Abstract
We introduce the notion of a c-sensitive triangulation based on the local notion of a c-sensitive triangulation edge. We show that any c-sensitive triangulation of a planar point set approximates the minmax length triangulation of the set within the factor 2(c+1). On the other hand we prove that the greedy triangulation and the Dclaunay triangulation of a planar straight-line graph are respectively 4-sensitive and 1-sensitive. We also generalize the relationship between c-sensitive triangulations and the minmax length triangulation to include appropriately augmented planar straight-line graphs. This enables us to obtain a O(n) log n)-time heuristic for the minmax length triangulation of an arbitrary planar straight-line graph with the approximation factor bounded by 3. A modification of the above heuristic for simple polygons runs in linear time.
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