A Mixed-Integer Program for Drawing Orthogonal Hyperedges in a Hierarchical Hypergraph

Abstract

This paper presents a new formulation and solution of a mixed-integer program for the hierarchical orthogonal hypergraph drawing problem, and the number of hyperedge crossings is minimized. The novel feature of the model is in combining several stages of the Sugiyama framework for graph drawing: vertex ordering, the assignment of vertices’ x-coordinates, and orthogonal hyperedge routing. The hyperedges of a hypergraph are assumed to be multi-source and multi-target, and vertices are depicted as rectangles with ports on their top and bottom sides. Such hypergraphs are used in data-flow diagrams and in a scheme of cooperation. The numerical results demonstrate the correctness and effectiveness of the proposed approach compared to mathematical heuristics. For instance, the proposed exact approach yields a 67.3% reduction of the number of crossings compared to that obtained by using a mathematical heuristic for a dataset of non-planar graphs.

Keywords

• directed acyclic hierarchical graph
• graph drawing
• hypergraph
• orthogonal hyperedge routing
• branch-and-bound method
• mathematical heuristic