A Geometric Heuristic for Rectilinear Crossing Minimization

Marcel Radermacher, Klara Reichard, Ignaz Rutter, Dorothea Wagner

Abstract: In this paper we consider the rectilinear crossing minimization problem, i.e., we seek a straight-line drawing Г of a graph G = (V, E) with a small number of edge crossings. Crossing minimization is an active field of research [1,9]. While there is a lot of work on heuristics for topological drawings, these techniques are typically not transferable to the rectilinear (i.e., straight-line) setting. We introduce and evaluate three heuristics for rectilinear crossing minimization. The approaches are based on the primitive operation of moving a single vertex to its crossing-minimal position in the current drawing Γ, for which we give an O ((kn + m)2 log (kn + m))-time algorithm, where k is the degree of the vertex and n and m are the numbers of vertices and edges of the graph, respectively. In an experimental evaluation, we demonstrate that our algorithms compute straight-line drawings with fewer crossings than energy-based algorithms implemented in the Open Graph Drawing Framework [10] on a varied set of benchmark instances. All experiments are evaluated with a statistical significance level of α = 0.05.