Progress on maximum weight triangulation

Authors:
Jianbo Qian;Cao An Wang
Affiliations:
School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada;Department of Computer Science, Memorial University of Newfoundland, St. John's, Newfoundland, Canada
Venue:
Computational Geometry: Theory and Applications
Year:
2006

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Quasi-greedy triangulations approximating the minimum weight triangulation

Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Maximum weight triangulation and graph drawing

Information Processing Letters

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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((2ε + 2)ċn + π(1-2ε)/8ε√1-ε2 + π/2 - 5(ε+1))D, where ε is any constant 0 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.