Abstract:
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). 1 Introduction Optimal triangulation has furnished a number of problems of longstanding interest in computational geometry. These problems have applications to cartography, spatial data analysis, and finite element methods. Optimization criteria for which e#cient algorithms are known include maximizing the minimum angle [19, 23], minimizing the maximum angle [6], minimizing the minimum angle [7], ...
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