number}
}