License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2020.8
URN: urn:nbn:de:0030-drops-133526
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/13352/
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Brückner, Guido ; Rutter, Ignaz

An SPQR-Tree-Like Embedding Representation for Level Planarity

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LIPIcs-ISAAC-2020-8.pdf (0.7 MB)

Abstract

An SPQR-tree is a data structure that efficiently represents all planar embeddings of a biconnected planar graph. It is a key tool in a number of constrained planarity testing algorithms, which seek a planar embedding of a graph subject to some given set of constraints.
We develop an SPQR-tree-like data structure that represents all level-planar embeddings of a biconnected level graph with a single source, called the LP-tree, and give a simple algorithm to compute it in linear time. Moreover, we show that LP-trees can be used to adapt three constrained planarity algorithms to the level-planar case by using them as a drop-in replacement for SPQR-trees.

BibTeX - Entry

@InProceedings{brckner_et_al:LIPIcs:2020:13352,
  author =	{Guido Br{\"u}ckner and Ignaz Rutter},
  title =	{{An SPQR-Tree-Like Embedding Representation for Level Planarity}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{8:1--8:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Yixin Cao and Siu-Wing Cheng and Minming Li},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/13352},
  URN =		{urn:nbn:de:0030-drops-133526},
  doi =		{10.4230/LIPIcs.ISAAC.2020.8},
  annote =	{Keywords: SPQR-tree, Level planarity, Partial drawings, Simultaneous drawings}
}

Keywords: SPQR-tree, Level planarity, Partial drawings, Simultaneous drawings
Collection: 31st International Symposium on Algorithms and Computation (ISAAC 2020)
Issue Date: 2020
Date of publication: 04.12.2020

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