Generalizing geometric graphs

Network visualization is essential for understanding the data obtained from huge real-world networks such as flight-networks, the AS-network or social networks. Although we can compute layouts for these networks reasonably fast, even the most recent display media are not capable of displaying these layouts in an adequate way. Moreover, the human viewer may be overwhelmed by the displayed level of detail. The increasing amount of data therefore requires techniques aiming at a sensible reduction of the visual complexity of huge layouts. We consider the problem of computing a generalization of a given layout reducing the complexity of the drawing to an amount that can be displayed without clutter and handled by a human viewer. We take a first step at formulating graph generalization within a mathematical model and we consider the resulting problems from an algorithmic point of view. We show that these problems are NP-hard in general, and provide efficient approximation algorithms as well as efficient and effective heuristics. We also showcase some sample generalizations.