Axis-by-axis stress minimization

Abstract

Graph drawing algorithms based on minimizing the so-called stress energy strive to place nodes in accordance with target distances. They were first introduced to the graph drawing field by Kamada and Kawai [11], and they had previously been used to visualize general kinds of data by multidimensional scaling. In this paper we suggest a novel algorithm for the minimization of the Stress energy. Unlike prior stress-minimization algorithms, our algorithm is suitable for a one-dimensional layout, where one axis of the drawing is already given and an additional axis needs to be computed. This 1-D drawing capability of the algorithm is a consequence of replacing the traditional node-by-node optimization with a more global axis-by-axis optimization. Moreover, our algorithm can be used for multidimensional graph drawing, where it has time and space complexity advantages compared with other stress minimization algorithms. © Springer-Verlag 2004.