One-Dimensional Graph Drawing: Part II — Axis-by-Axis Stress Minimization

Graph drawing algorithms based on minimizing the so-called stress energy strive to place nodes in accordance with target distances. Such algorithms 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 axis-by-axis minimization of the Stress energy. This 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. In general, the proposed algorithm produces aesthetically superior layouts compared to other 1-D drawing algorithms. Moreover, our algorithm can be used for multidimensional graph drawing, where it has time and space complexity advantages compared with other stress minimization algorithms.