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Title: On β-skeleton as a subgraph of the minimum weight triangulation
Authors: Cheng, Siu-Wing
Xu, Yin-Feng
Keywords: Minimum weight triangulation
Beta skeleton
Computational geometry
Issue Date: 2001
Citation: Theoretical Computer Science, v. 262, 2001, p. 459-471
Abstract: Given a set S of n points in the plane, a triangulation is a maximal set of non-intersecting edges connecting the points in S. The weight of the triangulation is the sum of the lengths of the edges. In this paper, we show that for β > 1/sin k, the β-skeleton of S is a subgraph of a minimum weight triangulation of S, where k=tan-1(3/√2√3)≈π /3.1. There exists a four point example such that the β-skeleton for β < 1/sin(π /3) is not a subgraph of the minimun weight triangulation.
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