We introduce the notion of a c-sensitive triangulation based on the local notion of a e-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 Delaunay 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.
CITATION STYLE
Levcopoulos, C., & Lingas, A. (1992). C-sensitive triangulations approximate the minmax length triangulation. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 652 LNCS, pp. 104–115). Springer Verlag. https://doi.org/10.1007/3-540-56287-7_98
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