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Lower Bounding the Number of Straight-Edge Triangulations of Planar Point Sets

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons44958

McCabe,  Paul
Algorithms and Complexity, MPI for Informatics, Max Planck Society;
International Max Planck Research School, MPI for Informatics, Max Planck Society;

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McCabe, P. (2003). Lower Bounding the Number of Straight-Edge Triangulations of Planar Point Sets. Master Thesis, Universität des Saarlandes, Saarbrücken.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0027-F823-4
Abstract
We examine the number of triangulations that any set of n points in the plane must have, and prove that (i) any set of n points has at least 0.00037*2.2n triangulations, (ii) any set with three extreme points and n interior points has at least 0.112*2.569n triangulation, and (iii) any set with n interior points has at least 0.238 * 2.38n triangulation. The best previously known lower bound for the number of triangulations for n points in the plane is 0.0822 * 2.0129n. We also give a method of automatically extending known bounds for small point sets to general lower bounds.