SCG '86 Proceedings of the second annual symposium on Computational geometry
An ω(√n) lower bound for the nonoptimality of the greedy triangulation
Information Processing Letters
An O(log n) time parallel algorithm for triangulating a set of points in the plane
Information Processing Letters
An optimal parallel algorithm for triangulating a set of points in the plane
International Journal of Parallel Programming
Quasi-greedy triangulations approximating the minimum weight triangulation
Journal of Algorithms
ICCI '91 Proceedings of the International Conference on Computing and Information: Advances in Computing and Information
C-sensitive Triangulations Approximate the MinMax Length Triangulation
Proceedings of the 12th Conference on Foundations of Software Technology and Theoretical Computer Science
On Parallel Complexity of Planar Triangulations
Proceedings of the 15th Conference on Foundations of Software Technology and Theoretical Computer Science
An incremental algorithm for distributed minimum weight triangulation
PDCN '08 Proceedings of the IASTED International Conference on Parallel and Distributed Computing and Networks
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In this paper we show a parallel algorithm that produces a triangulation which is within a constant factor longer than the Minimum Weight Triangulation (MWT) in time O(log n) using O(n) processors and linear space in the CRCW PRAM model. We present a relaxed version of the quasi-greedy triangulation algorithm which produces edges which are at most (1 + ε) longer than the shortest diagonal, where ε is some positive constant smaller than 1. The analysis shows that the relaxed version still outputs a triangulation which is within a constant factor longer than the minimum weight triangulation. We also show that the approximation behavior of the greedy algorithm may deteriorate dramatically, i.e. Ω(n) longer than a minimum weight triangulation, if the lengths of the edges are not computed with high precision.