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

War Story: Getting the Graph
``We are going to need a data structure consisting of an array with one element for every vertex in the
original data set. This element is going to be a list of all the triangles that pass through that vertex. When
we read in a new triangle, we will look up the three relevant lists in the array and compare each of these
against the new triangle. Actually, only two of the three lists are needed, since any adjacent triangle will
share two points in common. For anything sharing two vertices, we will add an adjacency to our graph.
Finally, we will add our new triangle to each of the three affected lists, so they will be updated for the
next triangle read.''
She thought about this for a while and smiled. ``Got it, Chief. I'll let you know what happens.''
The next day she reported that the graph could be built in seconds, even for much larger models. From
here, she went on to build a successful program for extracting triangle strips, as reported in Section .
The take-home lesson here is that even elementary problems like initializing data structures can prove to
be bottlenecks in algorithm development. Indeed, most programs working with large amounts of data
have to run in linear or almost linear time. With such tight performance demands, there is no room to be
sloppy. Once you focus on the need for linear-time performance, an appropriate algorithm or heuristic
can usually be found to do the job.
Next: Traversing a Graph Up: Graph Algorithms Previous: Data Structures for Graphs
Algorithms
Mon Jun 2 23:33:50 EDT 1997
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