23 Search Results for "Di Giacomo, Emilio"

Document
DOI: 10.4230/LIPIcs.SWAT.2026.6
How Many Slopes Does Polynomial Area Cost?

Authors: Michael A. Bekos, Eleni Katsanou, Philipp Kindermann, and Maria Eleni Pavlidi

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract
In this work, we study the interplay between the number of slopes, the number of bends per edge, and the area requirements for planar drawings of bounded-degree graphs. Our motivation stems from the fact that, while numerous algorithms produce planar drawings with few slopes for graphs of relatively small degree in polynomial area, existing approaches for higher-degree graphs often require super-polynomial area. We address this gap in the literature by presenting new constructions that yield polynomial-area drawings with few bends per edge while slightly increasing the required number of slopes, thereby providing the first systematic study of slopes, bends and area trade-offs.
Cite as

Michael A. Bekos, Eleni Katsanou, Philipp Kindermann, and Maria Eleni Pavlidi. How Many Slopes Does Polynomial Area Cost?. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 6:1-6:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bekos_et_al:LIPIcs.SWAT.2026.6,
  author =	{Bekos, Michael A. and Katsanou, Eleni and Kindermann, Philipp and Pavlidi, Maria Eleni},
  title =	{{How Many Slopes Does Polynomial Area Cost?}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{6:1--6:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.6},
  URN =		{urn:nbn:de:0030-drops-260424},
  doi =		{10.4230/LIPIcs.SWAT.2026.6},
  annote =	{Keywords: k-bend planar drawings, planar slope number, area requirements}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.36
Upward Book Embeddings of Partitioned Digraphs

Authors: Giordano Da Lozzo, Fabrizio Frati, and Ignaz Rutter

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
In 1999, Heath, Pemmaraju, and Trenk [SIAM J. Comput. 28(4), 1999] extended the classic notion of book embeddings to digraphs, introducing the concept of upward book embeddings, in which the vertices must appear along the spine in a topological order and the edges are partitioned into pages, so that no two edges in the same page cross. For a partitioned digraph G = (V, ⋃^k_{i=1} E_i), that is, a digraph whose edge set is partitioned into k subsets, an upward book embedding is required to assign edges to pages as prescribed by the given partition. In a companion paper, Heath and Pemmaraju [SIAM J. Comput. 28(5), 1999] proved that the problem of testing the existence of an upward book embedding of a partitioned digraph is linear-time solvable for k = 1 and recently Akitaya, Demaine, Hesterberg, and Liu [GD, 2017] have shown the problem NP-complete for k ≥ 3. In this paper, we study upward book embeddings of partitioned digraphs and focus on the unsolved case k = 2. Our first main result is a novel characterization of the upward embeddings that support an upward book embedding in two pages. We exploit this characterization in several ways, and obtain a rich picture of the complexity landscape of the problem. First, we show that the problem remains NP-complete when k = 2, thus closing the complexity gap for the problem. Second, we show that, for an n-vertex partitioned digraph with a prescribed planar embedding, the existence of an upward book embedding that respects the given planar embedding can be tested in O(n log³ n) time. Finally, leveraging the SPQ(R)-tree decomposition of biconnected graphs into triconnected components, we present a cubic-time testing algorithm for biconnected directed partial 2-trees.
Cite as

Giordano Da Lozzo, Fabrizio Frati, and Ignaz Rutter. Upward Book Embeddings of Partitioned Digraphs. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 36:1-36:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{dalozzo_et_al:LIPIcs.SoCG.2026.36,
  author =	{Da Lozzo, Giordano and Frati, Fabrizio and Rutter, Ignaz},
  title =	{{Upward Book Embeddings of Partitioned Digraphs}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{36:1--36:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.36},
  URN =		{urn:nbn:de:0030-drops-258424},
  doi =		{10.4230/LIPIcs.SoCG.2026.36},
  annote =	{Keywords: upward book embeddings, partitioned digraphs, SPQ-trees, 2-trees}
}
Document
DOI: 10.4230/LIPIcs.GD.2025.21
On Geometric Bipartite Graphs with Asymptotically Smallest Zarankiewicz Numbers

Authors: Parinya Chalermsook, Ly Orgo, and Minoo Zarsav

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

Abstract
This paper considers the Zarankiewicz problem in bipartite graphs with low-dimensional geometric representation (i.e., low Ferrers dimension). Let Z(n;k) be the maximum number of edges in a bipartite graph with n nodes and is free of a k-by-k biclique. Note that Z(n;k) ∈ Ω(nk) for all "natural" graph classes. Our first result reveals a separation between bipartite graphs of Ferrers dimension three and four: while we show that Z(n;k) ≤ 9n(k-1) for graphs of Ferrers dimension three, Z(n;k) ∈ Ω(n k ⋅ (log n)/(log log n)) for Ferrers dimension four graphs (Chan & Har-Peled, 2023) (Chazelle, 1990). To complement this, we derive a tight upper bound of 2n(k-1) for chordal bipartite graphs and 54n(k-1) for grid intersection graphs (GIG), a prominent graph class residing in four Ferrers dimensions and capturing planar bipartite graphs as well as bipartite intersection graphs of rectangles. Previously, the best-known bound for GIG was Z(n;k) ∈ O(2^{O(k)} n), implied by the results of Fox & Pach (2006) and Mustafa & Pach (2016). Our results advance and offer new insights into the interplay between Ferrers dimensions and extremal combinatorics.
Cite as

Parinya Chalermsook, Ly Orgo, and Minoo Zarsav. On Geometric Bipartite Graphs with Asymptotically Smallest Zarankiewicz Numbers. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 21:1-21:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chalermsook_et_al:LIPIcs.GD.2025.21,
  author =	{Chalermsook, Parinya and Orgo, Ly and Zarsav, Minoo},
  title =	{{On Geometric Bipartite Graphs with Asymptotically Smallest Zarankiewicz Numbers}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{21:1--21:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.21},
  URN =		{urn:nbn:de:0030-drops-250074},
  doi =		{10.4230/LIPIcs.GD.2025.21},
  annote =	{Keywords: Bipartite graph classes, extremal graph theory, geometric intersection graphs, Zarankiewicz problem, bicliques}
}
Document
DOI: 10.4230/LIPIcs.GD.2025.27
Geometry Matters in Planar Storyplans

Authors: Alexander Dobler, Maximilian Holzmüller, and Martin Nöllenburg

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

Abstract
A storyplan visualizes a graph G = (V,E) as a sequence of 𝓁 frames Γ₁, … , Γ_𝓁, each of which is a drawing of the induced subgraph G[V_i] of a vertex subset V_i ⊆ V. Moreover, each vertex v ∈ V is contained in a single consecutive sequence of frames Γ_i, … , Γ_j, all vertices and edges contained in consecutive frames are drawn identically, and the union of all frames is a drawing of G. In GD 2022, the concept of planar storyplans was introduced, in which each frame must be a planar (topological) drawing. Several (parameterized) complexity results for recognizing graphs that admit a planar storyplan were provided, including NP-hardness. In this paper, we investigate an open question posed in the GD paper and show that the geometric and topological settings of the planar storyplan problem differ: We provide an instance of a graph that admits a planar storyplan, but no planar geometric storyplan, in which each frame is a planar straight-line drawing. Still, by adapting the reduction proof from the topological to the geometric setting, we show that recognizing the graphs that admit planar geometric storyplans remains NP-hard.
Cite as

Alexander Dobler, Maximilian Holzmüller, and Martin Nöllenburg. Geometry Matters in Planar Storyplans. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 27:1-27:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dobler_et_al:LIPIcs.GD.2025.27,
  author =	{Dobler, Alexander and Holzm\"{u}ller, Maximilian and N\"{o}llenburg, Martin},
  title =	{{Geometry Matters in Planar Storyplans}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{27:1--27:9},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.27},
  URN =		{urn:nbn:de:0030-drops-250135},
  doi =		{10.4230/LIPIcs.GD.2025.27},
  annote =	{Keywords: geometric storyplan, planarity, straight-line drawing, dynamic graph drawing}
}
Document
Poster Abstract
DOI: 10.4230/LIPIcs.GD.2025.49
Defective Linear Layouts of Graphs (Poster Abstract)

Authors: Michael A. Bekos, Carla Binucci, Emilio Di Giacomo, Walter Didimo, Luca Grilli, Maria Eleni Pavlidi, Alessandra Tappini, and Alexandra Weinberger

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

Abstract
A linear layout of a graph defines a total order of the vertices and partitions the edges into either stacks or queues, i.e., crossing-free and non-nested sets of edges along the order, respectively. In this work, we study defective linear layouts that allow forbidden patterns among edges of the same set. Our focus is on k-defective stack layouts and k-defective queue layouts, in which the conflict graph representing the forbidden patterns among the edges of each stack or queue has maximum degree at most k.
Cite as

Michael A. Bekos, Carla Binucci, Emilio Di Giacomo, Walter Didimo, Luca Grilli, Maria Eleni Pavlidi, Alessandra Tappini, and Alexandra Weinberger. Defective Linear Layouts of Graphs (Poster Abstract). In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 49:1-49:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bekos_et_al:LIPIcs.GD.2025.49,
  author =	{Bekos, Michael A. and Binucci, Carla and Di Giacomo, Emilio and Didimo, Walter and Grilli, Luca and Pavlidi, Maria Eleni and Tappini, Alessandra and Weinberger, Alexandra},
  title =	{{Defective Linear Layouts of Graphs}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{49:1--49:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.49},
  URN =		{urn:nbn:de:0030-drops-250350},
  doi =		{10.4230/LIPIcs.GD.2025.49},
  annote =	{Keywords: Linear layouts, stack layouts, queue layouts, defective layouts}
}
Document
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.GD.2025.14
OOPS: Optimized One-Planarity Solver via SAT

Authors: Sergey Pupyrev

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

Abstract
We present OOPS (Optimized One-Planarity Solver), a practical heuristic for recognizing 1-planar graphs and several important subclasses. A graph is 1-planar if it can be drawn in the plane such that each edge is crossed at most once - a natural generalization of planar graphs that has received increasing attention in graph drawing and beyond-planar graph theory. Although testing planarity can be done in linear time, recognizing 1-planar graphs is NP-complete, making effective practical algorithms especially valuable. The core idea of our approach is to reduce the recognition of 1-planarity to a propositional satisfiability (SAT) instance, enabling the use of modern SAT solvers to efficiently explore the search space. Despite the inherent complexity of the problem, our method is substantially faster in practice than naïve or brute-force algorithms. In addition to demonstrating the empirical performance of our solver on synthetic and real-world instances, we show how OOPS can be used as a discovery tool in theoretical graph theory. Specifically, we employ OOPS to investigate two research problems concerning 1-planarity of specific graph families. Our implementation of the algorithm is publicly available to support further exploration in the field.
Cite as

Sergey Pupyrev. OOPS: Optimized One-Planarity Solver via SAT. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 14:1-14:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{pupyrev:LIPIcs.GD.2025.14,
  author =	{Pupyrev, Sergey},
  title =	{{OOPS: Optimized One-Planarity Solver via SAT}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{14:1--14:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.14},
  URN =		{urn:nbn:de:0030-drops-250004},
  doi =		{10.4230/LIPIcs.GD.2025.14},
  annote =	{Keywords: beyond planarity, 1-planar graph, SAT, book embeddings, upward 1-planarity}
}
Document
DOI: 10.4230/LIPIcs.GD.2025.9
The Page Number of Monotone Directed Acyclic Outerplanar Graphs Is Four or Five

Authors: Jawaherul Md. Alam, Michael A. Bekos, Martin Gronemann, and Michael Kaufmann

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

Abstract
A k-page book embedding of a directed acyclic graph consists of a topological order of its vertices and a k-coloring of its edges, such that no two edges of the same color cross, that is, their endpoints do not alternate in the order. The minimum value of k for which such an embedding exists is referred to as the page number of the graph. In contrast to general directed acyclic planar graphs, which may have unbounded page number [SIAM J. Comput. 28(5), 1999], it was recently shown that directed acyclic outerplanar graphs have bounded page number. In particular, Jungeblut, Merker and Ueckerdt provided an upper bound of 24,776 on their page number [FOCS 2023: 1937-1952]. In this work, we focus on so-called monotone directed acyclic outerplanar graphs. Starting from a single edge, these graphs are constructed by iteratively connecting a new vertex to the endpoints of an existing edge on the outer face using either two incoming or two outgoing edges incident to it. These graphs have twist-number 4 [GD 2023: 135-151] (i.e., they admit a topological order in which no more than four edges pairwise cross), a property, which was leveraged by Jungeblut, Merker and Ueckerdt to show that their page number is at most 128. We lower this upper bound to 5 and we also provide a lower bound of 4. A notable consequence of our result is a significant improvement of the upper bound on the page number of general directed outerplanar graphs from 24,776 to 1,160.
Cite as

Jawaherul Md. Alam, Michael A. Bekos, Martin Gronemann, and Michael Kaufmann. The Page Number of Monotone Directed Acyclic Outerplanar Graphs Is Four or Five. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{alam_et_al:LIPIcs.GD.2025.9,
  author =	{Alam, Jawaherul Md. and Bekos, Michael A. and Gronemann, Martin and Kaufmann, Michael},
  title =	{{The Page Number of Monotone Directed Acyclic Outerplanar Graphs Is Four or Five}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{9:1--9:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.9},
  URN =		{urn:nbn:de:0030-drops-249952},
  doi =		{10.4230/LIPIcs.GD.2025.9},
  annote =	{Keywords: Book embeddings, page number, directed outerplanar graphs}
}
Document
DOI: 10.4230/LIPIcs.GD.2025.13
Separability of Witness Gabriel Drawings

Authors: Carolina Haase, Philipp Kindermann, William Lenhart, and Giuseppe Liotta

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

Abstract
A witness Gabriel drawing Γ is a straight-line drawing of a graph in which any two vertices of Γ are adjacent if and only if the disk having these vertices as antipodal points contains no element of a special set of points called witnesses. A witness Gabriel drawing is linearly separable if the vertices and the witnesses lie in opposite half-planes. We prove that every outerplanar graph has a linearly separable witness Gabriel drawing by introducing and studying a new type of drawing that we call a border parabola drawing. We then use border parabola drawings to characterize those triangle-free graphs that admit a linearly separable witness Gabriel drawing. We also consider witness Gabriel drawings where no witness lies in the interior of the convex hull of the vertex set, which we call convexly separable drawings. We construct witness Gabriel drawable graphs for which any witness Gabriel drawing must be convexly separable and that do not admit any linearly separable witness Gabriel drawing.
Cite as

Carolina Haase, Philipp Kindermann, William Lenhart, and Giuseppe Liotta. Separability of Witness Gabriel Drawings. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 13:1-13:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{haase_et_al:LIPIcs.GD.2025.13,
  author =	{Haase, Carolina and Kindermann, Philipp and Lenhart, William and Liotta, Giuseppe},
  title =	{{Separability of Witness Gabriel Drawings}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{13:1--13:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.13},
  URN =		{urn:nbn:de:0030-drops-249998},
  doi =		{10.4230/LIPIcs.GD.2025.13},
  annote =	{Keywords: Proximity Drawings, Witness Gabriel Graphs, Geometric Graph Theory}
}
Document
DOI: 10.4230/LIPIcs.GD.2025.39
Optimizing Wiggle in Storylines

Authors: Alexander Dobler, Tim Hegemann, Martin Nöllenburg, and Alexander Wolff

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

Abstract
A storyline visualization shows interactions between characters over time. Each character is represented by an x-monotone curve. Time is mapped to the x-axis, and groups of characters that interact at a particular point t in time must be ordered consecutively in the y-dimension at x = t. The predominant objective in storyline optimization so far has been the minimization of crossings between (blocks of) characters. Building on this work, we investigate another important, but less studied quality criterion, namely the minimization of wiggle, i.e., the amount of vertical movement of the characters over time. Given a storyline instance together with an ordering of the characters at any point in time, we show that wiggle count minimization is NP-complete. In contrast, we provide algorithms based on mathematical programming to solve linear wiggle height minimization and quadratic wiggle height minimization efficiently. Finally, we introduce a new method for routing character curves that focuses on keeping distances between neighboring curves constant as long as they run in parallel. We have implemented our algorithms, and we conduct a case study that explores the differences between the three optimization objectives. We use existing benchmark data, but we also present a new use case for storylines, namely the visualization of rolling stock schedules in railway operation.
Cite as

Alexander Dobler, Tim Hegemann, Martin Nöllenburg, and Alexander Wolff. Optimizing Wiggle in Storylines. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 39:1-39:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dobler_et_al:LIPIcs.GD.2025.39,
  author =	{Dobler, Alexander and Hegemann, Tim and N\"{o}llenburg, Martin and Wolff, Alexander},
  title =	{{Optimizing Wiggle in Storylines}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{39:1--39:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.39},
  URN =		{urn:nbn:de:0030-drops-250252},
  doi =		{10.4230/LIPIcs.GD.2025.39},
  annote =	{Keywords: Storyline visualization, wiggle minimization, NP-complete, linear programming, quadratic programming, experimental analysis}
}
Document
DOI: 10.4230/LIPIcs.GD.2025.32
Planar Stories of Graph Drawings: Algorithms and Experiments

Authors: Carla Binucci, Sabine Cornelsen, Walter Didimo, Seok-Hee Hong, Eleni Katsanou, Maurizio Patrignani, Antonios Symvonis, and Samuel Wolf

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

Abstract
We address the problem of computing a dynamic visualization of a geometric graph G as a sequence of frames. Each frame shows only a portion of the graph but their union covers G entirely. The two main requirements of our dynamic visualization are: (i) guaranteeing drawing stability, so to preserve the user’s mental map; (ii) keeping the visual complexity of each frame low. To satisfy the first requirement, we never change the position of the vertices. Regarding the second requirement, we avoid edge crossings in each frame. More precisely, in the first frame we visualize a suitable subset of non-crossing edges; in each subsequent frame, exactly one new edge enters the visualization and all the edges that cross with it are deleted. We call such a sequence of frames a planar story of G. Our goal is to find a planar story whose minimum number of edges contemporarily displayed is maximized (i.e., a planar story that maximizes the minimum frame size). Besides studying our model from a theoretical point of view, we also design and experimentally compare different algorithms, both exact techniques and heuristics. These algorithms provide an array of alternative trade-offs between efficiency and effectiveness, also depending on the structure of the input graph.
Cite as

Carla Binucci, Sabine Cornelsen, Walter Didimo, Seok-Hee Hong, Eleni Katsanou, Maurizio Patrignani, Antonios Symvonis, and Samuel Wolf. Planar Stories of Graph Drawings: Algorithms and Experiments. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 32:1-32:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{binucci_et_al:LIPIcs.GD.2025.32,
  author =	{Binucci, Carla and Cornelsen, Sabine and Didimo, Walter and Hong, Seok-Hee and Katsanou, Eleni and Patrignani, Maurizio and Symvonis, Antonios and Wolf, Samuel},
  title =	{{Planar Stories of Graph Drawings: Algorithms and Experiments}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{32:1--32:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.32},
  URN =		{urn:nbn:de:0030-drops-250182},
  doi =		{10.4230/LIPIcs.GD.2025.32},
  annote =	{Keywords: Graph Drawing, Dynamic Graphs, Graph Stories, Heuristics, ILP}
}
Document
DOI: 10.4230/LIPIcs.GD.2025.35
A Walk on the Wild Side: A Shape-First Methodology for Orthogonal Drawings

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

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

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

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

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@InProceedings{andreola_et_al:LIPIcs.GD.2025.35,
  author =	{Andreola, Giordano and Caroppo, Susanna and Di Battista, Giuseppe and Grosso, Fabrizio and Patrignani, Maurizio and Strippoli, Allegra},
  title =	{{A Walk on the Wild Side: A Shape-First Methodology for Orthogonal Drawings}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{35:1--35:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.35},
  URN =		{urn:nbn:de:0030-drops-250218},
  doi =		{10.4230/LIPIcs.GD.2025.35},
  annote =	{Keywords: Non-planar Orthogonal Drawings, SAT Solver, Experimental Comparison}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.5
On Planar Straight-Line Dominance Drawings

Authors: Patrizio Angelini, Michael A. Bekos, Giuseppe Di Battista, Fabrizio Frati, Luca Grilli, and Giacomo Ortali

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
We study the following question, which has been considered since the 90’s: Does every st-planar graph admit a planar straight-line dominance drawing? We show concrete evidence for the difficulty of this question, by proving that, unlike upward planar straight-line drawings, planar straight-line dominance drawings with prescribed y-coordinates do not always exist and planar straight-line dominance drawings cannot always be constructed via a contract-draw-expand inductive approach. We also show several classes of st-planar graphs that always admit a planar straight-line dominance drawing. These include st-planar 3-trees in which every stacking operation introduces two edges incoming into the new vertex, st-planar graphs in which every vertex is adjacent to the sink, and st-planar graphs in which no face has the left boundary that is a single edge.
Cite as

Patrizio Angelini, Michael A. Bekos, Giuseppe Di Battista, Fabrizio Frati, Luca Grilli, and Giacomo Ortali. On Planar Straight-Line Dominance Drawings. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 5:1-5:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{angelini_et_al:LIPIcs.WADS.2025.5,
  author =	{Angelini, Patrizio and Bekos, Michael A. and Di Battista, Giuseppe and Frati, Fabrizio and Grilli, Luca and Ortali, Giacomo},
  title =	{{On Planar Straight-Line Dominance Drawings}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{5:1--5:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.5},
  URN =		{urn:nbn:de:0030-drops-242361},
  doi =		{10.4230/LIPIcs.WADS.2025.5},
  annote =	{Keywords: st-graphs, dominance drawings, planar straight-line drawings, upward planarity}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.29
Linear Layouts of Graphs with Priority Queues

Authors: Emilio Di Giacomo, Walter Didimo, Henry Förster, Torsten Ueckerdt, and Johannes Zink

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
A linear layout of a graph consists of a linear ordering of its vertices and a partition of its edges into pages such that the edges assigned to the same page obey some constraint. The two most prominent and widely studied types of linear layouts are stack and queue layouts, in which any two edges assigned to the same page are forbidden to cross and nest, respectively. The names of these two layouts derive from the fact that, when parsing the graph according to the linear vertex ordering, the edges in a single page can be stored using a single stack or queue, respectively. Recently, the concepts of stack and queue layouts have been extended by using a double-ended queue or a restricted-input queue for storing the edges of a page. We extend this line of study to edge-weighted graphs by introducing priority queue layouts, that is, the edges on each page are stored in a priority queue whose keys are the edge weights. First, we show that there are edge-weighted graphs that require a linear number of priority queues. Second, we characterize the graphs that admit a priority queue layout with a single queue, regardless of the edge-weight function, and we provide an efficient recognition algorithm. Third, we show that the number of priority queues required independently of the edge-weight function is bounded by the pathwidth of the graph, but can be arbitrarily large already for graphs of treewidth two. Finally, we prove that determining the minimum number of priority queues is NP-complete if the linear ordering of the vertices is fixed.
Cite as

Emilio Di Giacomo, Walter Didimo, Henry Förster, Torsten Ueckerdt, and Johannes Zink. Linear Layouts of Graphs with Priority Queues. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 29:1-29:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{digiacomo_et_al:LIPIcs.WADS.2025.29,
  author =	{Di Giacomo, Emilio and Didimo, Walter and F\"{o}rster, Henry and Ueckerdt, Torsten and Zink, Johannes},
  title =	{{Linear Layouts of Graphs with Priority Queues}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{29:1--29:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.29},
  URN =		{urn:nbn:de:0030-drops-242602},
  doi =		{10.4230/LIPIcs.WADS.2025.29},
  annote =	{Keywords: linear layouts, recognition and characterization, priority queue layouts}
}
Document
DOI: 10.4230/OASIcs.PARMA-DITAM.2025.3
System-Level Timing Performance Estimation Based on a Unifying HW/SW Performance Metric

Authors: Vittoriano Muttillo, Vincenzo Stoico, Giacomo Valente, Marco Santic, Luigi Pomante, and Daniele Frigioni

Published in: OASIcs, Volume 127, 16th Workshop on Parallel Programming and Run-Time Management Techniques for Many-Core Architectures and 14th Workshop on Design Tools and Architectures for Multicore Embedded Computing Platforms (PARMA-DITAM 2025)

Abstract
The rapidly increasing complexity of embedded systems and the critical impact of non-functional requirements demand the adoption of an appropriate system-level HW/SW co-design methodology. This methodology tries to satisfy all design requirements by simultaneously considering several alternative HW/SW implementations. In this context, early performance estimation approaches are crucial in reducing the design space, thereby minimizing design time and cost. To address the challenge of system-level performance estimation, this work presents and formalizes a novel approach based on a unifying HW/SW performance metric for early execution time estimation. The proposed approach estimates the execution time of a C function when executed by different HW/SW processor technologies. The approach is validated through an extensive experimental study, demonstrating its effectiveness and efficiency in terms of estimation error (i.e., lower than 10%) and estimation time (close to zero) when compared to existing methods in the literature.
Cite as

Vittoriano Muttillo, Vincenzo Stoico, Giacomo Valente, Marco Santic, Luigi Pomante, and Daniele Frigioni. System-Level Timing Performance Estimation Based on a Unifying HW/SW Performance Metric. In 16th Workshop on Parallel Programming and Run-Time Management Techniques for Many-Core Architectures and 14th Workshop on Design Tools and Architectures for Multicore Embedded Computing Platforms (PARMA-DITAM 2025). Open Access Series in Informatics (OASIcs), Volume 127, pp. 3:1-3:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{muttillo_et_al:OASIcs.PARMA-DITAM.2025.3,
  author =	{Muttillo, Vittoriano and Stoico, Vincenzo and Valente, Giacomo and Santic, Marco and Pomante, Luigi and Frigioni, Daniele},
  title =	{{System-Level Timing Performance Estimation Based on a Unifying HW/SW Performance Metric}},
  booktitle =	{16th Workshop on Parallel Programming and Run-Time Management Techniques for Many-Core Architectures and 14th Workshop on Design Tools and Architectures for Multicore Embedded Computing Platforms (PARMA-DITAM 2025)},
  pages =	{3:1--3:14},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-363-8},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{127},
  editor =	{Cattaneo, Daniele and Fazio, Maria and Kosmidis, Leonidas and Morabito, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.PARMA-DITAM.2025.3},
  URN =		{urn:nbn:de:0030-drops-229071},
  doi =		{10.4230/OASIcs.PARMA-DITAM.2025.3},
  annote =	{Keywords: embedded systems, hw/sw co-design, performance estimation, lasso, machine learning}
}
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