Heuristics and Experimental Design for Bigraph Crossing Number Minimization

The bigraph crossing problem, embedding the two vertex sets of a bipartite graph G = (V0; V1; E) along two parallel lines so that edge crossings are minimized, has application to circuit layout and graph drawing. We consider the case where both V0 and V1 can be permuted arbitrarily — both this and the case where the order of one vertex set is fixed are NP-hard. Two new heuristics that perform well on sparse graphs such as occur in circuit layout problems are presented. The new heuristics outperform existing heuristics on graph classes that range from application-specific to random. Our experimental design methodology ensures that differences in performance are statistically significant and not the result of minor variations in graph structure or input order.