Switch-Regular Upward Planarity Testing of Directed Trees

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 switchregular. 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. Submitted: April 2010 Reviewed: October 2010 Revised: November 2010 Accepted: December 2010 Final: December 2010 Published: October 2011 Article type: Regular paper Communicated by: M. S. Rahman and S. Fujita An extended abstract of this paper appeared in the proceedings of the 4th International Workshop on Algorithms and Computation 2010, WALCOM 2010 [4]. The problem studied in this paper was posed during the first Bertinoro Workshop on Graph Drawing (http://www.diei.unipg.it/~bwgd/). E-mail addresses: [email protected] (Carla Binucci) [email protected] (Emilio Di Giacomo) [email protected] (Walter Didimo) [email protected] (Aimal Rextin) 588 Binucci et al. Switch-Regular Upward Planarity Testing.