95 Search Results for "Montecchiani, Fabrizio"

Volume

LIPIcs, Volume 357

33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)

GD 2025, September 24-26, 2025, Norrköping, Sweden

Editors: Vida Dujmović and Fabrizio Montecchiani

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.SoCG.2026.16
Flip Distance of Non-Crossing Spanning Trees: NP-Hardness and Improved Bounds

Authors: Håvard Bakke Bjerkevik, Joseph Dorfer, Linda Kleist, Torsten Ueckerdt, and Birgit Vogtenhuber

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

Abstract
We consider the problem of reconfiguring non-crossing spanning trees on point sets. For a set P of n points in general position in the plane, the flip graph ℱ(P) has a vertex for each non-crossing spanning tree on P and an edge between any two spanning trees that can be transformed into each other by the exchange of a single edge (coined a flip). This flip graph has been intensively studied, lately with an emphasis on determining its diameter diam(ℱ(P)) for sets P of n points in convex position. For this case, the current best bounds are 14/9⋅n - O(1) ≤ diam(ℱ(P)) < 15/9⋅n - 3, obtained in a recent breakthrough work [Bjerkevik, Kleist, Ueckerdt, and Vogtenhuber; SODA 2025]. The crucial tool for both the upper and lower bound are so-called conflict graphs, which the authors stated might be the key ingredient for determining the diameter (up to lower-order terms). In this paper, we pick up the concept of conflict graphs from the above-mentioned work and show that this tool is even more versatile than previously hoped. As our first main result, we use conflict graphs to show that computing the flip distance between two non-crossing spanning trees is NP-hard, even for point sets in convex position. Interestingly, the result still holds for more constrained flip operations, concretely, compatible flips (where the removed and the added edge do not cross) and rotations (where the removed and the added edge share an endpoint). Additionally, we present new insights on the diameter of the flip graph, by this directly extending the line of research from [BKUV SODA25]. Their lower bound is based on a constant-size pair of trees, one of which is of a type we refer to as stacked. We show that if one of the trees is stacked, then the lower bound is indeed optimal up to a constant term, that is, there exists a flip sequence of length at most 14/9⋅(n-1) to any other tree. Lastly, we improve the lower bound on the diameter of the flip graph ℱ(P) for n points in convex position to 11/7⋅n-o(n).
Cite as

Håvard Bakke Bjerkevik, Joseph Dorfer, Linda Kleist, Torsten Ueckerdt, and Birgit Vogtenhuber. Flip Distance of Non-Crossing Spanning Trees: NP-Hardness and Improved Bounds. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bjerkevik_et_al:LIPIcs.SoCG.2026.16,
  author =	{Bjerkevik, H\r{a}vard Bakke and Dorfer, Joseph and Kleist, Linda and Ueckerdt, Torsten and Vogtenhuber, Birgit},
  title =	{{Flip Distance of Non-Crossing Spanning Trees: NP-Hardness and Improved Bounds}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{16:1--16:18},
  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.2026.16},
  URN =		{urn:nbn:de:0030-drops-258225},
  doi =		{10.4230/LIPIcs.SoCG.2026.16},
  annote =	{Keywords: Non-crossing, spanning tree, plane graph, flip graph, reconfiguration, diameter, complexity, NP-hard, edge exchange, compatible flip, rotation, happy edge property}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.42
Computing Twin-Width via Treedepth and Vertex Integrity

Authors: Robert Ganian and Mathis Rocton

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
Twin-width is a graph parameter that has become central to explaining the fixed-parameter tractability of first-order model checking across many graph classes. Despite its algorithmic importance, computing twin-width remains poorly understood: even recognizing graphs of twin-width at most four is NP-hard, and no fixed-parameter approximations parameterized by twin-width itself are known. A recent approach towards breaking this barrier focuses on first developing fixed-parameter algorithms for computing or approximating twin-width under parameterizations distinct from twin-width. Our first result establishes that approximating twin-width is fixed-parameter tractable when parameterized by treedepth, thereby breaking the long-standing barrier that all previous tractable parameterizations were based on deletion distance. The proof proceeds via oriented twin-width, yielding the first constructive evidence that this variant may be easier to handle algorithmically. As our second main result, we show that computing twin-width exactly is fixed-parameter tractable with respect to vertex integrity. This constitutes the first non-trivial parameterized algorithm for computing optimal contraction sequences.
Cite as

Robert Ganian and Mathis Rocton. Computing Twin-Width via Treedepth and Vertex Integrity. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 42:1-42:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ganian_et_al:LIPIcs.STACS.2026.42,
  author =	{Ganian, Robert and Rocton, Mathis},
  title =	{{Computing Twin-Width via Treedepth and Vertex Integrity}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{42:1--42:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.42},
  URN =		{urn:nbn:de:0030-drops-255318},
  doi =		{10.4230/LIPIcs.STACS.2026.42},
  annote =	{Keywords: twin-width, fixed-parameter algorithms, treedepth, vertex integrity}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.33
Higher Hardness Results for the Reconfiguration of Odd Matchings

Authors: Joseph Dorfer

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
We study the reconfiguration of odd matchings of combinatorial graphs. Odd matchings are matchings that cover all but one vertex of a graph. A reconfiguration step, or flip, is an operation that matches the isolated vertex and, consequently, isolates another vertex. The flip graph of odd matchings is a graph that has all odd matchings of a graph as vertices and an edge between two vertices if their corresponding matchings can be transformed into one another via a single flip. We show that computing the diameter of the flip graph of odd matchings is Π₂^p-hard. This complements a recent result by Wulf [FOCS25] that it is Π₂^p-hard to compute the diameter of the flip graph of perfect matchings where a flip swaps matching edges along a single cycle of unbounded size. Further, we show that computing the radius of the flip graph of odd matchings is Σ₃^p-hard. The respective decision problems for the diameter and the radius are also complete in the respective level of the polynomial hierarchy. This shows that computing the radius of the flip graph of odd matchings is provably harder than computing its diameter, unless the polynomial hierarchy collapses. Finally, we reduce set cover to the problem of finding shortest flip sequences. As a consequence, we show APX-hardness and that the problem cannot be approximated by a sublogarithmic factor. By doing so, we answer a question asked by Aichholzer, Brenner, Dorfer, Hoang, Perz, Rieck, and Verciani [GD25].
Cite as

Joseph Dorfer. Higher Hardness Results for the Reconfiguration of Odd Matchings. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 33:1-33:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{dorfer:LIPIcs.STACS.2026.33,
  author =	{Dorfer, Joseph},
  title =	{{Higher Hardness Results for the Reconfiguration of Odd Matchings}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{33:1--33:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.33},
  URN =		{urn:nbn:de:0030-drops-255222},
  doi =		{10.4230/LIPIcs.STACS.2026.33},
  annote =	{Keywords: Graph Reconfiguration Problems, Flip Graphs, Polynomial Hierarchy, APX-hardness}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.12
Timeline Problems in Temporal Graphs: Vertex Cover vs. Dominating Set

Authors: Anton Herrmann, Christian Komusiewicz, Nils Morawietz, and Frank Sommer

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
A temporal graph is a finite sequence of graphs, called snapshots, over the same vertex set. Many temporal graph problems turn out to be much more difficult than their static counterparts. One such problem is Timeline Vertex Cover (also known as MinTimeline_∞), a temporal analogue to the classical Vertex Cover problem. In this problem, one is given a temporal graph 𝒢 and two integers k and 𝓁, and the goal is to cover each edge of each snapshot by selecting for each vertex at most k activity intervals of length at most 𝓁 each. Here, an edge uv in the ith snapshot is covered, if an activity interval of u or v is active at time i. In this work, we continue the algorithmic study of Timeline Vertex Cover and introduce the Timeline Dominating Set problem where we want to dominate all vertices in each snapshot by the selected activity intervals. We analyze both problems from a classical and parameterized point of view and also consider partial problem versions, where the goal is to cover (dominate) at least t edges (vertices) of the snapshots. With respect to the parameterized complexity, we consider the temporal graph parameters vertex-interval-membership-width (vimw) and interval-membership-width (imw). We show that all considered problems admit FPT-algorithms when parameterized by vimw+k+𝓁. This provides a smaller parameter combination than the ones used for previously known FPT-algorithms for Timeline Vertex Cover. Surprisingly, for imw+k+𝓁, Timeline Dominating Set turns out to be easier than Timeline Vertex Cover, by also admitting an FPT-algorithm, whereas the vertex cover version is NP-hard even if imw+k+𝓁 is constant. We also consider parameterization by combinations of n, the vertex set size, with k or 𝓁 and parameterization by t. Here, we show for example that both partial problems are fixed-parameter tractable for t which significantly improves and generalizes a previous result for a special case of Partial Timeline Vertex Cover with k = 1.
Cite as

Anton Herrmann, Christian Komusiewicz, Nils Morawietz, and Frank Sommer. Timeline Problems in Temporal Graphs: Vertex Cover vs. Dominating Set. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 12:1-12:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{herrmann_et_al:LIPIcs.IPEC.2025.12,
  author =	{Herrmann, Anton and Komusiewicz, Christian and Morawietz, Nils and Sommer, Frank},
  title =	{{Timeline Problems in Temporal Graphs: Vertex Cover vs. Dominating Set}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{12:1--12:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.12},
  URN =		{urn:nbn:de:0030-drops-251446},
  doi =		{10.4230/LIPIcs.IPEC.2025.12},
  annote =	{Keywords: NP-hard problem, FPT-algorithm, interval-membership-width, Color coding}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.16
A Dichotomy for 1-Planarity with Restricted Crossing Types Parameterized by Treewidth

Authors: Sergio Cabello, Alexander Dobler, Gašper Fijavž, Thekla Hamm, and Mirko H. Wagner

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
A drawing of a graph is 1-planar if each edge participates in at most one crossing and adjacent edges do not cross. Up to symmetry, each crossing in a 1-planar drawing belongs to one out of six possible crossing types, where a type characterizes the subgraph induced by the four vertices of the crossing edges. Each of the 63 possible nonempty subsets 𝒮 of crossing types gives a recognition problem: does a given graph admit an 𝒮-restricted drawing, that is, a 1-planar drawing where the crossing type of each crossing is in 𝒮? We show that there is a set 𝒮_bad with three crossing types and the following properties: - If 𝒮 contains no crossing type from 𝒮_bad, then the recognition of graphs that admit an 𝒮-restricted drawing is fixed-parameter tractable with respect to the treewidth of the input graph. - If 𝒮 contains any crossing type from 𝒮_bad, then it is NP-hard to decide whether a graph has an 𝒮-restricted drawing, even when considering graphs of constant pathwidth. We also extend this characterization of crossing types to 1-planar straight-line drawings and show the same complexity behaviour parameterized by treewidth.
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Sergio Cabello, Alexander Dobler, Gašper Fijavž, Thekla Hamm, and Mirko H. Wagner. A Dichotomy for 1-Planarity with Restricted Crossing Types Parameterized by Treewidth. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 16:1-16:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cabello_et_al:LIPIcs.ISAAC.2025.16,
  author =	{Cabello, Sergio and Dobler, Alexander and Fijav\v{z}, Ga\v{s}per and Hamm, Thekla and Wagner, Mirko H.},
  title =	{{A Dichotomy for 1-Planarity with Restricted Crossing Types Parameterized by Treewidth}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{16:1--16:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.16},
  URN =		{urn:nbn:de:0030-drops-249248},
  doi =		{10.4230/LIPIcs.ISAAC.2025.16},
  annote =	{Keywords: 1-planar, crossing type, treewidth, pathwidth}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.25
Structural Parameterizations of Simultaneous Planarity

Authors: Thomas Depian, Simon D. Fink, Alexander Firbas, Robert Ganian, Matthias Pfretzschner, and Ignaz Rutter

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
Given a set of graphs on the same vertex set, the problem Simultaneous Embedding With Fixed Edges (SEFE) asks, whether there exist planar drawings of all input graphs, such that every pair of drawings coincides on their shared subgraph. It is known that SEFE is NP-complete [Elisabeth Gassner et al., 2006], even in the so-called sunflower case, where all pairs of input graphs have the same shared graph G_∩ [Marcus Schaefer, 2012]. Fink, Pfretzschner, and Rutter [Simon D. Fink et al., 2023] recently initiated the study of the parameterized complexity of SEFE in the sunflower case, mainly focusing on structural parameters of G_∩. In this work, we shift the focus towards parameters of the union graph G_∪ that contains the edges of all input graphs. On the positive side, we establish fixed-parameter tractability for the problem with respect to the feedback edge set number of G_∪. We complement this result by showing that it, surprisingly, remains NP-complete even if G_∪ has constant vertex cover number. These results settle two open questions posed by Fink et al. [Simon D. Fink et al., 2023].
Cite as

Thomas Depian, Simon D. Fink, Alexander Firbas, Robert Ganian, Matthias Pfretzschner, and Ignaz Rutter. Structural Parameterizations of Simultaneous Planarity. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 25:1-25:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{depian_et_al:LIPIcs.ISAAC.2025.25,
  author =	{Depian, Thomas and Fink, Simon D. and Firbas, Alexander and Ganian, Robert and Pfretzschner, Matthias and Rutter, Ignaz},
  title =	{{Structural Parameterizations of Simultaneous Planarity}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{25:1--25:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.25},
  URN =		{urn:nbn:de:0030-drops-249332},
  doi =		{10.4230/LIPIcs.ISAAC.2025.25},
  annote =	{Keywords: SEFE, Simultaneous Planarity, Fixed-Parameter Tractability, NP-hardness}
}
Document
DOI: 10.4230/LIPIcs.GD.2025.23
The Price of Connectivity Augmentation on Planar Graphs

Authors: Hugo A. Akitaya, Justin Dallant, Erik D. Demaine, Michael Kaufmann, Linda Kleist, Frederick Stock, Csaba D. Tóth, and Torsten Ueckerdt

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

Abstract
Given two classes of graphs, 𝒢₁ ⊆ 𝒢₂, and a c-connected graph G ∈ 𝒢₁, we wish to augment G with a smallest cardinality set of new edges F to obtain a k-connected graph G' = (V,E∪ F) ∈ 𝒢₂. In general, this is the c → k connectivity augmentation problem. Previous research considered variants where 𝒢₁ = 𝒢₂ is the class of planar graphs, plane graphs, or planar straight-line graphs. In all three settings, we prove that the c → k augmentation problem is NP-complete when 2 ≤ c < k ≤ 5. However, the connectivity of the augmented graph G' is at most 5 if 𝒢₂ is limited to planar graphs. We initiate the study of the c → k connectivity augmentation problem for arbitrary k ∈ ℕ, where 𝒢₁ is the class of planar graphs, plane graphs, or planar straight-line graphs, and 𝒢₂ is a beyond-planar class of graphs: 𝓁-planar, 𝓁-plane topological, or 𝓁-plane geometric graphs. We obtain tight bounds on the tradeoffs between the desired connectivity k and the local crossing number 𝓁 of the augmented graph G'. We also show that our hardness results apply to this setting. The connectivity augmentation problem for triangulations is intimately related to edge flips; and the minimum augmentation problem to the flip distance between triangulations. We prove that it is NP-complete to find the minimum flip distance between a given triangulation and a 4-connected triangulation, settling an open problem posed in 2014, and present an EPTAS for this problem.
Cite as

Hugo A. Akitaya, Justin Dallant, Erik D. Demaine, Michael Kaufmann, Linda Kleist, Frederick Stock, Csaba D. Tóth, and Torsten Ueckerdt. The Price of Connectivity Augmentation on Planar Graphs. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 23:1-23:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{a.akitaya_et_al:LIPIcs.GD.2025.23,
  author =	{A. Akitaya, Hugo and Dallant, Justin and Demaine, Erik D. and Kaufmann, Michael and Kleist, Linda and Stock, Frederick and T\'{o}th, Csaba D. and Ueckerdt, Torsten},
  title =	{{The Price of Connectivity Augmentation on Planar Graphs}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{23:1--23:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.23},
  URN =		{urn:nbn:de:0030-drops-250095},
  doi =		{10.4230/LIPIcs.GD.2025.23},
  annote =	{Keywords: connectivity augmentation, local crossing number, flip distance}
}
Document
DOI: 10.4230/LIPIcs.GD.2025.22
NNP-NET: Accelerating t-SNE Graph Drawing for Very Large Graphs by Neural Networks

Authors: Ilan Hartskeerl, Tamara Mchedlidze, Simon van Wageningen, Peter Vangorp, and Alexandru Telea

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

Abstract
tsNET is a recent graph drawing (GD) method that creates high quality layouts but suffers from a very high runtime. We present a new GD method, NNP-NET, which reduces tsNET’s time complexity to generate layouts for very large graphs in seconds. Additionally, we extend tsNET to support drawing graphs with edge weights. We accomplish this by replacing tsNET’s t-SNE projection with Neural Network Projection (NNP), a fast dimensionality reduction (DR) method that can imitate any given DR method. Our experiments show that NNP-NET gets good quality results when compared to other state-of-the art GD methods while yielding a better computational scalability.
Cite as

Ilan Hartskeerl, Tamara Mchedlidze, Simon van Wageningen, Peter Vangorp, and Alexandru Telea. NNP-NET: Accelerating t-SNE Graph Drawing for Very Large Graphs by Neural Networks. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 22:1-22:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hartskeerl_et_al:LIPIcs.GD.2025.22,
  author =	{Hartskeerl, Ilan and Mchedlidze, Tamara and van Wageningen, Simon and Vangorp, Peter and Telea, Alexandru},
  title =	{{NNP-NET: Accelerating t-SNE Graph Drawing for Very Large Graphs by Neural Networks}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{22:1--22:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.22},
  URN =		{urn:nbn:de:0030-drops-250087},
  doi =		{10.4230/LIPIcs.GD.2025.22},
  annote =	{Keywords: supervised graph drawing, dimensionality reduction, t-SNE}
}
Document
DOI: 10.4230/LIPIcs.GD.2025.19
Crossing and Non-Crossing Families

Authors: Todor Antić, Martin Balko, and Birgit Vogtenhuber

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

Abstract
For a finite set P of points in the plane in general position, a crossing family of size k in P is a collection of k line segments with endpoints in P that are pairwise crossing. It is a long-standing open problem to determine the largest size of a crossing family in any set of n points in the plane in general position. It is widely believed that this size should be linear in n. Motivated by results from the theory of partitioning complete geometric graphs, we study a variant of this problem for point sets P that do not contain a non-crossing family of size m, which is a collection of 4 disjoint subsets P₁, P₂, P₃, and P₄ of P, each containing m points of P, such that for every choice of 4 points p_i ∈ P_i, the set {p₁,p₂,p₃,p₄} is such that p₄ is in the interior of the triangle formed by p₁,p₂,p₃. We prove that, for every m ∈ ℕ, each set P of n points in the plane in general position contains either a crossing family of size n/2^{O(√{log{m}})} or a non-crossing family of size m, by this strengthening a recent breakthrough result by Pach, Rubin, and Tardos (2021). Our proof is constructive and we show that these families can be obtained in expected time O(nm^{1+o(1)}). We also prove that a crossing family of size Ω(n/m) or a non-crossing family of size m in P can be found in expected time O(n).
Cite as

Todor Antić, Martin Balko, and Birgit Vogtenhuber. Crossing and Non-Crossing Families. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 19:1-19:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{antic_et_al:LIPIcs.GD.2025.19,
  author =	{Anti\'{c}, Todor and Balko, Martin and Vogtenhuber, Birgit},
  title =	{{Crossing and Non-Crossing Families}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{19:1--19:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.19},
  URN =		{urn:nbn:de:0030-drops-250058},
  doi =		{10.4230/LIPIcs.GD.2025.19},
  annote =	{Keywords: crossing family, non-crossing family, geometric graph}
}
Document
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.2025.25
Characterizing and Recognizing Twistedness

Authors: Oswin Aichholzer, Alfredo García, Javier Tejel, Birgit Vogtenhuber, and Alexandra Weinberger

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

Abstract
In a simple drawing of a graph, any two edges intersect in at most one point (either a common endpoint or a proper crossing). A simple drawing is generalized twisted if it fulfills certain rather specific constraints on how the edges are drawn. An abstract rotation system of a graph assigns to each vertex a cyclic order of its incident edges. A realizable rotation system is one that admits a simple drawing such that at each vertex, the edges emanate in that cyclic order, and a generalized twisted rotation system can be realized as a generalized twisted drawing. Generalized twisted drawings have initially been introduced to obtain improved bounds on the size of plane substructures in any simple drawing of K_n. They have since gained independent interest due to their surprising properties. However, the definition of generalized twisted drawings is very geometric and drawing-specific. In this paper, we develop characterizations of generalized twisted drawings that enable a purely combinatorial view on these drawings and lead to efficient recognition algorithms. Concretely, we show that for any n ≥ 7, an abstract rotation system of K_n is generalized twisted if and only if all subrotation systems induced by five vertices are generalized twisted. This implies a drawing-independent and concise characterization of generalized twistedness. Besides, the result yields a simple O(n⁵)-time algorithm to decide whether an abstract rotation system is generalized twisted and sheds new light on the structural features of simple drawings. We further develop a characterization via the rotations of a pair of vertices in a drawing, which we then use to derive an O(n²)-time algorithm to decide whether a realizable rotation system is generalized twisted.
Cite as

Oswin Aichholzer, Alfredo García, Javier Tejel, Birgit Vogtenhuber, and Alexandra Weinberger. Characterizing and Recognizing Twistedness. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 25:1-25:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{aichholzer_et_al:LIPIcs.GD.2025.25,
  author =	{Aichholzer, Oswin and Garc{\'\i}a, Alfredo and Tejel, Javier and Vogtenhuber, Birgit and Weinberger, Alexandra},
  title =	{{Characterizing and Recognizing Twistedness}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{25:1--25:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.25},
  URN =		{urn:nbn:de:0030-drops-250116},
  doi =		{10.4230/LIPIcs.GD.2025.25},
  annote =	{Keywords: generalized twisted drawings, simple drawings, rotation systems, recognition, combinatorial characterization, efficient algorithms}
}
Document
DOI: 10.4230/LIPIcs.GD.2025.24
String Graph Obstacles of High Girth and of Bounded Degree

Authors: Maria Chudnovsky, David Eppstein, and David Fischer

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

Abstract
A string graph is the intersection graph of curves in the plane. Kratochvíl previously showed the existence of infinitely many obstacles: graphs that are not string graphs but for which any edge contraction or vertex deletion produces a string graph. Kratochvíl’s obstacles contain arbitrarily large cliques, so they have girth three and unbounded degree. We extend this line of working by studying obstacles among graphs of restricted girth and/or degree. We construct an infinite family of obstacles of girth four; in addition, our construction is K_{2,3}-subgraph-free and near-planar (planar plus one edge). Furthermore, we prove that there is a subcubic obstacle of girth three, and that there are no subcubic obstacles of high girth. We characterize the subcubic string graphs as having a matching whose contraction yields a planar graph, and based on this characterization we find a linear-time algorithm for recognizing subcubic string graphs of bounded treewidth.
Cite as

Maria Chudnovsky, David Eppstein, and David Fischer. String Graph Obstacles of High Girth and of Bounded Degree. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 24:1-24:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chudnovsky_et_al:LIPIcs.GD.2025.24,
  author =	{Chudnovsky, Maria and Eppstein, David and Fischer, David},
  title =	{{String Graph Obstacles of High Girth and of Bounded Degree}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{24:1--24:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.24},
  URN =		{urn:nbn:de:0030-drops-250108},
  doi =		{10.4230/LIPIcs.GD.2025.24},
  annote =	{Keywords: string graphs, induced minors, forbidden minors, sparsity, triangle-free graphs, near-planar graphs}
}
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