On an edge crossing problem

A bipartitioned graph G = (L, R, E) consists of two sets L (the “left side”) and R (the “right side”) of vertices and a set E C L x R of edges. Such graphs are commonly drawn with L on a vertical line on the left side of the page, and R on a vertical line on the right. These drawings are more useful if they have few edge crossings. In this paper we give a fast algorithm for drawing bipartitioned graphs without edge crossings, if possible. Further, we show that the problem of minimizing crossings by rearranging the left side (leaving the right side fixed) is NP-complete. K e y w o r d s a n d p h ra ses: Graphs, bipartite graphs, algorithms, NP-complete. C R c a te g o r ie s : F.2.2, G.2.2, 1.3.5.