Limit theorems for minimum-weight triangulations, other euclidean functionals, and probabilistic recurrence relations
- Hong Kong Univ. of Science and Technology, Kowloon (Hong Kong)
Let MWT(n) be the weight of a minimum-weight triangulation of n points chosen independently from the uniform distribution over [0, 1]{sup 2}. Previous work has shown that E(MWT(n)) = {Theta} ({radical}n). In this paper we develop techniques for proving that MWT(n)/{radical}n actually converges to a constant in both expectation and in probability. An immediate consequence is the development of an O(n{sup 2}) time algorithm that finds a triangulation whose competive ratio with the MWT is, in a probabilistic sense, exactly one. The techniques developed to prove the above results are quite general and can also prove the convergence of certain types of probabilistic recurrence equations and other Euclidean Functionals. This is illustrated by using them to prove the convergence of the weight of MWTs of random points in higher dimensions and a sketch of how to use them to prove the convergence of the degree probabilities for Delaunay triangulations in {Re}{sup 2}.
- OSTI ID:
- 416807
- Report Number(s):
- CONF-960121--
- Country of Publication:
- United States
- Language:
- English
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