7 Search Results for "Klesen, Felix"

Document
DOI: 10.4230/LIPIcs.GD.2025.17
Visualizing Treewidth

Authors: Alvin Chiu, Thomas Depian, David Eppstein, Michael T. Goodrich, and Martin Nöllenburg

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

Abstract
A witness drawing of a graph is a visualization that clearly shows a given property of a graph. We study and implement various drawing paradigms for witness drawings to clearly show that graphs have bounded pathwidth or treewidth. Our approach draws the tree decomposition or path decomposition as a tree of bags, with induced subgraphs shown in each bag, and with "tracks" for each graph vertex connecting its copies in multiple bags. Within bags, we optimize the vertex layout to avoid crossings of edges and tracks. We implement a visualization prototype for crossing minimization using dynamic programming for graphs of small width and heuristic approaches for graphs of larger width. We introduce a taxonomy of drawing styles, which render the subgraph for each bag as an arc diagram with one or two pages or as a circular layout with straight-line edges, and we render tracks either with straight lines or with orbital-radial paths.
Cite as

Alvin Chiu, Thomas Depian, David Eppstein, Michael T. Goodrich, and Martin Nöllenburg. Visualizing Treewidth. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 17:1-17:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chiu_et_al:LIPIcs.GD.2025.17,
  author =	{Chiu, Alvin and Depian, Thomas and Eppstein, David and Goodrich, Michael T. and N\"{o}llenburg, Martin},
  title =	{{Visualizing Treewidth}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{17:1--17:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.17},
  URN =		{urn:nbn:de:0030-drops-250034},
  doi =		{10.4230/LIPIcs.GD.2025.17},
  annote =	{Keywords: Graph drawing, witness drawings, pathwidth, treewidth}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.65
Recognizing 2-Layer and Outer k-Planar Graphs

Authors: Yasuaki Kobayashi, Yuto Okada, and Alexander Wolff

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
The crossing number of a graph is the least number of crossings over all drawings of the graph in the plane. Computing the crossing number of a given graph is NP-hard, but fixed-parameter tractable (FPT) with respect to the natural parameter. Two well-known variants of the problem are 2-layer crossing minimization and circular crossing minimization, where every vertex must lie on one of two layers, namely two parallel lines, or a circle, respectively. In both cases, edges are drawn as straight-line segments. Both variants are NP-hard, but admit FPT-algorithms with respect to the natural parameter. In recent years, in the context of beyond-planar graphs, a local version of the crossing number has also received considerable attention. A graph is k-planar if it admits a drawing with at most k crossings per edge. In contrast to the crossing number, recognizing k-planar graphs is NP-hard even if k = 1 and hence not likely to be FPT with respect to the natural parameter k. In this paper, we consider the two above variants in the local setting. The k-planar graphs that admit a straight-line drawing with vertices on two layers or on a circle are called 2-layer k-planar and outer k-planar graphs, respectively. We study the parameterized complexity of the two recognition problems with respect to the natural parameter k. For k = 0, the two classes of graphs are exactly the caterpillars and outerplanar graphs, respectively, which can be recognized in linear time. Two groups of researchers independently showed that outer 1-planar graphs can also be recognized in linear time [Hong et al., Algorithmica 2015; Auer et al., Algorithmica 2016]. One group asked explicitly whether outer 2-planar graphs can be recognized in polynomial time. Our main contribution consists of XP-algorithms for recognizing 2-layer k-planar graphs and outer k-planar graphs, which implies that both recognition problems can be solved in polynomial time for every fixed k. We complement these results by showing that recognizing 2-layer k-planar graphs is XNLP-complete and that recognizing outer k-planar graphs is XNLP-hard. This implies that both problems are W[t]-hard for every t and that it is unlikely that they admit FPT-algorithms. On the other hand, we present an FPT-algorithm for recognizing 2-layer k-planar graphs where the order of the vertices on one layer is specified.
Cite as

Yasuaki Kobayashi, Yuto Okada, and Alexander Wolff. Recognizing 2-Layer and Outer k-Planar Graphs. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 65:1-65:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kobayashi_et_al:LIPIcs.SoCG.2025.65,
  author =	{Kobayashi, Yasuaki and Okada, Yuto and Wolff, Alexander},
  title =	{{Recognizing 2-Layer and Outer k-Planar Graphs}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{65:1--65:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.65},
  URN =		{urn:nbn:de:0030-drops-232170},
  doi =		{10.4230/LIPIcs.SoCG.2025.65},
  annote =	{Keywords: 2-layer k-planar graphs, outer k-planar graphs, recognition algorithms, local crossing number, bandwidth, FPT, XNLP, XP, W\lbrackt\rbrack}
}
Document
DOI: 10.4230/LIPIcs.GD.2024.16
GraphTrials: Visual Proofs of Graph Properties

Authors: 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

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

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
DOI: 10.4230/LIPIcs.GD.2024.26
Storylines with a Protagonist

Authors: Tim Hegemann and Alexander Wolff

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

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
DOI: 10.4230/LIPIcs.SoCG.2024.20
Constrained and Ordered Level Planarity Parameterized by the Number of Levels

Authors: Václav Blažej, Boris Klemz, Felix Klesen, Marie Diana Sieper, Alexander Wolff, and Johannes Zink

Published in: LIPIcs, Volume 293, 40th International Symposium on Computational Geometry (SoCG 2024)

Abstract
The problem Level Planarity asks for a crossing-free drawing of a graph in the plane such that vertices are placed at prescribed y-coordinates (called levels) and such that every edge is realized as a y-monotone curve. In the variant Constrained Level Planarity (CLP), each level y is equipped with a partial order ≺_y on its vertices and in the desired drawing the left-to-right order of vertices on level y has to be a linear extension of ≺_y. Ordered Level Planarity (OLP) corresponds to the special case of CLP where the given partial orders ≺_y are total orders. Previous results by Brückner and Rutter [SODA 2017] and Klemz and Rote [ACM Trans. Alg. 2019] state that both CLP and OLP are NP-hard even in severely restricted cases. In particular, they remain NP-hard even when restricted to instances whose width (the maximum number of vertices that may share a common level) is at most two. In this paper, we focus on the other dimension: we study the parameterized complexity of CLP and OLP with respect to the height (the number of levels). We show that OLP parameterized by the height is complete with respect to the complexity class XNLP, which was first studied by Elberfeld, Stockhusen, and Tantau [Algorithmica 2015] (under a different name) and recently made more prominent by Bodlaender, Groenland, Nederlof, and Swennenhuis [FOCS 2021]. It contains all parameterized problems that can be solved nondeterministically in time f(k)⋅ n^O(1) and space f(k)⋅ log n (where f is a computable function, n is the input size, and k is the parameter). If a problem is XNLP-complete, it lies in XP, but is W[t]-hard for every t. In contrast to the fact that OLP parameterized by the height lies in XP, it turns out that CLP is NP-hard even when restricted to instances of height 4. We complement this result by showing that CLP can be solved in polynomial time for instances of height at most 3.
Cite as

Václav Blažej, Boris Klemz, Felix Klesen, Marie Diana Sieper, Alexander Wolff, and Johannes Zink. Constrained and Ordered Level Planarity Parameterized by the Number of Levels. In 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 293, pp. 20:1-20:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{blazej_et_al:LIPIcs.SoCG.2024.20,
  author =	{Bla\v{z}ej, V\'{a}clav and Klemz, Boris and Klesen, Felix and Sieper, Marie Diana and Wolff, Alexander and Zink, Johannes},
  title =	{{Constrained and Ordered Level Planarity Parameterized by the Number of Levels}},
  booktitle =	{40th International Symposium on Computational Geometry (SoCG 2024)},
  pages =	{20:1--20:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-316-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{293},
  editor =	{Mulzer, Wolfgang and Phillips, Jeff M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2024.20},
  URN =		{urn:nbn:de:0030-drops-199652},
  doi =		{10.4230/LIPIcs.SoCG.2024.20},
  annote =	{Keywords: Parameterized Complexity, Graph Drawing, XNLP, XP, W\lbrackt\rbrack-hard, Level Planarity, Planar Poset Diagram, Computational Geometry}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2023.36
Coloring and Recognizing Mixed Interval Graphs

Authors: Grzegorz Gutowski, Konstanty Junosza-Szaniawski, Felix Klesen, Paweł Rzążewski, Alexander Wolff, and Johannes Zink

Published in: LIPIcs, Volume 283, 34th International Symposium on Algorithms and Computation (ISAAC 2023)

Abstract
A mixed interval graph is an interval graph that has, for every pair of intersecting intervals, either an arc (directed arbitrarily) or an (undirected) edge. We are particularly interested in scenarios where edges and arcs are defined by the geometry of intervals. In a proper coloring of a mixed interval graph G, an interval u receives a lower (different) color than an interval v if G contains arc (u,v) (edge {u,v}). Coloring of mixed graphs has applications, for example, in scheduling with precedence constraints; see a survey by Sotskov [Mathematics, 2020]. For coloring general mixed interval graphs, we present a min {ω(G), λ(G)+1}-approximation algorithm, where ω(G) is the size of a largest clique and λ(G) is the length of a longest directed path in G. For the subclass of bidirectional interval graphs (introduced recently for an application in graph drawing), we show that optimal coloring is NP-hard. This was known for general mixed interval graphs. We introduce a new natural class of mixed interval graphs, which we call containment interval graphs. In such a graph, there is an arc (u,v) if interval u contains interval v, and there is an edge {u,v} if u and v overlap. We show that these graphs can be recognized in polynomial time, that coloring them with the minimum number of colors is NP-hard, and that there is a 2-approximation algorithm for coloring.
Cite as

Grzegorz Gutowski, Konstanty Junosza-Szaniawski, Felix Klesen, Paweł Rzążewski, Alexander Wolff, and Johannes Zink. Coloring and Recognizing Mixed Interval Graphs. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 36:1-36:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{gutowski_et_al:LIPIcs.ISAAC.2023.36,
  author =	{Gutowski, Grzegorz and Junosza-Szaniawski, Konstanty and Klesen, Felix and Rz\k{a}\.{z}ewski, Pawe{\l} and Wolff, Alexander and Zink, Johannes},
  title =	{{Coloring and Recognizing Mixed Interval Graphs}},
  booktitle =	{34th International Symposium on Algorithms and Computation (ISAAC 2023)},
  pages =	{36:1--36:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-289-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{283},
  editor =	{Iwata, Satoru and Kakimura, Naonori},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2023.36},
  URN =		{urn:nbn:de:0030-drops-193388},
  doi =		{10.4230/LIPIcs.ISAAC.2023.36},
  annote =	{Keywords: Interval Graphs, Mixed Graphs, Graph Coloring}
}
Document
DOI: 10.4230/LIPIcs.GIScience.2023.5
Visualizing Geophylogenies - Internal and External Labeling with Phylogenetic Tree Constraints

Authors: Jonathan Klawitter, Felix Klesen, Joris Y. Scholl, Thomas C. van Dijk, and Alexander Zaft

Published in: LIPIcs, Volume 277, 12th International Conference on Geographic Information Science (GIScience 2023)

Abstract
A geophylogeny is a phylogenetic tree where each leaf (biological taxon) has an associated geographic location (site). To clearly visualize a geophylogeny, the tree is typically represented as a crossing-free drawing next to a map. The correspondence between the taxa and the sites is either shown with matching labels on the map (internal labeling) or with leaders that connect each site to the corresponding leaf of the tree (external labeling). In both cases, a good order of the leaves is paramount for understanding the association between sites and taxa. We define several quality measures for internal labeling and give an efficient algorithm for optimizing them. In contrast, minimizing the number of leader crossings in an external labeling is NP-hard. We show nonetheless that optimal solutions can be found in a matter of seconds on realistic instances using integer linear programming. Finally, we provide several efficient heuristic algorithms and experimentally show them to be near optimal on real-world and synthetic instances.
Cite as

Jonathan Klawitter, Felix Klesen, Joris Y. Scholl, Thomas C. van Dijk, and Alexander Zaft. Visualizing Geophylogenies - Internal and External Labeling with Phylogenetic Tree Constraints. In 12th International Conference on Geographic Information Science (GIScience 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 277, pp. 5:1-5:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{klawitter_et_al:LIPIcs.GIScience.2023.5,
  author =	{Klawitter, Jonathan and Klesen, Felix and Scholl, Joris Y. and van Dijk, Thomas C. and Zaft, Alexander},
  title =	{{Visualizing Geophylogenies - Internal and External Labeling with Phylogenetic Tree Constraints}},
  booktitle =	{12th International Conference on Geographic Information Science (GIScience 2023)},
  pages =	{5:1--5:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-288-4},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{277},
  editor =	{Beecham, Roger and Long, Jed A. and Smith, Dianna and Zhao, Qunshan and Wise, Sarah},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GIScience.2023.5},
  URN =		{urn:nbn:de:0030-drops-189004},
  doi =		{10.4230/LIPIcs.GIScience.2023.5},
  annote =	{Keywords: geophylogeny, boundary labeling, external labeling, algorithms}
}
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