Discrete & Computational Geometry

, Volume 11, Issue 2, pp 163-191

First online:

Approximating the minimum weight steiner triangulation

  • David EppsteinAffiliated withDepartment of Information and Computer Science, University of California

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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. InO(n logn) time we can compute a triangulation withO(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 thanO(logn).