Exploring the dynamics of graph algorithms

In this paper, we describe an interactive visualization tool for representing the dynamics of graph algorithms. To reach this goal, we designed a web-based framework which illustrates the dynamics as time-to-space mappings of dynamic graphs. Such static diagrams of dynamic data have the benefit of being able to display longer time spans in one view, hence supporting the observer with comparison tasks which is challenging or even impossible for graph algorithm animations. Our tool can show details about how an algorithm traverses a graph step-by-step in a static and animated fashion, for graph algorithm exploration as well as educational purposes. The animation together with the time-to-space mapping hence forms an overview-and-detail approach. We also allow changing of speed, replaying, stopping, storing intermediate stages with parameter configurations, as well as measuring and monitoring performance and memory consumption to eventually identify bottlenecks in a graph algorithm. By using flight carrier data from the United States Department of Transportation and a network of autonomous systems we demonstrate how we used the tool to explore two standard graph-theoretic algorithms. Finally, we discuss scalability issues and limitations.