Switch-regular upward planar embeddings of 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 version of this problem: Deciding whether a digraph admits a switch-regular upward planar drawing, i.e., an upward planar drawing with specific topological properties. Switch-regular upward planar drawings have applications in the design of efficient checkers and in the design of effective compaction heuristics. 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. © 2010 Springer.