A Fixed-Parameter Algorithm for the Minimum Weight Triangulation Problem Based on Small Graph Separators

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Abstract

We present a fixed-parameter algorithm which computes for a set P of n points in the plane in \(O(2^{c \sqrt{k} \log k} \cdot k \sqrt{k} n^3)\) time a minimum weight triangulation. The parameter k is the number of points in P that lie in the interior of the convex hull of P and \(c = (2 + \sqrt{2})/(\sqrt{3} -- \sqrt{2}) < 11\) .