School of Information Technologies Circular Graph Drawings with Large Crossing Angles

This paper is motivated by empirical research that has shown that increasing the angle of edge crossings reduces the negative effect of crossings on human readability. We investigate circular graph drawings (where each vertex lies on a circle) with large crossing angles. In particular, we consider the case of right angle crossing (RAC) drawings, where each crossing angle is π/2. We characterize circular RAC graphs that admit a circular RAC drawing, and present a linear-time algorithm for constructing such a drawing, if it exists. We also describe a quadratic programming approach to construct circular drawings that maximise crossing angles. This method significantly increases crossing angles compared to the traditional equalspacing algorithm.