Quasi-Greedy Triangulations Approximating the Minimum Weight Triangulation

  title={Quasi-Greedy Triangulations Approximating the Minimum Weight Triangulation},
  author={Christos Levcopoulos and Drago Krznaric},
This paper settles the following two longstanding open problems: 1. What is the worst-case approximation ratio between the greedy and the minimum weight triangulation? 2. Is there a polynomial time algorithm that always produces a triangulation whose length is within a constant factor from the minimum? The answer to the rst question is that the known ( p n) lower bound is tight. The second question is answered in the a rmative by using a slight modi cation of an O(n logn) algorithm for the… CONTINUE READING
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