Volume
LIPIcs, Volume 320
32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)
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Part of:
Series:
Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Graph Drawing and Network Visualization (GD)
Event
GD 2024, September 18-20, 2024, Vienna, AustriaEditors
Publication Details
- published at: 2024-10-28
- Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- ISBN: 978-3-95977-343-0
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Document
Complete Volume
LIPIcs, Volume 320, GD 2024, Complete Volume
Abstract
LIPIcs, Volume 320, GD 2024, Complete Volume
Cite as
32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 1-754, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@Proceedings{felsner_et_al:LIPIcs.GD.2024,
title = {{LIPIcs, Volume 320, GD 2024, Complete Volume}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {1--754},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024},
URN = {urn:nbn:de:0030-drops-220891},
doi = {10.4230/LIPIcs.GD.2024},
annote = {Keywords: LIPIcs, Volume 320, GD 2024, Complete Volume}
}
Document
Front Matter
Front Matter, Table of Contents, Preface, Conference Organization
Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as
32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 0:i-0:xiv, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{felsner_et_al:LIPIcs.GD.2024.0,
author = {Felsner, Stefan and Klein, Karsten},
title = {{Front Matter, Table of Contents, Preface, Conference Organization}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {0:i--0:xiv},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.0},
URN = {urn:nbn:de:0030-drops-220882},
doi = {10.4230/LIPIcs.GD.2024.0},
annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Invited Talk
How Can Biclique Covers Help in Matching Problems (Invited Talk)
Abstract
In several settings one encounters assignment or matching problems between objects of two different types, and needs to run a computation on a bipartite graph. While this graph can potentially be dense, it can sometimes be represented compactly using a biclique cover. This is in particular often the case when the objects are geometric - we will look at examples, and see how recent progress on maximum flow can be combined with such biclique covers to obtain faster algorithms.
Cite as
Otfried Cheong. How Can Biclique Covers Help in Matching Problems (Invited Talk). In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, p. 1:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{cheong:LIPIcs.GD.2024.1,
author = {Cheong, Otfried},
title = {{How Can Biclique Covers Help in Matching Problems}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {1:1--1:1},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.1},
URN = {urn:nbn:de:0030-drops-212853},
doi = {10.4230/LIPIcs.GD.2024.1},
annote = {Keywords: Matching problems}
}
Document
Invited Talk
How Can Algorithms Help in Protecting Our Privacy (Invited Talk)
Abstract
Decisions are increasingly automated using rules that were learnt from personal data. Thus, it is important to guarantee that the privacy of the data is protected during the learning process. To formalize the notion of an algorithm that protects the privacy of its data, differential privacy was introduced by Dwork, McSherry, Nissim, and Smith in 2006. It is a rigorous mathematical definition to analyze the privacy properties of an algorithm - or the lack thereof. In this talk I will give an introduction to differential privacy with an emphasis on differential private algorithms that can handle dynamically changing input data.
Cite as
Monika Henzinger. How Can Algorithms Help in Protecting Our Privacy (Invited Talk). In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{henzinger:LIPIcs.GD.2024.2,
author = {Henzinger, Monika},
title = {{How Can Algorithms Help in Protecting Our Privacy}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {2:1--2:1},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.2},
URN = {urn:nbn:de:0030-drops-212864},
doi = {10.4230/LIPIcs.GD.2024.2},
annote = {Keywords: Matching problems}
}
Document
The Euclidean MST-Ratio for Bi-Colored Lattices
Abstract
Given a finite set, A ⊆ ℝ², and a subset, B ⊆ A, the MST-ratio is the combined length of the minimum spanning trees of B and A⧵B divided by the length of the minimum spanning tree of A. The question of the supremum, over all sets A, of the maximum, over all subsets B, is related to the Steiner ratio, and we prove this sup-max is between 2.154 and 2.427. Restricting ourselves to 2-dimensional lattices, we prove that the sup-max is 2, while the inf-max is 1.25. By some margin the most difficult of these results is the upper bound for the inf-max, which we prove by showing that the hexagonal lattice cannot have MST-ratio larger than 1.25.
Cite as
Sebastiano Cultrera di Montesano, Ondřej Draganov, Herbert Edelsbrunner, and Morteza Saghafian. The Euclidean MST-Ratio for Bi-Colored Lattices. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 3:1-3:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{cultreradimontesano_et_al:LIPIcs.GD.2024.3,
author = {Cultrera di Montesano, Sebastiano and Draganov, Ond\v{r}ej and Edelsbrunner, Herbert and Saghafian, Morteza},
title = {{The Euclidean MST-Ratio for Bi-Colored Lattices}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {3:1--3:23},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.3},
URN = {urn:nbn:de:0030-drops-212878},
doi = {10.4230/LIPIcs.GD.2024.3},
annote = {Keywords: Minimum spanning Trees, Steiner Ratio, Lattices, Partitions}
}
Document
Enumeration of Intersection Graphs of x-Monotone Curves
Abstract
A curve in the plane is x-monotone if every vertical line intersects it at most once. A family of curves are called pseudo-segments if every pair of them have at most one point in common. We construct 2^Ω(n^{4/3}) families, each consisting of n labelled x-monotone pseudo-segments such that their intersection graphs are different. On the other hand, we show that the number of such intersection graphs is at most 2^O(n^{3/2-ε}), where ε > 0 is a suitable constant. Our proof uses an upper bound on the number of set systems of size m on a ground set of size n, with VC-dimension at most d. Much better upper bounds are obtained if we only count bipartite intersection graphs, or, in general, intersection graphs with bounded chromatic number.
Cite as
Jacob Fox, János Pach, and Andrew Suk. Enumeration of Intersection Graphs of x-Monotone Curves. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 4:1-4:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{fox_et_al:LIPIcs.GD.2024.4,
author = {Fox, Jacob and Pach, J\'{a}nos and Suk, Andrew},
title = {{Enumeration of Intersection Graphs of x-Monotone Curves}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {4:1--4:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.4},
URN = {urn:nbn:de:0030-drops-212887},
doi = {10.4230/LIPIcs.GD.2024.4},
annote = {Keywords: Enumeration, intersection graphs, pseudo-segments, x-monotone}
}
Document
Holes in Convex and Simple Drawings
Abstract
Gons and holes in point sets have been extensively studied in the literature. For simple drawings of the complete graph a generalization of the Erdős-Szekeres theorem is known and empty triangles have been investigated. We introduce a notion of k-holes for simple drawings and study their existence with respect to the convexity hierarchy. We present a family of simple drawings without 4-holes and prove a generalization of Gerken’s empty hexagon theorem for convex drawings. A crucial intermediate step will be the structural investigation of pseudolinear subdrawings in convex drawings.
Cite as
Helena Bergold, Joachim Orthaber, Manfred Scheucher, and Felix Schröder. Holes in Convex and Simple Drawings. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 5:1-5:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{bergold_et_al:LIPIcs.GD.2024.5,
author = {Bergold, Helena and Orthaber, Joachim and Scheucher, Manfred and Schr\"{o}der, Felix},
title = {{Holes in Convex and Simple Drawings}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {5:1--5:9},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.5},
URN = {urn:nbn:de:0030-drops-212895},
doi = {10.4230/LIPIcs.GD.2024.5},
annote = {Keywords: simple topological graph, convexity hierarchy, k-gon, k-hole, empty k-cycle, Erd\H{o}s-Szekeres theorem, Empty Hexagon theorem, planar point set, pseudolinear drawing}
}
Document
1-Planar Unit Distance Graphs
Abstract
A matchstick graph is a plane graph with edges drawn as unit distance line segments. This class of graphs was introduced by Harborth who conjectured that a matchstick graph on n vertices can have at most ⌊3n-√{12n-3}⌋ edges. Recently his conjecture was settled by Lavollée and Swanepoel. In this paper we consider 1-planar unit distance graphs. We say that a graph is a 1-planar unit distance graph if it can be drawn in the plane such that all edges are drawn as unit distance line segments while each of them are involved in at most one crossing. We show that such graphs on n vertices can have at most 3n-∜{n}/10 edges.
Cite as
Panna Gehér and Géza Tóth. 1-Planar Unit Distance Graphs. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 6:1-6:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{geher_et_al:LIPIcs.GD.2024.6,
author = {Geh\'{e}r, Panna and T\'{o}th, G\'{e}za},
title = {{1-Planar Unit Distance Graphs}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {6:1--6:9},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.6},
URN = {urn:nbn:de:0030-drops-212900},
doi = {10.4230/LIPIcs.GD.2024.6},
annote = {Keywords: unit distance graph, 1-planar, matchstick graph}
}
Document
The Density Formula: One Lemma to Bound Them All
Abstract
We introduce the Density Formula for (topological) drawings of graphs in the plane or on the sphere, which relates the number of edges, vertices, crossings, and sizes of cells in the drawing. We demonstrate its capability by providing several applications: we prove tight upper bounds on the edge density of various beyond-planar graph classes, including so-called k-planar graphs with k = 1,2, fan-crossing/fan-planar graphs, k-bend RAC-graphs with k = 0,1,2, quasiplanar graphs, and k^+-real face graphs. In some cases (1-bend and 2-bend RAC-graphs and fan-crossing/fan-planar graphs), we thereby obtain the first tight upper bounds on the edge density of the respective graph classes. In other cases, we give new streamlined and significantly shorter proofs for bounds that were already known in the literature. Thanks to the Density Formula, all of our proofs are mostly elementary counting and mostly circumvent the typical intricate case analysis found in earlier proofs. Further, in some cases (simple and non-homotopic quasiplanar graphs), our alternative proofs using the Density Formula lead to the first tight lower bound examples.
Cite as
Michael Kaufmann, Boris Klemz, Kristin Knorr, Meghana M. Reddy, Felix Schröder, and Torsten Ueckerdt. The Density Formula: One Lemma to Bound Them All. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 7:1-7:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{kaufmann_et_al:LIPIcs.GD.2024.7,
author = {Kaufmann, Michael and Klemz, Boris and Knorr, Kristin and M. Reddy, Meghana and Schr\"{o}der, Felix and Ueckerdt, Torsten},
title = {{The Density Formula: One Lemma to Bound Them All}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {7:1--7:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.7},
URN = {urn:nbn:de:0030-drops-212913},
doi = {10.4230/LIPIcs.GD.2024.7},
annote = {Keywords: beyond-planar, density, fan-planar, fan-crossing, right-angle crossing, quasiplanar}
}
Document
Note on Min- k-Planar Drawings of Graphs
Abstract
The k-planar graphs, which are (usually with small values of k such as 1,2,3) subject to recent intense research, admit a drawing in which edges are allowed to cross, but each one edge is allowed to carry at most k crossings. In recently introduced [Binucci et al., GD 2023] min-k-planar drawings of graphs, edges may possibly carry more than k crossings, but in any two crossing edges, at least one of the two must have at most k crossings. In both concepts, one may consider general drawings or a popular restricted concept of drawings called simple. In a simple drawing, every two edges are allowed to cross at most once, and any two edges which share a vertex are forbidden to cross.
While, regarding the former concept, it is for k ≤ 3 known (but perhaps not widely known) that every general k-planar graph admits a simple k-planar drawing and this ceases to be true for any k ≤ 4, the difference between general and simple drawings in the latter concept is more striking. We prove that there exist graphs with a min-2-planar drawing, or with a min-3-planar drawing avoiding crossings of adjacent edges, which have no simple min-k-planar drawings for arbitrarily large fixed k.
Cite as
Petr Hliněný and Lili Ködmön. Note on Min- k-Planar Drawings of Graphs. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 8:1-8:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{hlineny_et_al:LIPIcs.GD.2024.8,
author = {Hlin\v{e}n\'{y}, Petr and K\"{o}dm\"{o}n, Lili},
title = {{Note on Min- k-Planar Drawings of Graphs}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {8:1--8:10},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.8},
URN = {urn:nbn:de:0030-drops-212924},
doi = {10.4230/LIPIcs.GD.2024.8},
annote = {Keywords: Crossing Number, Planarity, k-Planar Graph, Min-k-Planar Graph}
}
Document
Partitioning Complete Geometric Graphs on Dense Point Sets into Plane Subgraphs
Abstract
A complete geometric graph consists of a set P of n points in the plane, in general position, and all segments (edges) connecting them. It is a well known question of Bose, Hurtado, Rivera-Campo, and Wood, whether there exists a positive constant c < 1, such that every complete geometric graph on n points can be partitioned into at most cn plane graphs (that is, noncrossing subgraphs). We answer this question in the affirmative in the special case where the underlying point set P is dense, which means that the ratio between the maximum and the minimum distances in P is of the order of Θ(√n).
Cite as
Adrian Dumitrescu and János Pach. Partitioning Complete Geometric Graphs on Dense Point Sets into Plane Subgraphs. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 9:1-9:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{dumitrescu_et_al:LIPIcs.GD.2024.9,
author = {Dumitrescu, Adrian and Pach, J\'{a}nos},
title = {{Partitioning Complete Geometric Graphs on Dense Point Sets into Plane Subgraphs}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {9:1--9:10},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.9},
URN = {urn:nbn:de:0030-drops-212939},
doi = {10.4230/LIPIcs.GD.2024.9},
annote = {Keywords: Convexity, complete geometric Graph, crossing Family, plane Subgraph}
}
Document
Constrained Outer-String Representations
Abstract
An outer-string representation of a graph is an intersection representation in which each vertex is represented by a curve that is contained in the unit disk and has at least one endpoint on the boundary of the unit disk. In an outer-1-string representation the curves representing any two vertices are in addition allowed to intersect at most once.
In this paper, we consider the following constrained version: Given a graph G plus a cyclic order v_1,…,v_n of the vertices in G, test whether G has an outer-string or an outer-1-string representation in which the curves representing v_1,…,v_n intersect the boundary of the unit disk in this order. We first show that a graph has an outer-string representation for all possible cyclic orders of the vertices if and only if the graph is the complement of a chordal graph. Then we turn towards the situation where one particular cyclic order of the vertices is fixed.
We characterize the chordal graphs admitting a constrained outer-string representation and the trees and cycles admitting a constrained outer-1-string representation. The characterizations yield polynomial-time recognition and construction algorithms; in the case of outer-1-string representations the run time is linear. We also show how to decide in polynomial time whether an arbitrary graph admits a constrained L-shaped outer-1-string representation. In an L-shaped representation the curves are 1-bend orthogonal polylines anchored on a horizontal line, and they are contained in the half-plane below that line. However, not even all paths with a constrained outer-1-string representation admit one with L-shapes. We show that 2-bend orthogonal polylines are sufficient for trees and cycles with a constrained outer-1-string representation.
Cite as
Therese Biedl, Sabine Cornelsen, Jan Kratochvíl, and Ignaz Rutter. Constrained Outer-String Representations. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 10:1-10:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{biedl_et_al:LIPIcs.GD.2024.10,
author = {Biedl, Therese and Cornelsen, Sabine and Kratochv{\'\i}l, Jan and Rutter, Ignaz},
title = {{Constrained Outer-String Representations}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {10:1--10:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.10},
URN = {urn:nbn:de:0030-drops-212942},
doi = {10.4230/LIPIcs.GD.2024.10},
annote = {Keywords: String representation, outer-string, outer-1-string, chordal graphs, trees, polynomial-time algorithms, computational complexity}
}
Document
Monotone Arc Diagrams with Few Biarcs
Abstract
We show that every planar graph has a monotone topological 2-page book embedding where at most (4n-10)/5 (of potentially 3n-6) edges cross the spine, and every edge crosses the spine at most once; such an edge is called a biarc. We can also guarantee that all edges that cross the spine cross it in the same direction (e.g., from bottom to top). For planar 3-trees we can further improve the bound to (3n-9)/4, and for so-called Kleetopes we obtain a bound of at most (n-8)/3 edges that cross the spine. The bound for Kleetopes is tight, even if the drawing is not required to be monotone. A Kleetope is a plane triangulation that is derived from another plane triangulation T by inserting a new vertex v_f into each face f of T and then connecting v_f to the three vertices of f.
Cite as
Steven Chaplick, Henry Förster, Michael Hoffmann, and Michael Kaufmann. Monotone Arc Diagrams with Few Biarcs. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 11:1-11:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{chaplick_et_al:LIPIcs.GD.2024.11,
author = {Chaplick, Steven and F\"{o}rster, Henry and Hoffmann, Michael and Kaufmann, Michael},
title = {{Monotone Arc Diagrams with Few Biarcs}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {11:1--11:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.11},
URN = {urn:nbn:de:0030-drops-212955},
doi = {10.4230/LIPIcs.GD.2024.11},
annote = {Keywords: planar graph, topological book embedding, monotone drawing, linear layout}
}
Document
The Parameterized Complexity Of Extending Stack Layouts
Abstract
An 𝓁-page stack layout (also known as an 𝓁-page book embedding) of a graph is a linear order of the vertex set together with a partition of the edge set into 𝓁 stacks (or pages), such that the endpoints of no two edges on the same stack alternate. We study the problem of extending a given partial 𝓁-page stack layout into a complete one, which can be seen as a natural generalization of the classical NP-hard problem of computing a stack layout of an input graph from scratch. Given the inherent intractability of the problem, we focus on identifying tractable fragments through the refined lens of parameterized complexity analysis. Our results paint a detailed and surprisingly rich complexity-theoretic landscape of the problem which includes the identification of paraNP-hard, W[1]-hard and XP-tractable, as well as fixed-parameter tractable fragments of stack layout extension via a natural sequence of parameterizations.
Cite as
Thomas Depian, Simon D. Fink, Robert Ganian, and Martin Nöllenburg. The Parameterized Complexity Of Extending Stack Layouts. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 12:1-12:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{depian_et_al:LIPIcs.GD.2024.12,
author = {Depian, Thomas and Fink, Simon D. and Ganian, Robert and N\"{o}llenburg, Martin},
title = {{The Parameterized Complexity Of Extending Stack Layouts}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {12:1--12:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.12},
URN = {urn:nbn:de:0030-drops-212960},
doi = {10.4230/LIPIcs.GD.2024.12},
annote = {Keywords: Stack Layout, Drawing Extension, Parameterized Complexity, Book Embedding}
}
Document
The Price of Upwardness
Abstract
Not every directed acyclic graph (DAG) whose underlying undirected graph is planar admits an upward planar drawing. We are interested in pushing the notion of upward drawings beyond planarity by considering upward k-planar drawings of DAGs in which the edges are monotonically increasing in a common direction and every edge is crossed at most k times for some integer k ≥ 1. We show that the number of crossings per edge in a monotone drawing is in general unbounded for the class of bipartite outerplanar, cubic, or bounded pathwidth DAGs. However, it is at most two for outerpaths and it is at most quadratic in the bandwidth in general. From the computational point of view, we prove that upward-k-planarity testing is NP-complete already for k = 1 and even for restricted instances for which upward planarity testing is polynomial. On the positive side, we can decide in linear time whether a single-source DAG admits an upward 1-planar drawing in which all vertices are incident to the outer face.
Cite as
Patrizio Angelini, Therese Biedl, Markus Chimani, Sabine Cornelsen, Giordano Da Lozzo, Seok-Hee Hong, Giuseppe Liotta, Maurizio Patrignani, Sergey Pupyrev, Ignaz Rutter, and Alexander Wolff. The Price of Upwardness. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 13:1-13:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{angelini_et_al:LIPIcs.GD.2024.13,
author = {Angelini, Patrizio and Biedl, Therese and Chimani, Markus and Cornelsen, Sabine and Da Lozzo, Giordano and Hong, Seok-Hee and Liotta, Giuseppe and Patrignani, Maurizio and Pupyrev, Sergey and Rutter, Ignaz and Wolff, Alexander},
title = {{The Price of Upwardness}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {13:1--13:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.13},
URN = {urn:nbn:de:0030-drops-212977},
doi = {10.4230/LIPIcs.GD.2024.13},
annote = {Keywords: upward drawings, beyond planarity, upward k-planarity, upward outer-1-planarity}
}
Document
Bounding the Treewidth of Outer k-Planar Graphs via Triangulations
Abstract
The treewidth is a structural parameter that measures the tree-likeness of a graph. Many algorithmic and combinatorial results are expressed in terms of the treewidth. In this paper, we study the treewidth of outer k-planar graphs, that is, graphs that admit a straight-line drawing where all the vertices lie on a circle, and every edge is crossed by at most k other edges.
Wood and Telle [New York J. Math., 2007] showed that every outer k-planar graph has treewidth at most 3k + 11 using so-called planar decompositions, and later, Auer et al. [Algorithmica, 2016] proved that the treewidth of outer 1-planar graphs is at most 3, which is tight.
In this paper, we improve the general upper bound to 1.5k + 2 and give a tight bound of 4 for k = 2. We also establish a lower bound: we show that, for every even k, there is an outer k-planar graph with treewidth k+2. Our new bound immediately implies a better bound on the cop number, which answers an open question of Durocher et al. [GD 2023] in the affirmative.
Our treewidth bound relies on a new and simple triangulation method for outer k-planar graphs that yields few crossings with graph edges per edge of the triangulation. Our method also enables us to obtain a tight upper bound of k + 2 for the separation number of outer k-planar graphs, improving an upper bound of 2k + 3 by Chaplick et al. [GD 2017]. We also consider outer min-k-planar graphs, a generalization of outer k-planar graphs, where we achieve smaller improvements.
Cite as
Oksana Firman, Grzegorz Gutowski, Myroslav Kryven, Yuto Okada, and Alexander Wolff. Bounding the Treewidth of Outer k-Planar Graphs via Triangulations. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 14:1-14:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{firman_et_al:LIPIcs.GD.2024.14,
author = {Firman, Oksana and Gutowski, Grzegorz and Kryven, Myroslav and Okada, Yuto and Wolff, Alexander},
title = {{Bounding the Treewidth of Outer k-Planar Graphs via Triangulations}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {14:1--14:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.14},
URN = {urn:nbn:de:0030-drops-212988},
doi = {10.4230/LIPIcs.GD.2024.14},
annote = {Keywords: treewidth, outerplanar graphs, outer k-planar graphs, outer min-k-planar graphs, cop number, separation number}
}
Document
Bundling-Aware Graph Drawing
Abstract
Edge bundling algorithms significantly improve the visualization of dense graphs by reducing the clutter of many edges visible on screen by bundling them together. As such, bundling is often viewed as a post-processing step applied to a drawing, and the vast majority of edge bundling algorithms consider a graph and its drawing as input. Another way of thinking about edge bundling is to simultaneously optimize both the drawing and the bundling. In this paper, we investigate methods to simultaneously optimize a graph drawing and its bundling. We describe an algorithmic framework which consists of three main steps, namely Filter, Draw, and Bundle. We then propose two alternative implementations and experimentally compare them against the state-of-the-art approach and the simple idea of drawing and subsequently bundling the graph. The experiments confirm that bundled drawings created by our framework outperform previous approaches according to standard quality metrics for edge bundling.
Cite as
Daniel Archambault, Giuseppe Liotta, Martin Nöllenburg, Tommaso Piselli, Alessandra Tappini, and Markus Wallinger. Bundling-Aware Graph Drawing. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 15:1-15:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{archambault_et_al:LIPIcs.GD.2024.15,
author = {Archambault, Daniel and Liotta, Giuseppe and N\"{o}llenburg, Martin and Piselli, Tommaso and Tappini, Alessandra and Wallinger, Markus},
title = {{Bundling-Aware Graph Drawing}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {15:1--15:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.15},
URN = {urn:nbn:de:0030-drops-212995},
doi = {10.4230/LIPIcs.GD.2024.15},
annote = {Keywords: Edge Bundling, Experimental Comparison, Graph Sparsification}
}
Document
GraphTrials: Visual Proofs of Graph Properties
Abstract
Graph and network visualization supports exploration, analysis and communication of relational data arising in many domains: from biological and social networks, to transportation and powergrid systems. With the arrival of AI-based question-answering tools, issues of trustworthiness and explainability of generated answers motivate a greater role for visualization. In the context of graphs, we see the need for visualizations that can convince a critical audience that an assertion about the graph under analysis is valid. The requirements for such representations that convey precisely one specific graph property are quite different from standard network visualization criteria which optimize general aesthetics and readability.
In this paper, we aim to provide a comprehensive introduction to visual proofs of graph properties and a foundation for further research in the area. We present a framework that defines what it means to visually prove a graph property. In the process, we introduce the notion of a visual certificate, that is, a specialized faithful graph visualization that leverages the viewer’s perception, in particular, pre-attentive processing (e. g. via pop-out effects), to verify a given assertion about the represented graph. We also discuss the relationships between visual complexity, cognitive load and complexity theory, and propose a classification based on visual proof complexity. Finally, we provide examples of visual certificates for problems in different visual proof complexity classes.
Cite as
Henry Förster, Felix Klesen, Tim Dwyer, Peter Eades, Seok-Hee Hong, Stephen G. Kobourov, Giuseppe Liotta, Kazuo Misue, Fabrizio Montecchiani, Alexander Pastukhov, and Falk Schreiber. GraphTrials: Visual Proofs of Graph Properties. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{forster_et_al:LIPIcs.GD.2024.16,
author = {F\"{o}rster, Henry and Klesen, Felix and Dwyer, Tim and Eades, Peter and Hong, Seok-Hee and Kobourov, Stephen G. and Liotta, Giuseppe and Misue, Kazuo and Montecchiani, Fabrizio and Pastukhov, Alexander and Schreiber, Falk},
title = {{GraphTrials: Visual Proofs of Graph Properties}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {16:1--16:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.16},
URN = {urn:nbn:de:0030-drops-213005},
doi = {10.4230/LIPIcs.GD.2024.16},
annote = {Keywords: Graph Visualization, Theory of Visualization, Visual Proof}
}
Document
Connectivity-Faithful Graph Drawing
Abstract
Connectivity is one of the important fundamental structural properties of graphs, and a graph drawing D should faithfully represent the connectivity structure of the underlying graph G. This paper investigates connectivity-faithful graph drawing leveraging the famous Nagamochi-Ibaraki (NI) algorithm, which computes a sparsification G_NI, preserving the k-connectivity of a k-connected graph G.
Specifically, we first present CFNI, a divide-and-conquer algorithm, which computes a sparsification G_CFNI, which preserves the global k-connectivity of a graph G and the local h-connectivity of the h-connected components of G. We then present CFGD, a connectivity-faithful graph drawing algorithm based on CFNI, which faithfully displays the global and local connectivity structure of G. Extensive experiments demonstrate that CFNI outperforms NI with 66% improvement in the connectivity-related sampling quality metrics and 73% improvement in proxy quality metrics. Consequently, CFGD outperforms a naive application of NI for graph drawing, in particular with 62% improvement in stress metrics. Moreover, CFGD runs 51% faster than drawing the whole graph G, with a similar quality.
Cite as
Amyra Meidiana, Seok-Hee Hong, and Yongcheng Jing. Connectivity-Faithful Graph Drawing. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 17:1-17:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{meidiana_et_al:LIPIcs.GD.2024.17,
author = {Meidiana, Amyra and Hong, Seok-Hee and Jing, Yongcheng},
title = {{Connectivity-Faithful Graph Drawing}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {17:1--17:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.17},
URN = {urn:nbn:de:0030-drops-213015},
doi = {10.4230/LIPIcs.GD.2024.17},
annote = {Keywords: Graph connectivity, Faithful graph drawing, Graph sparsification}
}
Document
On the Uncrossed Number of Graphs
Abstract
Visualizing a graph G in the plane nicely, for example, without crossings, is unfortunately not always possible. To address this problem, Masařík and Hliněný [GD 2023] recently asked for each edge of G to be drawn without crossings while allowing multiple different drawings of G. More formally, a collection 𝒟 of drawings of G is uncrossed if, for each edge e of G, there is a drawing in 𝒟 such that e is uncrossed. The uncrossed number unc(G) of G is then the minimum number of drawings in some uncrossed collection of G.
No exact values of the uncrossed numbers have been determined yet, not even for simple graph classes. In this paper, we provide the exact values for uncrossed numbers of complete and complete bipartite graphs, partly confirming and partly refuting a conjecture posed by Hliněný and Masařík [GD 2023]. We also present a strong general lower bound on unc(G) in terms of the number of vertices and edges of G. Moreover, we prove NP-hardness of the related problem of determining the edge crossing number of a graph G, which is the smallest number of edges of G taken over all drawings of G that participate in a crossing. This problem was posed as open by Schaefer in his book [Crossing Numbers of Graphs 2018].
Cite as
Martin Balko, Petr Hliněný, Tomáš Masařík, Joachim Orthaber, Birgit Vogtenhuber, and Mirko H. Wagner. On the Uncrossed Number of Graphs. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 18:1-18:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{balko_et_al:LIPIcs.GD.2024.18,
author = {Balko, Martin and Hlin\v{e}n\'{y}, Petr and Masa\v{r}{\'\i}k, Tom\'{a}\v{s} and Orthaber, Joachim and Vogtenhuber, Birgit and Wagner, Mirko H.},
title = {{On the Uncrossed Number of Graphs}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {18:1--18:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.18},
URN = {urn:nbn:de:0030-drops-213028},
doi = {10.4230/LIPIcs.GD.2024.18},
annote = {Keywords: Uncrossed Number, Crossing Number, Planarity, Thickness}
}
Document
Weakly Leveled Planarity with Bounded Span
Abstract
This paper studies planar drawings of graphs in which each vertex is represented as a point along a sequence of horizontal lines, called levels, and each edge is either a horizontal segment or a strictly y-monotone curve. A graph is s-span weakly leveled planar if it admits such a drawing where the edges have span at most s; the span of an edge is the number of levels it touches minus one. We investigate the problem of computing s-span weakly leveled planar drawings from both the computational and the combinatorial perspectives. We prove the problem to be para-NP-hard with respect to its natural parameter s and investigate its complexity with respect to widely used structural parameters. We show the existence of a polynomial-size kernel with respect to vertex cover number and prove that the problem is FPT when parameterized by treedepth. We also present upper and lower bounds on the span for various graph classes. Notably, we show that cycle trees, a family of 2-outerplanar graphs generalizing Halin graphs, are Θ(log n)-span weakly leveled planar and 4-span weakly leveled planar when 3-connected. As a byproduct of these combinatorial results, we obtain improved bounds on the edge-length ratio of the graph families under consideration.
Cite as
Michael A. Bekos, Giordano Da Lozzo, Fabrizio Frati, Siddharth Gupta, Philipp Kindermann, Giuseppe Liotta, Ignaz Rutter, and Ioannis G. Tollis. Weakly Leveled Planarity with Bounded Span. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 19:1-19:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{bekos_et_al:LIPIcs.GD.2024.19,
author = {Bekos, Michael A. and Da Lozzo, Giordano and Frati, Fabrizio and Gupta, Siddharth and Kindermann, Philipp and Liotta, Giuseppe and Rutter, Ignaz and Tollis, Ioannis G.},
title = {{Weakly Leveled Planarity with Bounded Span}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {19:1--19:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.19},
URN = {urn:nbn:de:0030-drops-213035},
doi = {10.4230/LIPIcs.GD.2024.19},
annote = {Keywords: Leveled planar graphs, edge span, graph drawing, edge-length ratio}
}
Document
Quantum Algorithms for One-Sided Crossing Minimization
Abstract
We present singly-exponential quantum algorithms for the One-Sided Crossing Minimization (OSCM) problem. We show that OSCM can be viewed as a set problem amenable for exact algorithms with a quantum speedup with respect to their classical counterparts. First, we exploit the quantum dynamic programming framework of Ambainis et al. [Quantum Speedups for Exponential-Time Dynamic Programming Algorithms. SODA 2019] to devise a QRAM-based algorithm that solves OSCM in 𝒪^*(1.728ⁿ) time and space. Second, we use quantum divide and conquer to obtain an algorithm that solves OSCM without using QRAM in 𝒪^*(2ⁿ) time and polynomial space.
Cite as
Susanna Caroppo, Giordano Da Lozzo, and Giuseppe Di Battista. Quantum Algorithms for One-Sided Crossing Minimization. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 20:1-20:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{caroppo_et_al:LIPIcs.GD.2024.20,
author = {Caroppo, Susanna and Da Lozzo, Giordano and Di Battista, Giuseppe},
title = {{Quantum Algorithms for One-Sided Crossing Minimization}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {20:1--20:9},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.20},
URN = {urn:nbn:de:0030-drops-213045},
doi = {10.4230/LIPIcs.GD.2024.20},
annote = {Keywords: One-sided crossing minimization, quantum graph drawing, quantum dynamic programming, quantum divide and conquer, exact exponential algorithms}
}
Document
The Perception of Stress in Graph Drawings
Abstract
Most of the common graph layout principles (a.k.a. "aesthetics") on which many graph drawing algorithms are based are easy to define and to perceive. For example, the number of pairs of edges that cross each other, how symmetric a drawing looks, the aspect ratio of the bounding box, or the angular resolution at the nodes. The extent to which a graph drawing conforms to these principles can be determined by looking at how it is drawn - that is, by looking at the marks on the page - without consideration for the underlying structure of the graph. A key layout principle is that of optimising "stress", the basis for many algorithms such as the popular Kamada & Kawai algorithm and several force-directed algorithms. The stress of a graph drawing is, loosely speaking, the extent to which the geometric distance between each pair of nodes is proportional to the shortest path between them - over the whole graph drawing. The definition of stress therefore relies on the underlying structure of the graph (the "paths") in a way that other layout principles do not, making stress difficult to describe to novices unfamiliar with graph drawing principles, and, we believe, difficult to perceive. We conducted an experiment to see whether people (novices as well as experts) can see stress in graph drawings, and found that it is possible to train novices to "see" stress - even if their perception strategies are not based on the definitional concepts.
Cite as
Gavin J. Mooney, Helen C. Purchase, Michael Wybrow, Stephen G. Kobourov, and Jacob Miller. The Perception of Stress in Graph Drawings. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 21:1-21:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{mooney_et_al:LIPIcs.GD.2024.21,
author = {Mooney, Gavin J. and Purchase, Helen C. and Wybrow, Michael and Kobourov, Stephen G. and Miller, Jacob},
title = {{The Perception of Stress in Graph Drawings}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {21:1--21:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.21},
URN = {urn:nbn:de:0030-drops-213051},
doi = {10.4230/LIPIcs.GD.2024.21},
annote = {Keywords: Stress, Graph Drawing, Visual Perception}
}
Document
Boundary Labeling in a Circular Orbit
Abstract
Boundary labeling is a well-known method for displaying short textual labels for a set of point features in a figure alongside the boundary of that figure. Labels and their corresponding points are connected via crossing-free leaders. We propose orbital boundary labeling as a new variant of the problem, in which (i) the figure is enclosed by a circular contour and (ii) the labels are placed as disjoint circular arcs in an annulus-shaped orbit around the contour. The algorithmic objective is to compute an orbital boundary labeling with the minimum total leader length. We identify several parameters that define the corresponding problem space: two leader types (straight or orbital-radial), label size and order, presence of candidate label positions, and constraints on where a leader attaches to its label. Our results provide polynomial-time algorithms for many variants and NP-hardness for others, using a variety of geometric and combinatorial insights.
Cite as
Annika Bonerath, Martin Nöllenburg, Soeren Terziadis, Markus Wallinger, and Jules Wulms. Boundary Labeling in a Circular Orbit. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 22:1-22:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{bonerath_et_al:LIPIcs.GD.2024.22,
author = {Bonerath, Annika and N\"{o}llenburg, Martin and Terziadis, Soeren and Wallinger, Markus and Wulms, Jules},
title = {{Boundary Labeling in a Circular Orbit}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {22:1--22:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.22},
URN = {urn:nbn:de:0030-drops-213060},
doi = {10.4230/LIPIcs.GD.2024.22},
annote = {Keywords: External labeling, Orthoradial drawing, NP-hardness, Polynomial algorithms}
}
Document
Intersection Graphs with and Without Product Structure
Abstract
A graph class 𝒢 admits product structure if there exists a constant k such that every G ∈ 𝒢 is a subgraph of H ⊠ P for a path P and some graph H of treewidth k. Famously, the class of planar graphs, as well as many beyond-planar graph classes are known to admit product structure. However, we have only few tools to prove the absence of product structure, and hence know of only a few interesting examples of classes. Motivated by the transition between product structure and no product structure, we investigate subclasses of intersection graphs in the plane (e.g., disk intersection graphs) and present necessary and sufficient conditions for these to admit product structure.
Specifically, for a set S ⊂ ℝ² (e.g., a disk) and a real number α ∈ [0,1], we consider intersection graphs of α-free homothetic copies of S. That is, each vertex v is a homothetic copy of S of which at least an α-portion is not covered by other vertices, and there is an edge between u and v if and only if u ∩ v ≠ ∅. For α = 1 we have contact graphs, which are in most cases planar, and hence admit product structure. For α = 0 we have (among others) all complete graphs, and hence no product structure. In general, there is a threshold value α^*(S) ∈ [0,1] such that α-free homothetic copies of S admit product structure for all α > α^*(S) and do not admit product structure for all α < α^*(S).
We show for a large family of sets S, including all triangles and all trapezoids, that it holds α^*(S) = 1, i.e., we have no product structure, except for the contact graphs (when α = 1). For other sets S, including regular n-gons for infinitely many values of n, we show that 0 < α^*(S) < 1 by proving upper and lower bounds.
Cite as
Laura Merker, Lena Scherzer, Samuel Schneider, and Torsten Ueckerdt. Intersection Graphs with and Without Product Structure. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 23:1-23:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{merker_et_al:LIPIcs.GD.2024.23,
author = {Merker, Laura and Scherzer, Lena and Schneider, Samuel and Ueckerdt, Torsten},
title = {{Intersection Graphs with and Without Product Structure}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {23:1--23:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.23},
URN = {urn:nbn:de:0030-drops-213070},
doi = {10.4230/LIPIcs.GD.2024.23},
annote = {Keywords: Product structure, intersection graphs, linear local treewidth}
}
Document
Upward Pointset Embeddings of Planar st-Graphs
Abstract
We study upward pointset embeddings (UPSEs) of planar st-graphs. Let G be a planar st-graph and let S ⊂ ℝ² be a pointset with |S| = |V(G)|. An UPSE of G on S is an upward planar straight-line drawing of G that maps the vertices of G to the points of S. We consider both the problem of testing the existence of an UPSE of G on S (UPSE Testing) and the problem of enumerating all UPSEs of G on S. We prove that UPSE Testing is NP-complete even for st-graphs that consist of a set of directed st-paths sharing only s and t. On the other hand, for n-vertex planar st-graphs whose maximum st-cutset has size k, we prove that it is possible to solve UPSE Testing in 𝒪(n^{4k}) time with 𝒪(n^{3k}) space, and to enumerate all UPSEs of G on S with 𝒪(n) worst-case delay, using 𝒪(k n^{4k} log n) space, after 𝒪(k n^{4k} log n) set-up time. Moreover, for an n-vertex st-graph whose underlying graph is a cycle, we provide a necessary and sufficient condition for the existence of an UPSE on a given poinset, which can be tested in 𝒪(n log n) time. Related to this result, we give an algorithm that, for a set S of n points, enumerates all the non-crossing monotone Hamiltonian cycles on S with 𝒪(n) worst-case delay, using 𝒪(n²) space, after 𝒪(n²) set-up time.
Cite as
Carlos Alegría, Susanna Caroppo, Giordano Da Lozzo, Marco D'Elia, Giuseppe Di Battista, Fabrizio Frati, Fabrizio Grosso, and Maurizio Patrignani. Upward Pointset Embeddings of Planar st-Graphs. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 24:1-24:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{alegria_et_al:LIPIcs.GD.2024.24,
author = {Alegr{\'\i}a, Carlos and Caroppo, Susanna and Da Lozzo, Giordano and D'Elia, Marco and Di Battista, Giuseppe and Frati, Fabrizio and Grosso, Fabrizio and Patrignani, Maurizio},
title = {{Upward Pointset Embeddings of Planar st-Graphs}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {24:1--24:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.24},
URN = {urn:nbn:de:0030-drops-213082},
doi = {10.4230/LIPIcs.GD.2024.24},
annote = {Keywords: Upward pointset embeddings, planar st-graphs, st-cutset, non-crossing monotone Hamiltonian cycles, graph drawing enumeration}
}
Document
Parameterized Algorithms for Beyond-Planar Crossing Numbers
Abstract
Beyond-planar graph classes are usually defined via forbidden configurations or patterns in a drawing. In this paper, we formalize these concepts on a combinatorial level and show that, for any fixed family ℱ of crossing patterns, deciding whether a given graph G admits a drawing that avoids all patterns in F and that has at most c crossings is FPT w.r.t. c. In particular, we show that for any fixed k, deciding whether a graph is k-planar, k-quasi-planar, fan-crossing, fan-crossing-free or min-k-planar, respectively, is FPT with respect to the corresponding beyond-planar crossing number.
Cite as
Miriam Münch and Ignaz Rutter. Parameterized Algorithms for Beyond-Planar Crossing Numbers. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 25:1-25:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{munch_et_al:LIPIcs.GD.2024.25,
author = {M\"{u}nch, Miriam and Rutter, Ignaz},
title = {{Parameterized Algorithms for Beyond-Planar Crossing Numbers}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {25:1--25:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.25},
URN = {urn:nbn:de:0030-drops-213096},
doi = {10.4230/LIPIcs.GD.2024.25},
annote = {Keywords: FPT, Beyond-planarity, Crossing-number, Crossing Patterns}
}
Document
Storylines with a Protagonist
Abstract
Storyline visualizations show interactions between a given set of characters over time. Each character is represented by an x-monotone curve. A meeting is represented by a vertical bar that is crossed by the curves of exactly those characters that participate in the meeting. Therefore, character curves may have to cross each other. In the context of publication networks, we consider storylines where the characters are authors and the meetings are joint publications. We are especially interested in visualizing a group of colleagues centered around an author, the protagonist, who participates in all selected publications. For such instances, we propose a drawing style where the protagonist’s curve is drawn at a prominent position and never crossed by any other author’s curve.
We consider two variants of storylines with a protagonist. In the one-sided variant, the protagonist is required to be drawn at the top position. In this restricted setting, we can efficiently compute a drawing with the minimum number of pairwise crossings, whereas we show that it is NP-hard to minimize the number of block crossings (i.e., pairs of blocks of parallel curves that intersect each other). In the two-sided variant, the task is to split the set of co-authors of the protagonist into two groups, and to place the curves of one group above and the curves of the other group below the protagonist’s curve such that the total number of (block) crossings is minimized.
As our main result, we present an algorithm for bundling a sequence of pairwise crossings into a sequence of few block crossings (in the absence of meetings). It exploits a connection to a rectangle dissection problem. In the presence of meetings, it yields results that are very close to a lower bound. Based on this bundling algorithm and our exact algorithm for the one-sided variant, we present a new heuristic for computing two-sided storylines with few block crossings.
We perform an extensive experimental study using publication data of 81 protagonists from GD 2023 and their most frequent collaborators over the last ten years. Our study shows that, for two-sided storylines with a protagonist, our new heuristic uses fewer block crossings (and fewer pairwise crossings) than two heuristics for block crossing minimization in general storylines.
Cite as
Tim Hegemann and Alexander Wolff. Storylines with a Protagonist. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 26:1-26:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{hegemann_et_al:LIPIcs.GD.2024.26,
author = {Hegemann, Tim and Wolff, Alexander},
title = {{Storylines with a Protagonist}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {26:1--26:22},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.26},
URN = {urn:nbn:de:0030-drops-213109},
doi = {10.4230/LIPIcs.GD.2024.26},
annote = {Keywords: Storyline visualization, storyline with a protagonist, crossing minimization, block crossings}
}
Document
On k-Planar Graphs Without Short Cycles
Abstract
We study the impact of forbidding short cycles to the edge density of k-planar graphs; a k-planar graph is one that can be drawn in the plane with at most k crossings per edge. Specifically, we consider three settings, according to which the forbidden substructures are 3-cycles, 4-cycles or both of them (i.e., girth ≥ 5). For all three settings and all k ∈ {1,2,3}, we present lower and upper bounds on the maximum number of edges in any k-planar graph on n vertices. Our bounds are of the form c n, for some explicit constant c that depends on k and on the setting. For general k ≥ 4 our bounds are of the form c√kn, for some explicit constant c. These results are obtained by leveraging different techniques, such as the discharging method, the recently introduced density formula for non-planar graphs, and new upper bounds for the crossing number of 2- and 3-planar graphs in combination with corresponding lower bounds based on the Crossing Lemma.
Cite as
Michael A. Bekos, Prosenjit Bose, Aaron Büngener, Vida Dujmović, Michael Hoffmann, Michael Kaufmann, Pat Morin, Saeed Odak, and Alexandra Weinberger. On k-Planar Graphs Without Short Cycles. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 27:1-27:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{bekos_et_al:LIPIcs.GD.2024.27,
author = {Bekos, Michael A. and Bose, Prosenjit and B\"{u}ngener, Aaron and Dujmovi\'{c}, Vida and Hoffmann, Michael and Kaufmann, Michael and Morin, Pat and Odak, Saeed and Weinberger, Alexandra},
title = {{On k-Planar Graphs Without Short Cycles}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {27:1--27:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.27},
URN = {urn:nbn:de:0030-drops-213117},
doi = {10.4230/LIPIcs.GD.2024.27},
annote = {Keywords: Beyond-planar Graphs, k-planar Graphs, Local Crossing Number, Crossing Number, Discharging Method, Crossing Lemma}
}
Document
On the Edge Density of Bipartite 3-Planar and Bipartite Gap-Planar Graphs
Abstract
We show that if a bipartite graph G with n ≥ 3 vertices can be drawn in the plane such that (i) each edge is involved in at most three crossings per edge or (ii) each crossing is assigned to one of the two involved edges and each edge is assigned at most one crossing, then G has at most 4n-8 edges. In both cases, this bound is tight up to an additive constant as witnessed by lower-bound constructions. The former result can be used to improve the leading constant for the crossing lemma for bipartite graphs which in turn improves various results such as the biplanar crossing number or the maximum number of edges a bipartite k-planar graph can have.
Cite as
Aaron Büngener and Maximilian Pfister. On the Edge Density of Bipartite 3-Planar and Bipartite Gap-Planar Graphs. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 28:1-28:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{bungener_et_al:LIPIcs.GD.2024.28,
author = {B\"{u}ngener, Aaron and Pfister, Maximilian},
title = {{On the Edge Density of Bipartite 3-Planar and Bipartite Gap-Planar Graphs}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {28:1--28:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.28},
URN = {urn:nbn:de:0030-drops-213123},
doi = {10.4230/LIPIcs.GD.2024.28},
annote = {Keywords: Edge Density, Beyond Planarity, bipartite Graphs, Discharging Method}
}
Document
Improving the Crossing Lemma by Characterizing Dense 2-Planar and 3-Planar Graphs
Abstract
The classical Crossing Lemma by Ajtai et al. and Leighton from 1982 gave an important lower bound of cm³/n² for the number of crossings in any drawing of a given graph of n vertices and m edges. The original value was c = 1/100, which then has gradually been improved. Here, the bounds for the density of k-planar graphs played a central role. Our new insight is that for k = 2,3 the k-planar graphs have substantially fewer edges if specific local configurations that occur in drawings of k-planar graphs of maximum density are forbidden. Therefore, we are able to derive better bounds for the crossing number cr(G) of a given graph G. In particular, we achieve a bound of cr(G) ≥ 73/18m-305/18(n-2) for the range of 5n < m ≤ 6n, while our second bound cr(G) ≥ 5m - 407/18(n-2) is even stronger for larger m > 6n.
For m > 6.79n, we finally apply the standard probabilistic proof from the BOOK and obtain an improved constant of c > 1/27.61 in the Crossing Lemma. Note that the previous constant was 1/29. Although this improvement is not too impressive, we consider our technique as an important new tool, which might be helpful in various other applications.
Cite as
Aaron Büngener and Michael Kaufmann. Improving the Crossing Lemma by Characterizing Dense 2-Planar and 3-Planar Graphs. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 29:1-29:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{bungener_et_al:LIPIcs.GD.2024.29,
author = {B\"{u}ngener, Aaron and Kaufmann, Michael},
title = {{Improving the Crossing Lemma by Characterizing Dense 2-Planar and 3-Planar Graphs}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {29:1--29:22},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.29},
URN = {urn:nbn:de:0030-drops-213136},
doi = {10.4230/LIPIcs.GD.2024.29},
annote = {Keywords: Crossing Lemma, k-planar graphs, discharging method}
}
Document
Flips in Colorful Triangulations
Abstract
The associahedron is the graph G_N that has as nodes all triangulations of a convex N-gon, and an edge between any two triangulations that differ in a flip operation. A flip removes an edge shared by two triangles and replaces it by the other diagonal of the resulting 4-gon. In this paper, we consider a large collection of induced subgraphs of G_N obtained by Ramsey-type colorability properties. Specifically, coloring the points of the N-gon red and blue alternatingly, we consider only colorful triangulations, namely triangulations in which every triangle has points in both colors, i.e., monochromatic triangles are forbidden. The resulting induced subgraph of G_N on colorful triangulations is denoted by F_N. We prove that F_N has a Hamilton cycle for all N ≥ 8, resolving a problem raised by Sagan, i.e., all colorful triangulations on N points can be listed so that any two cyclically consecutive triangulations differ in a flip. In fact, we prove that for an arbitrary fixed coloring pattern of the N points with at least 10 changes of color, the resulting subgraph of G_N on colorful triangulations (for that coloring pattern) admits a Hamilton cycle. We also provide an efficient algorithm for computing a Hamilton path in F_N that runs in time O(1) on average per generated node. This algorithm is based on a new and algorithmic construction of a tree rotation Gray code for listing all n-vertex k-ary trees that runs in time O(k) on average per generated tree.
Cite as
Rohan Acharya, Torsten Mütze, and Francesco Verciani. Flips in Colorful Triangulations. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 30:1-30:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{acharya_et_al:LIPIcs.GD.2024.30,
author = {Acharya, Rohan and M\"{u}tze, Torsten and Verciani, Francesco},
title = {{Flips in Colorful Triangulations}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {30:1--30:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.30},
URN = {urn:nbn:de:0030-drops-213143},
doi = {10.4230/LIPIcs.GD.2024.30},
annote = {Keywords: Flip graph, associahedron, triangulation, binary tree, vertex coloring, Hamilton cycle, Gray code}
}
Document
Revisiting ILP Models for Exact Crossing Minimization in Storyline Drawings
Abstract
Storyline drawings are a popular visualization of interactions of a set of characters over time, e.g., to show participants of scenes in a book or movie. Characters are represented as x-monotone curves that converge vertically for interactions and diverge otherwise. Combinatorially, the task of computing storyline drawings reduces to finding a sequence of permutations of the character curves for the different time points, with the primary objective being crossing minimization of the induced character trajectories. In this paper, we revisit exact integer linear programming (ILP) approaches for this NP-hard problem. By enriching previous formulations with additional problem-specific insights and new heuristics, we obtain exact solutions for an extended new benchmark set of larger and more complex instances than had been used before. Our experiments show that our enriched formulations lead to better performing algorithms when compared to state-of-the–art modelling techniques. In particular, our best algorithms are on average 2.6-3.2 times faster than the state-of-the-art and succeed in solving complex instances that could not be solved before within the given time limit. Further, we show in an ablation study that our enrichment components contribute considerably to the performance of the new ILP formulation.
Cite as
Alexander Dobler, Michael Jünger, Paul J. Jünger, Julian Meffert, Petra Mutzel, and Martin Nöllenburg. Revisiting ILP Models for Exact Crossing Minimization in Storyline Drawings. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 31:1-31:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{dobler_et_al:LIPIcs.GD.2024.31,
author = {Dobler, Alexander and J\"{u}nger, Michael and J\"{u}nger, Paul J. and Meffert, Julian and Mutzel, Petra and N\"{o}llenburg, Martin},
title = {{Revisiting ILP Models for Exact Crossing Minimization in Storyline Drawings}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {31:1--31:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.31},
URN = {urn:nbn:de:0030-drops-213159},
doi = {10.4230/LIPIcs.GD.2024.31},
annote = {Keywords: Storyline drawing, crossing minimization, integer linear programming, algorithm engineering, computational experiments}
}
Document
On the Complexity of Recognizing k^+-Real Face Graphs
Abstract
A nonplanar drawing Γ of a graph G divides the plane into topologically connected regions, called faces (or cells). The boundary of each face is formed by vertices, crossings, and edge segments. Given a positive integer k, we say that Γ is a k^+-real face drawing of G if the boundary of each face of Γ contains at least k vertices of G. The study of k^+-real face drawings started in a paper by Binucci et al. (WG 2023), where edge density bounds and relationships with other beyond-planar graph classes are proved. In this paper, we investigate the complexity of recognizing k^+-real face graphs, i.e., graphs that admit a k^+-real face drawing. We study both the general unconstrained scenario and the 2-layer scenario in which the graph is bipartite, the vertices of the two partition sets lie on two distinct horizontal layers, and the edges are straight-line segments. We give NP-completeness results for the unconstrained scenario and efficient recognition algorithms for the 2-layer setting.
Cite as
Michael A. Bekos, Giuseppe Di Battista, Emilio Di Giacomo, Walter Didimo, Michael Kaufmann, and Fabrizio Montecchiani. On the Complexity of Recognizing k^+-Real Face Graphs. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 32:1-32:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{bekos_et_al:LIPIcs.GD.2024.32,
author = {Bekos, Michael A. and Di Battista, Giuseppe and Di Giacomo, Emilio and Didimo, Walter and Kaufmann, Michael and Montecchiani, Fabrizio},
title = {{On the Complexity of Recognizing k^+-Real Face Graphs}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {32:1--32:22},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.32},
URN = {urn:nbn:de:0030-drops-213167},
doi = {10.4230/LIPIcs.GD.2024.32},
annote = {Keywords: Beyond planarity, k^+-real face drawings, 2-layer drawings, recognition algorithm, NP-hardness}
}
Document
Crossing Numbers of Beyond Planar Graphs Re-Revisited: A Framework Approach
Abstract
Beyond planarity concepts (prominent examples include k-planarity or fan-planarity) apply certain restrictions on the allowed patterns of crossings in drawings. It is natural to ask, how much the number of crossings may increase over the traditional (unrestricted) crossing number. Previous approaches to bound such ratios, e.g. [Markus Chimani et al., 2022; Nathan van Beusekom et al., 2022], require very specialized constructions and arguments for each considered beyond planarity concept, and mostly only yield asymptotically non-tight bounds. We propose a very general proof framework that allows us to obtain asymptotically tight bounds, and where the concept-specific parts of the proof typically boil down to a couple of lines. We show the strength of our approach by giving improved or first bounds for several beyond planarity concepts.
Cite as
Markus Chimani, Torben Donzelmann, Nick Kloster, Melissa Koch, Jan-Jakob Völlering, and Mirko H. Wagner. Crossing Numbers of Beyond Planar Graphs Re-Revisited: A Framework Approach. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 33:1-33:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{chimani_et_al:LIPIcs.GD.2024.33,
author = {Chimani, Markus and Donzelmann, Torben and Kloster, Nick and Koch, Melissa and V\"{o}llering, Jan-Jakob and Wagner, Mirko H.},
title = {{Crossing Numbers of Beyond Planar Graphs Re-Revisited: A Framework Approach}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {33:1--33:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.33},
URN = {urn:nbn:de:0030-drops-213175},
doi = {10.4230/LIPIcs.GD.2024.33},
annote = {Keywords: Beyond planarity, crossing number, crossing ratio, proof framework}
}
Document
Separable Drawings: Extendability and Crossing-Free Hamiltonian Cycles
Abstract
Generalizing pseudospherical drawings, we introduce a new class of simple drawings, which we call separable drawings. In a separable drawing, every edge can be closed to a simple curve that intersects each other edge at most once. Curves of different edges might interact arbitrarily. Most notably, we show that (1) every separable drawing of any graph on n vertices in the plane can be extended to a simple drawing of the complete graph K_n, (2) every separable drawing of K_n contains a crossing-free Hamiltonian cycle and is plane Hamiltonian connected, and (3) every generalized convex drawing and every 2-page book drawing is separable. Further, the class of separable drawings is a proper superclass of the union of generalized convex and 2-page book drawings. Hence, our results on plane Hamiltonicity extend recent work on generalized convex drawings by Bergold et al. (SoCG 2024).
Cite as
Oswin Aichholzer, Joachim Orthaber, and Birgit Vogtenhuber. Separable Drawings: Extendability and Crossing-Free Hamiltonian Cycles. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 34:1-34:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{aichholzer_et_al:LIPIcs.GD.2024.34,
author = {Aichholzer, Oswin and Orthaber, Joachim and Vogtenhuber, Birgit},
title = {{Separable Drawings: Extendability and Crossing-Free Hamiltonian Cycles}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {34:1--34:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.34},
URN = {urn:nbn:de:0030-drops-213187},
doi = {10.4230/LIPIcs.GD.2024.34},
annote = {Keywords: Simple drawings, Pseudospherical drawings, Generalized convex drawings, Plane Hamiltonicity, Extendability of drawings, Recognition of drawing classes}
}
Document
On k-Plane Insertion into Plane Drawings
Abstract
We introduce the k-Plane Insertion into Plane drawing (k-PIP) problem: given a plane drawing of a planar graph G and a set F of edges, insert the edges in F into the drawing such that the resulting drawing is k-plane. In this paper, we show that the problem is NP-complete for every k ≥ 1, even when G is biconnected and the set F of edges forms a matching or a path. On the positive side, we present a linear-time algorithm for the case that k = 1 and G is a triangulation.
Cite as
Julia Katheder, Philipp Kindermann, Fabian Klute, Irene Parada, and Ignaz Rutter. On k-Plane Insertion into Plane Drawings. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 35:1-35:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{katheder_et_al:LIPIcs.GD.2024.35,
author = {Katheder, Julia and Kindermann, Philipp and Klute, Fabian and Parada, Irene and Rutter, Ignaz},
title = {{On k-Plane Insertion into Plane Drawings}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {35:1--35:11},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.35},
URN = {urn:nbn:de:0030-drops-213190},
doi = {10.4230/LIPIcs.GD.2024.35},
annote = {Keywords: Graph drawing, edge insertion, k-planarity}
}
Document
Noncrossing Longest Paths and Cycles
Abstract
Edge crossings in geometric graphs are sometimes undesirable as they could lead to unwanted situations such as collisions in motion planning and inconsistency in VLSI layout. Short geometric structures such as shortest perfect matchings, shortest spanning trees, shortest spanning paths, and shortest spanning cycles on a given point set are inherently noncrossing. However, the longest such structures need not be noncrossing. In fact, it is intuitive to expect many edge crossings in various geometric graphs that are longest.
Recently, Álvarez-Rebollar, Cravioto-Lagos, Marín, Solé-Pi, and Urrutia (Graphs and Combinatorics, 2024) constructed a set of points for which the longest perfect matching is noncrossing. They raised several challenging questions in this direction. In particular, they asked whether the longest spanning path, on any finite set of points in the plane, must have a pair of crossing edges. They also conjectured that the longest spanning cycle must have a pair of crossing edges.
In this paper, we give a negative answer to the question and also refute the conjecture. We present a framework for constructing arbitrarily large point sets for which the longest perfect matchings, the longest spanning paths, and the longest spanning cycles are noncrossing.
Cite as
Greg Aloupis, Ahmad Biniaz, Prosenjit Bose, Jean-Lou De Carufel, David Eppstein, Anil Maheshwari, Saeed Odak, Michiel Smid, Csaba D. Tóth, and Pavel Valtr. Noncrossing Longest Paths and Cycles. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 36:1-36:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{aloupis_et_al:LIPIcs.GD.2024.36,
author = {Aloupis, Greg and Biniaz, Ahmad and Bose, Prosenjit and De Carufel, Jean-Lou and Eppstein, David and Maheshwari, Anil and Odak, Saeed and Smid, Michiel and T\'{o}th, Csaba D. and Valtr, Pavel},
title = {{Noncrossing Longest Paths and Cycles}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {36:1--36:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.36},
URN = {urn:nbn:de:0030-drops-213203},
doi = {10.4230/LIPIcs.GD.2024.36},
annote = {Keywords: Longest Paths, Longest Cycles, Noncrossing Paths, Noncrossing Cycles}
}
Document
Rectilinear Crossing Number of Graphs Excluding a Single-Crossing Graph as a Minor
Abstract
The rectilinear crossing number of G is the minimum number of crossings in a straight-line drawing of G. A single-crossing graph is a graph whose crossing number is at most one. We prove that every n-vertex graph G that excludes a single-crossing graph as a minor has rectilinear crossing number O(Δ n), where Δ is the maximum degree of G. This dependence on n and Δ is best possible. The result applies, for example, to K₅-minor-free graphs, and bounded treewidth graphs. Prior to our work, the only bounded degree minor-closed families known to have linear rectilinear crossing number were bounded degree graphs of bounded treewidth as well as bounded degree K_{3,3}-minor-free graphs. In the case of bounded treewidth graphs, our O(Δ n) result is again tight and it improves on the previous best known bound of O(Δ² n) by Wood and Telle, 2007.
Cite as
Vida Dujmović and Camille La Rose. Rectilinear Crossing Number of Graphs Excluding a Single-Crossing Graph as a Minor. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 37:1-37:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{dujmovic_et_al:LIPIcs.GD.2024.37,
author = {Dujmovi\'{c}, Vida and La Rose, Camille},
title = {{Rectilinear Crossing Number of Graphs Excluding a Single-Crossing Graph as a Minor}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {37:1--37:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.37},
URN = {urn:nbn:de:0030-drops-213219},
doi = {10.4230/LIPIcs.GD.2024.37},
annote = {Keywords: (rectilinear) crossing number, graph minors, maximum degree, clique-sums}
}
Document
Harborth’s Conjecture for 4-Regular Planar Graphs
Abstract
We show that every 4-regular planar graph has a straight-line embedding in the plane where all edges have integer length. The construction extends earlier ideas for finding such embeddings for 4-regular planar graphs with diamond subgraphs or small edge cuts.
Cite as
Daniel J. Chang and Timothy Sun. Harborth’s Conjecture for 4-Regular Planar Graphs. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 38:1-38:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{chang_et_al:LIPIcs.GD.2024.38,
author = {Chang, Daniel J. and Sun, Timothy},
title = {{Harborth’s Conjecture for 4-Regular Planar Graphs}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {38:1--38:9},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.38},
URN = {urn:nbn:de:0030-drops-213227},
doi = {10.4230/LIPIcs.GD.2024.38},
annote = {Keywords: Planar graph, straight-line embedding, Diophantine equation}
}
Document
Drawing Planar Graphs and 1-Planar Graphs Using Cubic Bézier Curves with Bounded Curvature
Abstract
We study algorithms for drawing planar graphs and 1-planar graphs using cubic Bézier curves with bounded curvature. We show that any n-vertex 1-planar graph has a 1-planar RAC drawing using a single cubic Bézier curve per edge, and this drawing can be computed in O(n) time given a combinatorial 1-planar drawing. We also show that any n-vertex planar graph G can be drawn in O(n) time with a single cubic Bézier curve per edge, in an O(n)× O(n) bounding box, such that the edges have Θ(1/degree(v)) angular resolution, for each v ∈ G, and O(√n) curvature.
Cite as
David Eppstein, Michael T. Goodrich, and Abraham M. Illickan. Drawing Planar Graphs and 1-Planar Graphs Using Cubic Bézier Curves with Bounded Curvature. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 39:1-39:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{eppstein_et_al:LIPIcs.GD.2024.39,
author = {Eppstein, David and Goodrich, Michael T. and Illickan, Abraham M.},
title = {{Drawing Planar Graphs and 1-Planar Graphs Using Cubic B\'{e}zier Curves with Bounded Curvature}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {39:1--39:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.39},
URN = {urn:nbn:de:0030-drops-213237},
doi = {10.4230/LIPIcs.GD.2024.39},
annote = {Keywords: graph drawing, planar graphs, B\'{e}zier curves, and RAC drawings}
}
Document
Morphing Planar Graph Drawings via Orthogonal Box Drawings
Abstract
We give an algorithm to morph planar graph drawings that achieves small grid size at the expense of allowing a constant number of bends on each edge. The input is an n-vertex planar graph and two planar straight-line drawings of the graph on an O(n) × O(n) grid. The planarity-preserving morph is composed of O(n) linear morphs between successive pairs of drawings, each on an O(n) × O(n) grid with a constant number of bends per edge. The algorithm to compute the morph runs in O(n²) time on a word RAM model with standard arithmetic operations - in particular no square roots or cube roots are required.
The first step of the algorithm is to morph each input drawing to a planar orthogonal box drawing where vertices are represented by boxes and each edge is drawn as a horizontal or vertical segment. The second step is to morph between planar orthogonal box drawings. This is done by extending known techniques for morphing planar orthogonal drawings with point vertices.
Cite as
Therese Biedl, Anna Lubiw, and Jack Spalding-Jamieson. Morphing Planar Graph Drawings via Orthogonal Box Drawings. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 40:1-40:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{biedl_et_al:LIPIcs.GD.2024.40,
author = {Biedl, Therese and Lubiw, Anna and Spalding-Jamieson, Jack},
title = {{Morphing Planar Graph Drawings via Orthogonal Box Drawings}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {40:1--40:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.40},
URN = {urn:nbn:de:0030-drops-213242},
doi = {10.4230/LIPIcs.GD.2024.40},
annote = {Keywords: morphing, graph morphing, linear morph, planar graph drawing, orthogonal box drawing, orthogonal drawing, algorithm}
}
Document
Graph Drawing Contest Report
Graph Drawing Contest Report (Graph Drawing Contest Report)
Abstract
This report describes the 31st Annual Graph Drawing Contest, held in conjunction with the 32nd International Symposium on Graph Drawing and Network Visualization (GD'24) at TU Wien, Vienna, Austria. 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 track in which participants visualized a dataset based on the Olympic medal track-record of countries and a live challenge held at the conference where participants had to draw a graph on a given point-set with as few crossings as possible.
Cite as
Sara Di Bartolomeo, Fabian Klute, Debajyoti Mondal, and Jules Wulms. Graph Drawing Contest Report (Graph Drawing Contest Report). In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 41:1-41:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{dibartolomeo_et_al:LIPIcs.GD.2024.41,
author = {Di Bartolomeo, Sara and Klute, Fabian and Mondal, Debajyoti and Wulms, Jules},
title = {{Graph Drawing Contest Report}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {41:1--41:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.41},
URN = {urn:nbn:de:0030-drops-213256},
doi = {10.4230/LIPIcs.GD.2024.41},
annote = {Keywords: Information Visualization, Graph Drawing Contest}
}
Document
Poster Abstract
From Planar via Outerplanar to Outerpath – Engineering NP-Hardness Constructions (Poster Abstract)
Abstract
A typical question in graph drawing is to determine, for a given graph drawing style, the boundary between polynomial-time solvability and NP-hardness. For two examples from the area of drawing graphs with few slopes, we sharpen this boundary. We suggest a framework for a certain type of NP-hardness constructions where graphs have some parts that can only be realized as rigid structures, whereas other parts allow a controllable degree of flexibility. Starting with an NP-complete problem involving planarity (here, we use planar monotone rectilinear 3-SAT), we consider first a reduction to a planar graph, which can be adjusted to an outerplanar graph, and finally to an outerpath. An outerplanar graph is a graph admitting an outerplanar drawing, that is, a crossing-free drawing where every vertex lies on the outer face, and an outerpath is a graph admitting an outerplanar drawing where the weak dual is a path. The (weak) dual of a graph drawing is the graph that has a node for every (inner) face and a link if two faces share an edge.
Specifically, we first show that, for every upward-planar directed outerpath G, it is NP-hard to decide whether G admits an upward-planar straight-line drawing where every edge has one of three distinct slopes, and we second show that, for every undirected outerpath G, it is NP-hard to decide whether G admits a proper level-planar straight-line drawing where every edge has one of two distinct slopes. For both problems, NP-hardness has been known before for outerplanar graphs.
Cite as
Joshua Geis and Johannes Zink. From Planar via Outerplanar to Outerpath – Engineering NP-Hardness Constructions (Poster Abstract). In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 42:1-42:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{geis_et_al:LIPIcs.GD.2024.42,
author = {Geis, Joshua and Zink, Johannes},
title = {{From Planar via Outerplanar to Outerpath – Engineering NP-Hardness Constructions}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {42:1--42:3},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.42},
URN = {urn:nbn:de:0030-drops-213263},
doi = {10.4230/LIPIcs.GD.2024.42},
annote = {Keywords: NP-hardness, outerplanar, outerpath}
}
Document
Poster Abstract
Minimizing Switches in Cased Graph Drawings (Poster Abstract)
Abstract
In cased drawings of graphs, edges are drawn in front of others in order to decrease the negative impact of crossings on readability. In this context, a switch on an edge is defined as two consecutive crossings, where the edge is drawn in the front at one crossing and behind another edge at the next crossing. We investigate the problem of minimizing the maximum number of switches on any edge - both in a fixed drawing as well as for non-embedded graphs. We resolve an open question by Eppstein, van Kreveld, Mumford, and Speckmann (2009) by establishing the NP-hardness of minimizing the number of switches in a fixed drawing, provide a fixed-parameter algorithm for this problem, and obtain a full characterization of the problem for non-embedded graphs.
Cite as
Robert Ganian, Martin Nöllenburg, and Sebastian Röder. Minimizing Switches in Cased Graph Drawings (Poster Abstract). In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 43:1-43:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{ganian_et_al:LIPIcs.GD.2024.43,
author = {Ganian, Robert and N\"{o}llenburg, Martin and R\"{o}der, Sebastian},
title = {{Minimizing Switches in Cased Graph Drawings}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {43:1--43:3},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.43},
URN = {urn:nbn:de:0030-drops-213271},
doi = {10.4230/LIPIcs.GD.2024.43},
annote = {Keywords: beyond planarity, complexity theory, non-planar drawings, crossings}
}
Document
Poster Abstract
Graph-Drawing Supported Identification of Influential Students at Schools (Poster Abstract)
Abstract
We consider the real-world problem of identifying a set of "influential" students at schools for a workshop on tolerance. We report on a tool that visualizes the networks of social connections between students, identifies sets of influential students, and lets one explore and understand the solution space with a focus on usability for teachers who are untrained in network analysis.
Cite as
Markus Chimani, Lea Kröger, Juliane Liedtke, Jonah Mevert, Maor Shani, and Maarten van Zalk. Graph-Drawing Supported Identification of Influential Students at Schools (Poster Abstract). In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 44:1-44:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{chimani_et_al:LIPIcs.GD.2024.44,
author = {Chimani, Markus and Kr\"{o}ger, Lea and Liedtke, Juliane and Mevert, Jonah and Shani, Maor and van Zalk, Maarten},
title = {{Graph-Drawing Supported Identification of Influential Students at Schools}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {44:1--44:3},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.44},
URN = {urn:nbn:de:0030-drops-213282},
doi = {10.4230/LIPIcs.GD.2024.44},
annote = {Keywords: social network tool, force-directed graph drawing, group centrality}
}
Document
Poster Abstract
GdMetriX - A NetworkX Extension For Graph Drawing Metrics (Poster Abstract)
Abstract
networkX is a well-established Python library for network analysis. With gdMetriX, we aim to extend the functionality of networkX and provide common quality metrics used in the field of graph drawing, such as the number of crossings or the angular resolution. In addition, the package provides easy-to-use access to the graph datasets provided by the ’Graph Layout Benchmark Datasets’ project from the Northeastern University Visualization Lab.
Cite as
Martin Nöllenburg, Sebastian Röder, and Markus Wallinger. GdMetriX - A NetworkX Extension For Graph Drawing Metrics (Poster Abstract). In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 45:1-45:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{nollenburg_et_al:LIPIcs.GD.2024.45,
author = {N\"{o}llenburg, Martin and R\"{o}der, Sebastian and Wallinger, Markus},
title = {{GdMetriX - A NetworkX Extension For Graph Drawing Metrics}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {45:1--45:3},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.45},
URN = {urn:nbn:de:0030-drops-213294},
doi = {10.4230/LIPIcs.GD.2024.45},
annote = {Keywords: Graph Drawing Metrics}
}
Document
Poster Abstract
AdMaTilE: Visualizing Event-Based Adjacency Matrices in a Multiple-Coordinated-Views System (Poster Abstract)
Abstract
Conventional dynamic networks represent network changes via a discrete sequence of timeslices, which usually entails loss of information on fine-grained dynamics. Recently, event-based networks emerged as an approach to model this temporal (event-based) information more precisely. Adjacency-matrix-based visualizations of temporal networks are under-investigated in related literature and present a promising research direction for network visualization. Our approach AdMaTilE (Adjacency Matrix and Timeline Explorer) is designed to visualize event-based networks using multiple matrix views, timelines, difference maps, and staged transitions.
Cite as
Nikolaus-Mathias Herl and Velitchko Filipov. AdMaTilE: Visualizing Event-Based Adjacency Matrices in a Multiple-Coordinated-Views System (Poster Abstract). In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 46:1-46:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{herl_et_al:LIPIcs.GD.2024.46,
author = {Herl, Nikolaus-Mathias and Filipov, Velitchko},
title = {{AdMaTilE: Visualizing Event-Based Adjacency Matrices in a Multiple-Coordinated-Views System}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {46:1--46:3},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.46},
URN = {urn:nbn:de:0030-drops-213307},
doi = {10.4230/LIPIcs.GD.2024.46},
annote = {Keywords: Event-based, Temporal Graphs, Adjacency Matrix, Network Visualization}
}
Document
Poster Abstract
Strict Upward Planar Grid Drawings of Binary Trees with Minimal Area (Poster Abstract)
Abstract
Given a rooted binary tree T and a tuple (w, h), we wish to test whether there exists a strict upward drawing of T on a w × h grid; that is, a planar grid drawing with straight-line edges where every vertex has a strictly lower y-coordinate than its parent.
[Biedl and Mondal, 2017] prove that this problem is NP-hard for general trees; their construction crucially uses nodes of very high degree. [Akatiya et al., 2018] prove that the problem is also NP-hard for binary trees with a fixed combinatorial embedding; their construction crucially relies on the fixed embedding. Both pose the question for binary trees and a free embedding as an open problem.
Here, we show that this problem is also NP-hard.
Cite as
Maarten Löffler. Strict Upward Planar Grid Drawings of Binary Trees with Minimal Area (Poster Abstract). In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 47:1-47:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{loffler:LIPIcs.GD.2024.47,
author = {L\"{o}ffler, Maarten},
title = {{Strict Upward Planar Grid Drawings of Binary Trees with Minimal Area}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {47:1--47:3},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.47},
URN = {urn:nbn:de:0030-drops-213311},
doi = {10.4230/LIPIcs.GD.2024.47},
annote = {Keywords: Upward drawings, grid drawings, minimal area}
}
Document
Poster Abstract
Determining Sugiyama Topology with Model Order (Poster Abstract)
Abstract
Traditional implementations of the Sugiyama algorithm optimize aesthetic criteria such as the number of backward edges, edge length, or edge crossings. If we, however, utilize the model order, as provided e.g. by a textual graph input file, we can determine the topology of a Sugiyama layout in a one-pass algorithm while controlling the secondary notation and with it the intention expressed by the underlying model, which typically cannot be captured by layout algorithms.
Cite as
Sören Domrös and Reinhard von Hanxleden. Determining Sugiyama Topology with Model Order (Poster Abstract). In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 48:1-48:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{domros_et_al:LIPIcs.GD.2024.48,
author = {Domr\"{o}s, S\"{o}ren and von Hanxleden, Reinhard},
title = {{Determining Sugiyama Topology with Model Order}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {48:1--48:3},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.48},
URN = {urn:nbn:de:0030-drops-213322},
doi = {10.4230/LIPIcs.GD.2024.48},
annote = {Keywords: Automatic Layout, Model Order, Layered Layout}
}
Document
Poster Abstract
Introducing Fairness in Graph Visualization (Poster Abstract)
Abstract
Information visualization tools are an essential component of many data-driven decision-making systems that rely on human feedback. The aim of this paper is to propose a novel research direction focused on fair visualizations of graphs.
Cite as
Seok-Hee Hong, Giuseppe Liotta, Fabrizio Montecchiani, Martin Nöllenburg, and Tommaso Piselli. Introducing Fairness in Graph Visualization (Poster Abstract). In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 49:1-49:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{hong_et_al:LIPIcs.GD.2024.49,
author = {Hong, Seok-Hee and Liotta, Giuseppe and Montecchiani, Fabrizio and N\"{o}llenburg, Martin and Piselli, Tommaso},
title = {{Introducing Fairness in Graph Visualization}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {49:1--49:3},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.49},
URN = {urn:nbn:de:0030-drops-213338},
doi = {10.4230/LIPIcs.GD.2024.49},
annote = {Keywords: Network visualization, Fairness, Stress minimization}
}
Document
Poster Abstract
Level Planarity Is More Difficult Than We Thought (Poster Abstract)
Abstract
We consider three simple quadratic-time algorithms for Level Planarity and give a level-planar instance that they either falsely classify as negative or for which they output a non-planar drawing.
Cite as
Simon D. Fink, Matthias Pfretzschner, Ignaz Rutter, and Peter Stumpf. Level Planarity Is More Difficult Than We Thought (Poster Abstract). In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 50:1-50:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{fink_et_al:LIPIcs.GD.2024.50,
author = {Fink, Simon D. and Pfretzschner, Matthias and Rutter, Ignaz and Stumpf, Peter},
title = {{Level Planarity Is More Difficult Than We Thought}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {50:1--50:3},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.50},
URN = {urn:nbn:de:0030-drops-213341},
doi = {10.4230/LIPIcs.GD.2024.50},
annote = {Keywords: level planarity, 2-SAT, simple algorithm, counterexample}
}
Document
Poster Abstract
Evolutionary Algorithms for One-Sided Bipartite Crossing Minimisation (Poster Abstract)
Abstract
Evolutionary algorithms (EAs) are universal solvers inspired by principles of natural evolution. In many applications, EAs produce astonishingly good solutions. To complement recent theoretical advances in the analysis of EAs on graph drawing [Baumann et al., 2024], we contribute a fundamental empirical study.
We consider the so-called One-Sided Bipartite Crossing Minimisation (OBCM): given two layers of a bipartite graph and a fixed horizontal order of vertices on the first layer, the task is to order the vertices on the second layer to minimise the number of edge crossings. We empirically analyse the performance of simple EAs for OBCM and compare different mutation operators on the underlying permutation ordering problem: exchanging two elements (exchange), swapping adjacent elements (swap) and jumping an element to a new position (jump). EAs using jumps easily outperform all deterministic algorithms in terms of solution quality after a reasonable number of generations. We also design variations of the best-performing EAs to reduce the execution time for each generation. The improved EAs can obtain the same solution quality as before and run up to 100 times faster.
Cite as
Jakob Baumann, Ignaz Rutter, and Dirk Sudholt. Evolutionary Algorithms for One-Sided Bipartite Crossing Minimisation (Poster Abstract). In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 51:1-51:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{baumann_et_al:LIPIcs.GD.2024.51,
author = {Baumann, Jakob and Rutter, Ignaz and Sudholt, Dirk},
title = {{Evolutionary Algorithms for One-Sided Bipartite Crossing Minimisation}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {51:1--51:3},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.51},
URN = {urn:nbn:de:0030-drops-213353},
doi = {10.4230/LIPIcs.GD.2024.51},
annote = {Keywords: Mutation Operator, Layered Graphs, Crossing Minimisation}
}
Document
Poster Abstract
Polygonally Anchored Graph Drawing (Poster Abstract)
Abstract
We investigate force-directed graph drawing techniques under the constraint that some nodes must be anchored to stay within a given polygonal region associated with it (i.e. some positional information is known). The low energy layouts produced by such algorithms may reveal geographic information about nodes with no such knowledge a priori. Some applications of graph drawing with partial positional information include location-based social networks and rail networks, where the geographical locations need not be precise.
Cite as
Alvin Chiu, Ahmed Eldawy, and Michael T. Goodrich. Polygonally Anchored Graph Drawing (Poster Abstract). In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 52:1-52:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{chiu_et_al:LIPIcs.GD.2024.52,
author = {Chiu, Alvin and Eldawy, Ahmed and Goodrich, Michael T.},
title = {{Polygonally Anchored Graph Drawing}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {52:1--52:3},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.52},
URN = {urn:nbn:de:0030-drops-213369},
doi = {10.4230/LIPIcs.GD.2024.52},
annote = {Keywords: polygonal anchors, force-directed}
}
Document
Poster Abstract
String Graph with Cop Number 4 (Poster Abstract)
Abstract
Cops and Robbers is a well-studied pursuit-evasion game in which a set of cops seeks to catch a robber in a graph G, where cops and the robber move along edges of G. The cop number of G is the minimum number of cops that is sufficient to catch the robber. The game of Cops and Robbers has been well-studied on beyond-planar graphs (that is, graphs that can be drawn with only few crossings) [M. Aigner and M. Fromme, 1984; Durocher et al., 2023] as well as intersection graphs (that is, graphs where the vertices represent geometric objects, and an edge exists between two vertices if the corresponding objects intersect). We consider a well-known subclass of intersection graphs called string graphs where the objects are curves. So far no string graph with cop number larger than three was known. We construct the first string graph with cop number four, which improves the previous bound and answers an open question by Gavenčiak et al. [Tomáš Gavenčiak et al., 2018].
Cite as
Stephane Durocher, Myroslav Kryven, and Maarten Löffler. String Graph with Cop Number 4 (Poster Abstract). In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 53:1-53:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{durocher_et_al:LIPIcs.GD.2024.53,
author = {Durocher, Stephane and Kryven, Myroslav and L\"{o}ffler, Maarten},
title = {{String Graph with Cop Number 4}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {53:1--53:3},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.53},
URN = {urn:nbn:de:0030-drops-213376},
doi = {10.4230/LIPIcs.GD.2024.53},
annote = {Keywords: point set embedding, upward planar path embedding, dynamic programming}
}
Document
Poster Abstract
Approximating the Crossing Number of Dense Graphs (Poster Abstract)
Abstract
We present a deterministic n^(2+o(1))-time algorithm that approximates the crossing number of any graph G of order n up to an additive error of o(n⁴), as well as a randomized polynomial-time algorithm that constructs a drawing of G with cr(G)+o(n⁴) crossings. These results imply a (1+o(1))-approximation algorithm for the crossing number of dense graphs. Our work builds on the machinery used by Fox, Pach and Súk [Fox et al., 2016], who obtained similar results for the rectilinear crossing number.
Cite as
Oriol Solé Pi. Approximating the Crossing Number of Dense Graphs (Poster Abstract). In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 54:1-54:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{solepi:LIPIcs.GD.2024.54,
author = {Sol\'{e} Pi, Oriol},
title = {{Approximating the Crossing Number of Dense Graphs}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {54:1--54:3},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.54},
URN = {urn:nbn:de:0030-drops-213387},
doi = {10.4230/LIPIcs.GD.2024.54},
annote = {Keywords: Crossing numbers, Approximation algorithms, Geometric graph theory}
}
Document
Software Abstract
yFiles - From Data to Meaningful Visualizations (Software Abstract)
Abstract
Graph visualizations help with complex data analysis but often require expert knowledge to apply and configure advanced algorithms. yFiles, a diagramming SDK, bridges this gap by enabling developers to create interactive visualizations easily. This work demonstrates how yFiles helps transform raw data into accessible graph visualizations.
Cite as
Evmorfia Argyriou and Benjamin Niedermann. yFiles - From Data to Meaningful Visualizations (Software Abstract). In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 55:1-55:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{argyriou_et_al:LIPIcs.GD.2024.55,
author = {Argyriou, Evmorfia and Niedermann, Benjamin},
title = {{yFiles - From Data to Meaningful Visualizations}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {55:1--55:3},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.55},
URN = {urn:nbn:de:0030-drops-213398},
doi = {10.4230/LIPIcs.GD.2024.55},
annote = {Keywords: diagramming SDK, layout algorithms, interactive graph visualization}
}
Document
Software Abstract
The Eclipse Layout Kernel (Software Abstract)
Abstract
The Eclipse Layout Kernel (ELK) is an open-source framework written in Java, which is transpiled to the JavaScript library elkjs. ELK provides extensible and modular algorithms, visibility for diagramming research, and has an active community. The ELK project is both a validation platform for graph drawing algorithm researchers, and a freely available library put in production use to provide automatic layout for academic and commercial applications.
The report [S. Domrös et al., 2023] presents an overview of the available algorithms, the development history, related publications, as well as lessons learned from developing the open-source framework. ELK welcomes new users as well as new contributors.
Cite as
Maximilian Kasperowski, Sören Domrös, and Reinhard von Hanxleden. The Eclipse Layout Kernel (Software Abstract). In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 56:1-56:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{kasperowski_et_al:LIPIcs.GD.2024.56,
author = {Kasperowski, Maximilian and Domr\"{o}s, S\"{o}ren and von Hanxleden, Reinhard},
title = {{The Eclipse Layout Kernel}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {56:1--56:2},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.56},
URN = {urn:nbn:de:0030-drops-213401},
doi = {10.4230/LIPIcs.GD.2024.56},
annote = {Keywords: Automatic Layout, Layered Layout, Layout Library}
}
Document
Software Abstract
Immersive Analytics of Graphs in Virtual Reality with GAV-VR (Software Abstract)
Abstract
The design space for interactive graph visualisation in immersive environments creates opportunities to improve on established solutions in traditional desktop settings. Exploiting this potential requires careful analysis of achievable benefits, required tradeoffs, and disadvantages for particular designs and use-cases. GAV-VR is a modular and user-extensible framework for graph visualisation and analysis in Virtual Reality (VR). It provides the platform to easily create interactive graph visualisations, facilitating both applied graph analysis and evaluation of approaches and methods for visualisation of and interaction with graphs in VR.
Cite as
Stefan P. Feyer, Wilhelm Kerle-Malcharek, Ying Zhang, Falk Schreiber, and Karsten Klein. Immersive Analytics of Graphs in Virtual Reality with GAV-VR (Software Abstract). In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 57:1-57:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{feyer_et_al:LIPIcs.GD.2024.57,
author = {Feyer, Stefan P. and Kerle-Malcharek, Wilhelm and Zhang, Ying and Schreiber, Falk and Klein, Karsten},
title = {{Immersive Analytics of Graphs in Virtual Reality with GAV-VR}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {57:1--57:3},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.57},
URN = {urn:nbn:de:0030-drops-213413},
doi = {10.4230/LIPIcs.GD.2024.57},
annote = {Keywords: Networks, Immersive Analytics, Software}
}
Document
Software Abstract
Graph Harvester (Software Abstract)
Abstract
We present Graph Harvester, a website for extracting graphs from illustrations in scientific papers. For every graph that has been extracted, Graph Harvester queries the graph database House of Graphs. If the graph is not already present there, the user can upload the graph into the database, possibly after modifying it, and with a reference to the paper that contains the drawing of the graph.
Cite as
Julius Deynet, Tim Hegemann, Sebastian Kempf, and Alexander Wolff. Graph Harvester (Software Abstract). In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 58:1-58:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{deynet_et_al:LIPIcs.GD.2024.58,
author = {Deynet, Julius and Hegemann, Tim and Kempf, Sebastian and Wolff, Alexander},
title = {{Graph Harvester}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {58:1--58:3},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.58},
URN = {urn:nbn:de:0030-drops-213427},
doi = {10.4230/LIPIcs.GD.2024.58},
annote = {Keywords: House of Graphs, Graph recognition, Information extraction}
}
Document
Software Abstract
CentralityViz: Comprehending Node-Centrality in Large Networks (Software Abstract)
Abstract
CentralityVis is a software tool designed for visualizing large graphs using two community-centric methods: spiral visualization and linear visualization. Both visualizations are highly scalable, capable of handling networks with hundreds of thousands of nodes and edges. The tool leverages community detection algorithms to group nodes into communities and then orders the nodes of community on centrality in descending order, arranging them in either a spiral or linear layout. CentralityVis provides clear insights into both node and community properties, facilitating the analysis of complex networks. Each visualization method has its strengths: spiral visualization is intuitive and resembles traditional node-link diagrams, while linear visualization facilitates easy comparison of communities and offers greater scalability in terms of the number of communities that can be represented. To minimize visual clutter, edges are drawn only when needed, ensuring that even large graphs remain clear and comprehensible. CentralityVis is a powerful tool for understanding complex networks, emphasizing both individual nodes and the communities to which they belong.
Cite as
Garima Jindal and Kamalakar Karlapalem. CentralityViz: Comprehending Node-Centrality in Large Networks (Software Abstract). In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 59:1-59:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{jindal_et_al:LIPIcs.GD.2024.59,
author = {Jindal, Garima and Karlapalem, Kamalakar},
title = {{CentralityViz: Comprehending Node-Centrality in Large Networks}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {59:1--59:3},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.59},
URN = {urn:nbn:de:0030-drops-213439},
doi = {10.4230/LIPIcs.GD.2024.59},
annote = {Keywords: Visual Analytics, Graph Drawing, Community Detection, Node Centrality}
}
Document
Software Abstract
NodeXL - A few Clicks to Network Insights (Software Abstract)
Abstract
Network analysis and visualization are crucial for unraveling complex relationships across diverse fields, from social networks to biological systems. NodeXL is a versatile network analysis tool that supports a wide range of network data types and provides seamless access to various social media platforms.
Cite as
Harald Meier and Arber Ceni. NodeXL - A few Clicks to Network Insights (Software Abstract). In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 60:1-60:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{meier_et_al:LIPIcs.GD.2024.60,
author = {Meier, Harald and Ceni, Arber},
title = {{NodeXL - A few Clicks to Network Insights}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {60:1--60:2},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.60},
URN = {urn:nbn:de:0030-drops-213440},
doi = {10.4230/LIPIcs.GD.2024.60},
annote = {Keywords: Network Analysis, NodeXL, Social Networks}
}
Document
Software Abstract
Knowledge Graph Builder - Constructing a Graph from Arbitrary Text Using an LLM (Software Abstract)
Abstract
Knowledge graphs improve many information retrieval tasks over structured and unstructured data. However, knowledge graph construction can be challenging even for domain experts. The Knowledge Graph Builder is an application incorporating advanced techniques for deriving a knowledge graph from unstructured data using an LLM.
Cite as
Andreas Benno Kollegger, Alexander Erdl, and Michael Hunger. Knowledge Graph Builder - Constructing a Graph from Arbitrary Text Using an LLM (Software Abstract). In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 61:1-61:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
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@InProceedings{kollegger_et_al:LIPIcs.GD.2024.61,
author = {Kollegger, Andreas Benno and Erdl, Alexander and Hunger, Michael},
title = {{Knowledge Graph Builder - Constructing a Graph from Arbitrary Text Using an LLM}},
booktitle = {32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
pages = {61:1--61:2},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-343-0},
ISSN = {1868-8969},
year = {2024},
volume = {320},
editor = {Felsner, Stefan and Klein, Karsten},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.61},
URN = {urn:nbn:de:0030-drops-213451},
doi = {10.4230/LIPIcs.GD.2024.61},
annote = {Keywords: Knowledge Graph, Lexical Graph}
}