Chapter

Graph-Theoretic Concepts in Computer Science

Volume 4271 of the series Lecture Notes in Computer Science pp 49-57

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

  • Christian KnauerAffiliated withInstitute of Computer Science, Freie Universität Berlin
  • , Andreas SpillnerAffiliated withInstitute of Computer Science, Friedrich-Schiller-Universität Jena

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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 \(c = (2 + \sqrt{2})/(\sqrt{3} -- \sqrt{2}) < 11\).