Navigating Graph Surfaces

A broad spectrum of massive data sets can be modeled as dynamic weighted multi-digraphs with sizes ranging from tens of gigabytes to petabytes. The sheer size of these data repositories brings with it interesting visualization and computational challenges. We introduce the notion of graph surfaces as a metaphor that allows the integration of visualization and computation over these data sets. By using out-of-core algorithms we build a hierarchy of graph surfaces that represents a virtual geography for the data set. In order to provide the user with navigation control and interactive response, we incorporate a number of geometric techniques from 3D computer graphics like terrain triangulation and mesh simplification. We highlight the main algorithmic ideas behind the tools and formulate two novel mathematical problems that have surfaced along the way.