Elsevier

Computational Geometry

Volume 33, Issue 3, February 2006, Pages 99-105
Computational Geometry

Progress on maximum weight triangulation

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Abstract

In this paper, we investigate various properties and problems associated with the maximum weight triangulation of a point set in the plane. We prove that the weight of a maximum weight triangulation of any planar point set with diameter D is bounded above by ((2ɛ+2)n+π(12ɛ)8ɛ1ɛ2+π25(ɛ+1))D, where ɛ is any constant 0<ɛ12 and n is the number of points in the set. If we use the so-called spoke-scan algorithm to find a triangulation of the point set, we obtain an approximation ratio of 4.238. Furthermore, if the point set forms a semi-circled convex polygon, then its maximum weight triangulation can be found in O(n2) time.

Keywords

Algorithm
Approximation
Maximum weight triangulation

Cited by (0)

The first author is supported by NSERC grant OGP0046506 and the National Natural Science Foundation of China under Grant No. 70221001, the second author is supported by NSERC grant OPG0041629.