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Documents authored by Kindermann, Philipp

Document
DOI: 10.4230/LIPIcs.GD.2024.19
Weakly Leveled Planarity with Bounded Span

Authors: Michael A. Bekos, Giordano Da Lozzo, Fabrizio Frati, Siddharth Gupta, Philipp Kindermann, Giuseppe Liotta, Ignaz Rutter, and Ioannis G. Tollis

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

Abstract
This paper studies planar drawings of graphs in which each vertex is represented as a point along a sequence of horizontal lines, called levels, and each edge is either a horizontal segment or a strictly y-monotone curve. A graph is s-span weakly leveled planar if it admits such a drawing where the edges have span at most s; the span of an edge is the number of levels it touches minus one. We investigate the problem of computing s-span weakly leveled planar drawings from both the computational and the combinatorial perspectives. We prove the problem to be para-NP-hard with respect to its natural parameter s and investigate its complexity with respect to widely used structural parameters. We show the existence of a polynomial-size kernel with respect to vertex cover number and prove that the problem is FPT when parameterized by treedepth. We also present upper and lower bounds on the span for various graph classes. Notably, we show that cycle trees, a family of 2-outerplanar graphs generalizing Halin graphs, are Θ(log n)-span weakly leveled planar and 4-span weakly leveled planar when 3-connected. As a byproduct of these combinatorial results, we obtain improved bounds on the edge-length ratio of the graph families under consideration.
Cite as

Michael A. Bekos, Giordano Da Lozzo, Fabrizio Frati, Siddharth Gupta, Philipp Kindermann, Giuseppe Liotta, Ignaz Rutter, and Ioannis G. Tollis. Weakly Leveled Planarity with Bounded Span. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 19:1-19:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bekos_et_al:LIPIcs.GD.2024.19,
  author =	{Bekos, Michael A. and Da Lozzo, Giordano and Frati, Fabrizio and Gupta, Siddharth and Kindermann, Philipp and Liotta, Giuseppe and Rutter, Ignaz and Tollis, Ioannis G.},
  title =	{{Weakly Leveled Planarity with Bounded Span}},
  booktitle =	{32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
  pages =	{19:1--19:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-343-0},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{320},
  editor =	{Felsner, Stefan and Klein, Karsten},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.19},
  URN =		{urn:nbn:de:0030-drops-213035},
  doi =		{10.4230/LIPIcs.GD.2024.19},
  annote =	{Keywords: Leveled planar graphs, edge span, graph drawing, edge-length ratio}
}
Document
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)

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@InProceedings{katheder_et_al:LIPIcs.GD.2024.35,
  author =	{Katheder, Julia and Kindermann, Philipp and Klute, Fabian and Parada, Irene and Rutter, Ignaz},
  title =	{{On k-Plane Insertion into Plane Drawings}},
  booktitle =	{32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
  pages =	{35:1--35:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-343-0},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{320},
  editor =	{Felsner, Stefan and Klein, Karsten},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.35},
  URN =		{urn:nbn:de:0030-drops-213190},
  doi =		{10.4230/LIPIcs.GD.2024.35},
  annote =	{Keywords: Graph drawing, edge insertion, k-planarity}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2023.46
The st-Planar Edge Completion Problem Is Fixed-Parameter Tractable

Authors: Liana Khazaliya, Philipp Kindermann, Giuseppe Liotta, Fabrizio Montecchiani, and Kirill Simonov

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

Abstract
The problem of deciding whether a biconnected planar digraph G = (V,E) can be augmented to become an st-planar graph by adding a set of oriented edges E' ⊆ V × V is known to be NP-complete. We show that the problem is fixed-parameter tractable when parameterized by the size of the set E'.
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Liana Khazaliya, Philipp Kindermann, Giuseppe Liotta, Fabrizio Montecchiani, and Kirill Simonov. The st-Planar Edge Completion Problem Is Fixed-Parameter Tractable. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 46:1-46:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{khazaliya_et_al:LIPIcs.ISAAC.2023.46,
  author =	{Khazaliya, Liana and Kindermann, Philipp and Liotta, Giuseppe and Montecchiani, Fabrizio and Simonov, Kirill},
  title =	{{The st-Planar Edge Completion Problem Is Fixed-Parameter Tractable}},
  booktitle =	{34th International Symposium on Algorithms and Computation (ISAAC 2023)},
  pages =	{46:1--46:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-289-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{283},
  editor =	{Iwata, Satoru and Kakimura, Naonori},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2023.46},
  URN =		{urn:nbn:de:0030-drops-193483},
  doi =		{10.4230/LIPIcs.ISAAC.2023.46},
  annote =	{Keywords: st-planar graphs, parameterized complexity, upward planarity}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2019.23
Finding Tutte Paths in Linear Time

Authors: Therese Biedl and Philipp Kindermann

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Abstract
It is well-known that every planar graph has a Tutte path, i.e., a path P such that any component of G-P has at most three attachment points on P. However, it was only recently shown that such Tutte paths can be found in polynomial time. In this paper, we give a new proof that 3-connected planar graphs have Tutte paths, which leads to a linear-time algorithm to find Tutte paths. Furthermore, our Tutte path has special properties: it visits all exterior vertices, all components of G-P have exactly three attachment points, and we can assign distinct representatives to them that are interior vertices. Finally, our running time bound is slightly stronger; we can bound it in terms of the degrees of the faces that are incident to P. This allows us to find some applications of Tutte paths (such as binary spanning trees and 2-walks) in linear time as well.
Cite as

Therese Biedl and Philipp Kindermann. Finding Tutte Paths in Linear Time. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 23:1-23:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{biedl_et_al:LIPIcs.ICALP.2019.23,
  author =	{Biedl, Therese and Kindermann, Philipp},
  title =	{{Finding Tutte Paths in Linear Time}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{23:1--23:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.23},
  URN =		{urn:nbn:de:0030-drops-105991},
  doi =		{10.4230/LIPIcs.ICALP.2019.23},
  annote =	{Keywords: planar graph, Tutte path, Hamiltonian path, 2-walk, linear time}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2017.4
Placing your Coins on a Shelf

Authors: Helmut Alt, Kevin Buchin, Steven Chaplick, Otfried Cheong, Philipp Kindermann, Christian Knauer, and Fabian Stehn

Published in: LIPIcs, Volume 92, 28th International Symposium on Algorithms and Computation (ISAAC 2017)

Abstract
We consider the problem of packing a family of disks 'on a shelf,' that is, such that each disk touches the x-axis from above and such that no two disks overlap. We prove that the problem of minimizing the distance between the leftmost point and the rightmost point of any disk is NP-hard. On the positive side, we show how to approximate this problem within a factor of 4/3 in O(n log n) time, and provide an O(n log n)-time exact algorithm for a special case, in particular when the ratio between the largest and smallest radius is at most four.
Cite as

Helmut Alt, Kevin Buchin, Steven Chaplick, Otfried Cheong, Philipp Kindermann, Christian Knauer, and Fabian Stehn. Placing your Coins on a Shelf. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 4:1-4:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{alt_et_al:LIPIcs.ISAAC.2017.4,
  author =	{Alt, Helmut and Buchin, Kevin and Chaplick, Steven and Cheong, Otfried and Kindermann, Philipp and Knauer, Christian and Stehn, Fabian},
  title =	{{Placing your Coins on a Shelf}},
  booktitle =	{28th International Symposium on Algorithms and Computation (ISAAC 2017)},
  pages =	{4:1--4:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-054-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{92},
  editor =	{Okamoto, Yoshio and Tokuyama, Takeshi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.4},
  URN =		{urn:nbn:de:0030-drops-82145},
  doi =		{10.4230/LIPIcs.ISAAC.2017.4},
  annote =	{Keywords: packing problems, approximation algorithms, NP-hardness}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2016.37
Strongly Monotone Drawings of Planar Graphs

Authors: Stefan Felsner, Alexander Igamberdiev, Philipp Kindermann, Boris Klemz, Tamara Mchedlidze, and Manfred Scheucher

Published in: LIPIcs, Volume 51, 32nd International Symposium on Computational Geometry (SoCG 2016)

Abstract
A straight-line drawing of a graph is a monotone drawing if for each pair of vertices there is a path which is monotonically increasing in some direction, and it is called a strongly monotone drawing if the direction of monotonicity is given by the direction of the line segment connecting the two vertices. We present algorithms to compute crossing-free strongly monotone drawings for some classes of planar graphs; namely, 3-connected planar graphs, outerplanar graphs, and 2-trees. The drawings of 3-connected planar graphs are based on primal-dual circle packings. Our drawings of outerplanar graphs depend on a new algorithm that constructs strongly monotone drawings of trees which are also convex. For irreducible trees, these drawings are strictly convex.
Cite as

Stefan Felsner, Alexander Igamberdiev, Philipp Kindermann, Boris Klemz, Tamara Mchedlidze, and Manfred Scheucher. Strongly Monotone Drawings of Planar Graphs. In 32nd International Symposium on Computational Geometry (SoCG 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 51, pp. 37:1-37:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{felsner_et_al:LIPIcs.SoCG.2016.37,
  author =	{Felsner, Stefan and Igamberdiev, Alexander and Kindermann, Philipp and Klemz, Boris and Mchedlidze, Tamara and Scheucher, Manfred},
  title =	{{Strongly Monotone Drawings of Planar Graphs}},
  booktitle =	{32nd International Symposium on Computational Geometry (SoCG 2016)},
  pages =	{37:1--37:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-009-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{51},
  editor =	{Fekete, S\'{a}ndor and Lubiw, Anna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2016.37},
  URN =		{urn:nbn:de:0030-drops-59292},
  doi =		{10.4230/LIPIcs.SoCG.2016.37},
  annote =	{Keywords: graph drawing, planar graphs, strongly monotone, strictly convex, primal-dual circle packing}
}
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