How to draw a series-parallel digraph

Abstract

Upward and dominance drawings of acyclic digraphs find important applications in the display of hierarchical structures such as PERT diagrams, subroutine-call charts, and is-a relationships. The combinatorial model underlying such hierarchical structures is often a series-parallel digraph. In this paper the problem of constructing upward and dominance drawings of series-parallel digraphs is investigated. We show that the area requirement of upward and dominance drawings of series-parallel digraphs crucially depends on the choice of planar embedding. Also, we present parallel and sequential drawing algorithms that axe optimal with respect to both the time complexity and to the area achieved. Our results show that while series-parallel digraphs have a rather simple and well understood combinatorial structure, naive drawing strategies lead to drawings with exponential area, and clever algorithms are needed to achieve optimal area