Switch-Regular Upward Planarity Testing of Directed Trees

Abstract

Upward planar drawings of digraphs are crossing free drawings where all edges flow in the upward direction. The problem of deciding whether a digraph admits an upward planar drawing is called the upward planarity testing problem, and it has been widely studied in the literature. In this paper we investigate a new upward planarity testing problem, that is, deciding whether a digraph admits an upward planar drawing having some special topological properties: such a drawing is called switch-regular. Switch-regular upward planar drawings have practical algorithmic impacts in several graph drawing applications. We provide characterizations for the class of directed trees that admit a switch-regular upward planar drawing. Based on these characterizations we describe an optimal linear-time testing and embedding algorithm.