Automatic graphic object layout methods have long been studied in many application areas in which graphic objects should be laid out to satisfy the constraints specific to each application. In those areas, carefully designed layout algorithms should be used to satisfy each application's constraints. However, those algorithms tend to be complicated and not reusable for other applications. Moreover, it is difficult to add each user's preferences to the layout scheme of the algorithm. To overcome these difficulties, we developed a general-purpose interactive graphic layout system GALAPAGOS based on genetic algorithms. GALAPAGOS is general-purpose because graphic objects are laid out not by specifying how to lay them out, but just by specifying the preferences for the layout. GALAPAGOS can not only lay out complicated graphs automatically, but also allow users to modify the constraints at run time so that users can tell the system their own preferences.

A upward plane drawing of a directed acyclic graph is a straight line drawing in the Euclidean plane such that all directed arcs point upwards. Thomassen [30] has given a non-algorithmic, graph-theoretic characterization of those directed graphs with a single source that admit an upward drawing. We present an efficient algorithm to test whether a given single-source acyclic digraph has a plane upward drawing and, if so, to find a representation of one such drawing. The algorithm decomposes the graph into biconnected and triconnected components, and defines conditions for merging the components into an upward drawing of the original graph. For the triconnected components we provide a linear algorithm to test whether a given plane representation admits an upward drawing with the same faces and outer face, which also gives a simpler (and algorithmic) proof of Thomassen's result. The entire testing algorithm (for general single source directed acyclic graphs) operates in O(n²) time and...

. Although graph drawing has been extensively studied, little attention has been paid to the problem of node overlapping. The problem arises because almost all existing graph layout algorithms assume that nodes are points. In practice, however, nodes may be labelled and these labels may overlap. We propose four dierent approaches for removing node overlapping, all of which are based on constrained optimization techniques. The rst is the simplest. It performs the minimal linear scaling which will remove node-overlapping. The second approach relies on formulating the node overlapping problem as a convex quadratic programming problem which can then be solved by any quadratic solver. The disadvantage is that since constraints must be linear the node overlapping constraints cannot be expressed directly but must be strengthened to obtain a linear constraint strong enough to ensure no node overlapping. The third and fourth approaches are based on local search methods. The third is an adapta...

In software visualization and algorithm animation it is important that advances in system technologies are accompanied by corresponding advances in animation presentations. In this paper we describe methods for animating tree manipulation algorithms, one of the most challenging algorithm animation domains. In particular, we animate operations on pairing heap data structures which are used to implement priority queues. Our animations use tree layout heuristics and and smooth transitions for illustrating intermediate algorithm states to promote viewer understanding. This paper describes the visual techniques and methodologies used to display the pairing heap operations. The paper also details the implementation requirements and how our particular support platform, the XTango system, facilitates meeting these requirements. 1 Introduction Algorithm animations[Bro88b] visually depict how algorithms function to promote understanding of the algorithm's methodologies. Usually, the animation...