Radial Level Planarity Testing and Embedding in Linear Time

A graph with an ordered k-partition of the vertices is radial level planar if there is a strictly outward drawing on k concentric levels without crossings. Radial level planarity extends level planarity, where the vertices are placed on k horizontal lines and the edges are routed strictly downwards without crossings. The extension is characterised by rings, which are certain level non-planar biconnected components. Our main results are linear time algorithms for radial level planarity testing and for computing a radial level planar embedding. We introduce PQR-trees as a new data structure where R-nodes and associated templates for their manipulation are introduced to deal with rings. Our algorithms extend level planarity testing and embedding algorithms, which use PQ-trees.