Crossing minimization and layouts of directed hypergraphs with port constraints

Abstract

Many practical applications for drawing graphs are modeled by directed graphs with domain specific constraints. In this paper, we consider the problem of drawing directed hypergraphs with (and without) port constraints, which cover multiple real-world graph drawing applications like data flow diagrams and electric schematics. Most existing algorithms for drawing hypergraphs with port constraints are adaptions of the framework originally proposed by Sugiyama et al. in 1981 for simple directed graphs. Recently, a practical approach for upward crossing minimization of directed graphs based on the planarization method was proposed [7]. With respect to the number of arc crossings, it clearly outperforms prior (mostly layering-based) approaches. We show how to adopt this idea for hypergraphs with given port constraints, obtaining an upward-planar representation (UPR) of the input hypergraph where crossings are modeled by dummy nodes. Furthermore, we present the new problem of computing an orthogonal upward drawing with minimal number of crossings from such an UPR, and show that it can be solved efficiently by providing a simple method. © 2011 Springer-Verlag.