Crossing Minimization Problems of Drawing Bipartite Graphs in Two Clusters

Abstract

The crossing minimization problem is a classic and very important problem in graph drawing (Pach, Toth 1997); the results directly a#ect the e#ectiveness of the layout, especially for very large scale graphs. But in many cases crossings cannot be avoided. In this paper we present two models for bipartite graph drawing, aiming to reduce crossings that cannot be avoided in the traditional bilayer drawings. We characterize crossing minimization problems in these models, and prove that they are NP-complete