论文信息 - WHICH TRIANGULATIONS APPROXIMATE THE COMPLETE GRAPH?

WHICH TRIANGULATIONS APPROXIMATE THE COMPLETE GRAPH?

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.

Gautam Das | Deborah Joseph | W H I C H T R I A N G U L A T I O N S A P P R O X I

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