An SPQR-Tree-Like Embedding Representation for Level Planarity

Authors Guido Brückner , Ignaz Rutter

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Guido Brückner
  • Karlsruhe Institute of Technology (KIT), Germany
Ignaz Rutter
  • Universität Passau, Germany

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Guido Brückner and Ignaz Rutter. An SPQR-Tree-Like Embedding Representation for Level Planarity. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 8:1-8:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Theory of computation → Data structures design and analysis
  • Theory of computation → Graph algorithms analysis
  • SPQR-tree
  • Level planarity
  • Partial drawings
  • Simultaneous drawings


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