An SPQR-Tree-Like Embedding Representation for Level Planarity

TL;DR

This paper introduces an LP-tree data structure, similar to SPQR-trees, that efficiently represents all level-planar embeddings of biconnected level graphs with a single source, enabling improved planarity algorithms.

Contribution

It presents the LP-tree, a new data structure for level planarity, and provides a linear-time algorithm to compute it, extending planarity testing methods to level graphs.

Findings

LP-trees represent all level-planar embeddings of biconnected level graphs.

The algorithm to compute LP-trees runs in linear time.

LP-trees can adapt existing planarity algorithms for level planarity.

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.