SPQR-tree-like embedding representation for level planarity

An SPQR-tree is a data structure that efficiently represents all planar embeddings of a connected 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 an 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 LP-trees as a drop-in replacement for SPQR-trees.