An improved approximation to the one-sided bilayer drawing

Abstract

Given a bipartite graph G =(V, W, E), a bilayer drawing consists of placing nodes in the first vertex set V on a straight line LI and placing nodes in the second vertex set W on a parallel line L2The one-sided crossing minimization problem asks to find an ordering of nodes in V to be placed on L1 so that the number of arc crossings is minimized. In this paper, we prove that there always exits a solution whose crossing number is at most 1.4664 times of a well-known lower bound that is obtained by summing up min{cuv,cvu} over all node pairs u, v ε V, where Cuv denotes the number of crossings generated by arcs incident to it and v when u precedes v in an ordering. © Springer-Verlag 2004.