7 Search Results for "Katheder, Julia"

Document
DOI: 10.4230/LIPIcs.ESA.2025.21
A Unified FPT Framework for Crossing Number Problems

Authors: Éric Colin de Verdière and Petr Hliněný

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
The basic (and traditional) crossing number problem is to determine the minimum number of crossings in a topological drawing of an input graph in the plane. We develop a unified framework that smoothly captures many generalized crossing number problems, and that yields fixed-parameter tractable (FPT) algorithms for them not only in the plane but also on surfaces. Our framework takes the following form. We fix a surface S, an integer r, and a map κ from the set of topological drawings of graphs in S to ℤ_+ ∪ {∞}, satisfying some natural monotonicity conditions, but essentially describing the allowed drawings and how we want to count the crossings in them. Then deciding whether an input graph G has an allowed drawing D on S with κ(D) ≤ r can be done in time quadratic in the size of G (and exponential in other parameters). More generally, we may take as input an edge-colored graph, and distinguish crossings by the colors of the involved edges; and we may allow to perform a bounded number of edge removals and vertex splits to G before drawing it. The proof is a reduction to the embeddability of a graph on a two-dimensional simplicial complex. This framework implies, in a unified way, quadratic FPT algorithms for many topological crossing number variants established in the graph drawing community. Some of these variants already had previously published FPT algorithms, mostly relying on Courcelle’s metatheorem, but for many of those, we obtain an algorithm with a better runtime. Moreover, our framework extends, at no cost, to these crossing number variants in any fixed surface.
Cite as

Éric Colin de Verdière and Petr Hliněný. A Unified FPT Framework for Crossing Number Problems. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 21:1-21:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{colindeverdiere_et_al:LIPIcs.ESA.2025.21,
  author =	{Colin de Verdi\`{e}re, \'{E}ric and Hlin\v{e}n\'{y}, Petr},
  title =	{{A Unified FPT Framework for Crossing Number Problems}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{21:1--21:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.21},
  URN =		{urn:nbn:de:0030-drops-244897},
  doi =		{10.4230/LIPIcs.ESA.2025.21},
  annote =	{Keywords: computational geometry, fixed-parameter tractability, graph drawing, graph embedding, crossing number, two-dimensional simplicial complex, surface}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.15
Linear Layouts Revisited: Stacks, Queues, and Exact Algorithms

Authors: Thomas Depian, Simon D. Fink, Robert Ganian, and Vaishali Surianarayanan

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
In spite of the extensive study of stack and queue layouts, many fundamental questions remain open concerning the complexity-theoretic frontiers for computing stack and queue layouts. A stack (resp. queue) layout places vertices along a line and assigns edges to pages so that no two edges on the same page are crossing (resp. nested). We provide three new algorithms which together substantially expand our understanding of these problems: 1) A fixed-parameter algorithm for computing minimum-page stack and queue layouts w.r.t. the vertex integrity of an n-vertex graph G. This result is motivated by an open question in the literature and generalizes the previous algorithms parameterizing by the vertex cover number of G. The proof relies on a newly developed Ramsey pruning technique. Vertex integrity intuitively measures the vertex deletion distance to a subgraph with only small connected components. 2) An n^𝒪(q 𝓁) algorithm for computing 𝓁-page stack and queue layouts of page width at most q. This is the first algorithm avoiding a double-exponential dependency on the parameters. The page width of a layout measures the maximum number of edges one needs to cross on any page to reach the outer face. 3) A 2^𝒪(n) algorithm for computing 1-page queue layouts. This improves upon the previously fastest n^𝒪(n) algorithm and can be seen as a counterpart to the recent subexponential algorithm for computing 2-page stack layouts [ICALP'24], but relies on an entirely different technique.
Cite as

Thomas Depian, Simon D. Fink, Robert Ganian, and Vaishali Surianarayanan. Linear Layouts Revisited: Stacks, Queues, and Exact Algorithms. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{depian_et_al:LIPIcs.ESA.2025.15,
  author =	{Depian, Thomas and Fink, Simon D. and Ganian, Robert and Surianarayanan, Vaishali},
  title =	{{Linear Layouts Revisited: Stacks, Queues, and Exact Algorithms}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{15:1--15:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.15},
  URN =		{urn:nbn:de:0030-drops-244835},
  doi =		{10.4230/LIPIcs.ESA.2025.15},
  annote =	{Keywords: stack layouts, queue layouts, parameterized algorithms, vertex integrity, Ramsey theory}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.45
Forbidden Patterns in Mixed Linear Layouts

Authors: Deborah Haun, Laura Merker, and Sergey Pupyrev

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
An ordered graph is a graph with a total order over its vertices. A linear layout of an ordered graph is a partition of the edges into sets of either non-crossing edges, called stacks, or non-nesting edges, called queues. The stack (queue) number of an ordered graph is the minimum number of required stacks (queues). Mixed linear layouts combine these layouts by allowing each set of edges to form either a stack or a queue. The minimum number of stacks plus queues is called the mixed page number. It is well known that ordered graphs with small stack number are characterized, up to a function, by the absence of large twists (that is, pairwise crossing edges). Similarly, ordered graphs with small queue number are characterized by the absence of large rainbows (that is, pairwise nesting edges). However, no such characterization via forbidden patterns is known for mixed linear layouts. We address this gap by introducing patterns similar to twists and rainbows, which we call thick patterns; such patterns allow a characterization, again up to a function, of mixed linear layouts of bounded-degree graphs. That is, we show that a family of ordered graphs with bounded maximum degree has bounded mixed page number if and only if the size of the largest thick pattern is bounded. In addition, we investigate an exact characterization of ordered graphs whose mixed page number equals a fixed integer k via a finite set of forbidden patterns. We show that for k = 2, there is no such characterization, which supports the nature of our first result.
Cite as

Deborah Haun, Laura Merker, and Sergey Pupyrev. Forbidden Patterns in Mixed Linear Layouts. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 45:1-45:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{haun_et_al:LIPIcs.STACS.2025.45,
  author =	{Haun, Deborah and Merker, Laura and Pupyrev, Sergey},
  title =	{{Forbidden Patterns in Mixed Linear Layouts}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{45:1--45:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine 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.2025.45},
  URN =		{urn:nbn:de:0030-drops-228717},
  doi =		{10.4230/LIPIcs.STACS.2025.45},
  annote =	{Keywords: Ordered Graphs, linear Layout, mixed linear Layout, Stack Layout, Queue Layout}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.56
Transforming Stacks into Queues: Mixed and Separated Layouts of Graphs

Authors: Julia Katheder, Michael Kaufmann, Sergey Pupyrev, and Torsten Ueckerdt

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
Some of the most important open problems for linear layouts of graphs ask for the relation between a graph’s queue number and its stack number or mixed number. In such, we seek a vertex order and edge partition of G into parts with pairwise non-crossing edges (a stack) or with pairwise non-nesting edges (a queue). Allowing only stacks, only queues, or both, the minimum number of required parts is the graph’s stack number sn(G), queue number qn(G), and mixed number mn(G), respectively. Already in 1992, Heath and Rosenberg asked whether qn(G) is bounded in terms of sn(G), that is, whether stacks "can be transformed into" queues. This is equivalent to bipartite 3-stack graphs having bounded queue number (Dujmović and Wood, 2005). Recently, Alam et al. asked whether qn(G) is bounded in terms of mn(G), which we show to also be equivalent to the previous questions. We approach the problem by considering separated linear layouts of bipartite graphs. In this natural setting all vertices of one part must precede all vertices of the other part. Separated stack and queue numbers coincide, and for fixed vertex orders, graphs with bounded separated stack/queue number can be characterized and efficiently recognized, whereas the separated mixed layouts are more challenging. In this work, we thoroughly investigate the relationship between separated and non-separated, mixed and pure linear layouts.
Cite as

Julia Katheder, Michael Kaufmann, Sergey Pupyrev, and Torsten Ueckerdt. Transforming Stacks into Queues: Mixed and Separated Layouts of Graphs. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 56:1-56:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{katheder_et_al:LIPIcs.STACS.2025.56,
  author =	{Katheder, Julia and Kaufmann, Michael and Pupyrev, Sergey and Ueckerdt, Torsten},
  title =	{{Transforming Stacks into Queues: Mixed and Separated Layouts of Graphs}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{56:1--56:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine 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.2025.56},
  URN =		{urn:nbn:de:0030-drops-228819},
  doi =		{10.4230/LIPIcs.STACS.2025.56},
  annote =	{Keywords: Separated linear Layouts, Stack Number, Queue Number, mixed Number, bipartite Graphs}
}
Document
DOI: 10.4230/LIPIcs.GD.2024.35
On k-Plane Insertion into Plane Drawings

Authors: Julia Katheder, Philipp Kindermann, Fabian Klute, Irene Parada, and Ignaz Rutter

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

Abstract
We introduce the k-Plane Insertion into Plane drawing (k-PIP) problem: given a plane drawing of a planar graph G and a set F of edges, insert the edges in F into the drawing such that the resulting drawing is k-plane. In this paper, we show that the problem is NP-complete for every k ≥ 1, even when G is biconnected and the set F of edges forms a matching or a path. On the positive side, we present a linear-time algorithm for the case that k = 1 and G is a triangulation.
Cite as

Julia Katheder, Philipp Kindermann, Fabian Klute, Irene Parada, and Ignaz Rutter. On k-Plane Insertion into Plane Drawings. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 35:1-35:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{katheder_et_al:LIPIcs.GD.2024.35,
  author =	{Katheder, Julia and Kindermann, Philipp and Klute, Fabian and Parada, Irene and Rutter, Ignaz},
  title =	{{On k-Plane Insertion into Plane Drawings}},
  booktitle =	{32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
  pages =	{35:1--35:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-343-0},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{320},
  editor =	{Felsner, Stefan and Klein, Karsten},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.35},
  URN =		{urn:nbn:de:0030-drops-213190},
  doi =		{10.4230/LIPIcs.GD.2024.35},
  annote =	{Keywords: Graph drawing, edge insertion, k-planarity}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.9
Axis-Parallel Right Angle Crossing Graphs

Authors: Patrizio Angelini, Michael A. Bekos, Julia Katheder, Michael Kaufmann, Maximilian Pfister, and Torsten Ueckerdt

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
A RAC graph is one admitting a RAC drawing, that is, a polyline drawing in which each crossing occurs at a right angle. Originally motivated by psychological studies on readability of graph layouts, RAC graphs form one of the most prominent graph classes in beyond planarity. In this work, we study a subclass of RAC graphs, called axis-parallel RAC (or apRAC, for short), that restricts the crossings to pairs of axis-parallel edge-segments. apRAC drawings combine the readability of planar drawings with the clarity of (non-planar) orthogonal drawings. We consider these graphs both with and without bends. Our contribution is as follows: (i) We study inclusion relationships between apRAC and traditional RAC graphs. (ii) We establish bounds on the edge density of apRAC graphs. (iii) We show that every graph with maximum degree 8 is 2-bend apRAC and give a linear time drawing algorithm. Some of our results on apRAC graphs also improve the state of the art for general RAC graphs. We conclude our work with a list of open questions and a discussion of a natural generalization of the apRAC model.
Cite as

Patrizio Angelini, Michael A. Bekos, Julia Katheder, Michael Kaufmann, Maximilian Pfister, and Torsten Ueckerdt. Axis-Parallel Right Angle Crossing Graphs. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 9:1-9:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{angelini_et_al:LIPIcs.ESA.2023.9,
  author =	{Angelini, Patrizio and Bekos, Michael A. and Katheder, Julia and Kaufmann, Michael and Pfister, Maximilian and Ueckerdt, Torsten},
  title =	{{Axis-Parallel Right Angle Crossing Graphs}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{9:1--9:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.9},
  URN =		{urn:nbn:de:0030-drops-186623},
  doi =		{10.4230/LIPIcs.ESA.2023.9},
  annote =	{Keywords: Graph drawing, RAC graphs, Graph drawing algorithms}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2022.11
RAC Drawings of Graphs with Low Degree

Authors: Patrizio Angelini, Michael A. Bekos, Julia Katheder, Michael Kaufmann, and Maximilian Pfister

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

Abstract
Motivated by cognitive experiments providing evidence that large crossing-angles do not impair the readability of a graph drawing, RAC (Right Angle Crossing) drawings were introduced to address the problem of producing readable representations of non-planar graphs by supporting the optimal case in which all crossings form 90° angles. In this work, we make progress on the problem of finding RAC drawings of graphs of low degree. In this context, a long-standing open question asks whether all degree-3 graphs admit straight-line RAC drawings. This question has been positively answered for the Hamiltonian degree-3 graphs. We improve on this result by extending to the class of 3-edge-colorable degree-3 graphs. When each edge is allowed to have one bend, we prove that degree-4 graphs admit such RAC drawings, a result which was previously known only for degree-3 graphs. Finally, we show that 7-edge-colorable degree-7 graphs admit RAC drawings with two bends per edge. This improves over the previous result on degree-6 graphs.
Cite as

Patrizio Angelini, Michael A. Bekos, Julia Katheder, Michael Kaufmann, and Maximilian Pfister. RAC Drawings of Graphs with Low Degree. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 11:1-11:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{angelini_et_al:LIPIcs.MFCS.2022.11,
  author =	{Angelini, Patrizio and Bekos, Michael A. and Katheder, Julia and Kaufmann, Michael and Pfister, Maximilian},
  title =	{{RAC Drawings of Graphs with Low Degree}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{11:1--11:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.11},
  URN =		{urn:nbn:de:0030-drops-168090},
  doi =		{10.4230/LIPIcs.MFCS.2022.11},
  annote =	{Keywords: Graph Drawing, RAC graphs, Straight-line and bent drawings}
}
  • Refine by Type
  • 7 Document/PDF
  • 4 Document/HTML

  • Refine by Publication Year
  • 4 2025
  • 1 2024
  • 1 2023
  • 1 2022

  • Refine by Author
  • 4 Katheder, Julia
  • 3 Kaufmann, Michael
  • 2 Angelini, Patrizio
  • 2 Bekos, Michael A.
  • 2 Pfister, Maximilian
  • Show More...

  • Refine by Series/Journal
  • 7 LIPIcs

  • Refine by Classification
  • 3 Mathematics of computing → Graph theory
  • 3 Theory of computation → Computational geometry
  • 2 Mathematics of computing → Graph algorithms
  • 1 Mathematics of computing → Combinatoric problems
  • 1 Mathematics of computing → Combinatorics
  • Show More...

  • Refine by Keyword
  • 2 Graph drawing
  • 2 RAC graphs
  • 1 Graph Drawing
  • 1 Graph drawing algorithms
  • 1 Ordered Graphs
  • Show More...

Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact