Constraint-based spring-model algorithm for graph layout

Abstract

In this paper we will discuss the question of how to develop an algorithm for automatically designing an optimal layout of a given constraint graph. This automatic layout algorithm must observe certain aesthetic principles, which facilitate the user's interpretation of the graph. The constraint graph is generated by the visualization algorithm AVE (Automatic Visualisation Engine) which decides in this case that the object relation between the objects which are to be graphically represented must be visually realized by lines. The constraints describe how subsets of objects are geometrically represented relative to each other. We require that each individual object be of fixed size throughout the algorithm, but we allow for each of these sizes to differ one from another. This automatic layout algorithm is developed along the lines of a (spring) force model, a method which has its roots in such works as [Eade]. As a measure of any particular layout's fidelity to our aesthetic principles, we have developed a function which assigns a real value to each possible layout. We have insured that this function has good differentiability properties, in order that we may exploit gradient descent methods to arrive at a layout that minimizes this function. Any such layout is then by definition the optimal layout we seek. These gradient methods are integral in assuring that the algorithm we develop can efficiently implement the aesthetic principles so that we obtain a very fast routine.