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.
@InProceedings{bruckner_et_al:LIPIcs.ISAAC.2020.8, author = {Br\"{u}ckner, Guido and Rutter, Ignaz}, 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 = {Cao, Yixin and Cheng, Siu-Wing and Li, Minming}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.8}, URN = {urn:nbn:de:0030-drops-133526}, doi = {10.4230/LIPIcs.ISAAC.2020.8}, annote = {Keywords: SPQR-tree, Level planarity, Partial drawings, Simultaneous drawings} }
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