Approximating the Minimum Weight Triangulation

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Approximating the Minimum Weight Triangulation
We show that the length of the minimum weight Steiner triangulation (MWST) of a point set can be approximated within a constant factor by a triangulation algorithm based on quadtrees. In O(n log n) time we can compute a triangulation with O(n) new points, and no obtuse triangles, that approximates the MWST. We can also approximate the MWST with triangulations having no sharp angles. We generalize some of our results to higher dimensional triangulation problems. No previous polynomial time triangulation algorithm was known to approximate the MWST within a factor better than O(log n).
David Eppstein
Added 07 Nov 2010
Updated 07 Nov 2010
Type Conference
Year 1992
Where SODA
Authors David Eppstein
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