One-dimensional layout optimization, with applications to graph drawing by axis separation

In this paper we discuss a useful family of graph drawing algorithms, characterized by their ability to draw graphs in one dimension. We define the special requirements from such algorithms and show how several graph drawing techniques can be extended to handle this task. In particular, we suggest a novel optimization algorithm that facilitates using the Kamada and Kawai model [Inform. Process. Lett. 31 (1989) 7-15] for producing one-dimensional layouts. The most important application of the algorithms seems to be in achieving graph drawing by axis separation, where each axis of the drawing addresses different aspects of aesthetics.