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Abstract: 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 first question is that the known \Omega\Gamma p n) lower bound is tight. The second question is answered in the affirmative by using a slight modification of an O(n log n) ... (Update)
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BibTeX entry: (Update)
C. Levcopoulos and D. Krznaric, Quasi-greedy triangulations approximating the minimum weight triangulation, in: Proc. 7th Ann. ACM-SIAM Symp. Discrete Algorithms (SODA), Association for Computing Machinery, 1996, pp. 392--401. http://citeseer.ist.psu.edu/article/levcopoulos96quasigreedy.html More
@inproceedings{ levcopoulos96quasigreedy,
author = "Levcopoulos and Krznaric",
title = "Quasi-Greedy Triangulations Approximating the Minimum Weight Triangulation",
booktitle = "{SODA}: {ACM}-{SIAM} Symposium on Discrete Algorithms (A Conference on Theoretical and Experimental Analysis of Discrete Algorithms)",
year = "1996",
url = "citeseer.ist.psu.edu/article/levcopoulos96quasigreedy.html" }
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26 New results in planar triangulations (context) - Gilbert - 1979
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7 The greedy triangulation can be computed from the Delaunay i.. (context) - Levcopoulos, Krznaric - 1994
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6 Information Processing Letters (context) - Kirkpatrick, on et al. - 1980
5 On approximating behavior of the greedy triangulation for co.. (context) - Levcopoulos, Lingas - 1987
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