The.Algorithm.Design.Manual.Springer-Verlag.1998

War Story: Getting the Graph
Next: Traversing a Graph Up: Graph Algorithms Previous: Data Structures for Graphs
War Story: Getting the Graph
``It takes five minutes just to read the data. We will never have time to make it do something
interesting.''
The young graduate student was bright and eager, but green to the power of data structures. She would
soon come to appreciate the power.
Figure: The dual graph (dashed lines) of a triangulation
As described in a previous war story (see Section ), we were experimenting with algorithms for
extracting triangular strips for the fast rendering of triangulated surfaces. The task of finding a small
number of strips that cover each triangle in a mesh could be modeled as a graph problem, where the
graph has a vertex for every triangle of the mesh, and there is an edge between every pair of vertices
representing adjacent triangles. This dual graph representation of the planar subdivision representing the
triangulation (see Figure ) captures all the information about the triangulation needed to partition it
into triangle strips.
The first step in crafting a program that constructs a good set of strips was to build the dual graph of the
triangulation. This I sent the student off to do. A few days later, she came back and announced that it
took over five CPU minutes just to construct this dual graph of an object with a few thousand triangles.
``Nonsense!'' I proclaimed. ``You must be doing something very wasteful in building the graph. What
format is the data in?''
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