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

War Story: Stripping Triangulations
Figure: A comparison of the naive versus greedy heuristics for several triangular meshes
How much better did the greedy heuristic do than the naive heuristic? Consider the table in Figure . In
all cases, the greedy heuristic led to a set of strips that cost less, as measured by the total size of the
strips. The savings ranged from about 10% to 50%, quite remarkable, since the greatest possible
improvement (going from three vertices per triangle down to one) could yield a savings of only 66.6%.
After implementing the greedy heuristic with our priority queue data structure, our complete algorithm
ran in time, where n is the number of triangles and k is the length of the average strip. Thus the
torus, which consisted of a small number of very long strips, took longer than the jaw, even though the
latter contained over three times as many triangles.
There are several lessons to be gleaned from this story. First, whenever we are working with a large
enough data set, only linear or close to linear algorithms (say ) are likely to be fast enough.
Second, choosing the right data structure is often the key to getting the time complexity down to this
point. Finally, using a greedy or somewhat smarter heuristic over the naive approach is likely to
significantly improve the quality of the results. How much the improvement is likely to be can be
determined only by experimentation. Our final, optimized triangle strip program is described in [ESV96].
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Algorithms
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