Which Triangulations Approximate the Complete Graph?

nce Abstract) 1 GAUTAM DAS - University of Wisconsin DEBORAH JOSEPH - University of Wisconsin Chew and Dobkin et. al. have shown that the Delaunay triangulation and its variants are sparse approximations of the complete graph, in that the shortest distance between two sites within the triangulation is bounded by a constant multiple of their Euclidean separation. In this paper, we show that other classical triangulation algorithms, such as the greedy triangulation, and more notably, the minimum weight triangulation, also approximate the complete graph in this sense. We also design an algorithm for constructing extremely sparse (nontriangular) planar graphs that approximate the complete graph. We define a sufficiency condition and show that any Euclidean planar graph constructing algorithm which satisfies this condition always produces good approximations of the complete graph. This condition is quite general because it is satisfied by all the triangulation algorithms mentioned above, an...

• Type: Conference
• Year: 1989
• Where: OA
• Authors: Gautam Das, Deborah Joseph
• Keywords: Algorithms, Complete Graph, Minimum Weight Triangulations, OA 1989, Triangulation Algorithms