Planar Confluent Orthogonal Drawings of 4-Modal Digraphs

TL;DR

This paper investigates the properties and constraints of planar confluent orthogonal drawings of 4-modal digraphs, focusing on split complexity and upwardness, to understand their structural and visual characteristics.

Contribution

It introduces new bounds and insights into the split complexity of PCODs and (quasi-)upward PCODs for different graph classes, advancing the understanding of their geometric representations.

Findings

Bounds on split complexity for various graph classes

Characterization of upward and quasi-upward PCODs

Insights into the geometric constraints of 4-modal digraphs

Abstract

In a planar confluent orthogonal drawing (PCOD) of a directed graph (digraph) vertices are drawn as points in the plane and edges as orthogonal polylines starting with a vertical segment and ending with a horizontal segment. Edges may overlap in their first or last segment, but must not intersect otherwise. PCODs can be seen as a directed variant of Kandinsky drawings or as planar L-drawings of subdivisions of digraphs. The maximum number of subdivision vertices in an edge is then the split complexity. A PCOD is upward if each edge is drawn with monotonically increasing y-coordinates and quasi-upward if no edge starts with decreasing y-coordinates. We study the split complexity of PCODs and (quasi-)upward PCODs for various classes of graphs.