3 years ago

Dynamic Distribution-Sensitive Point Location. (arXiv:2003.08288v1 [cs.CG])

Siu-Wing Cheng, Man-Kit Lau
We propose a dynamic data structure for the distribution-sensitive point location problem. Suppose that there is a fixed query distribution in , and we are given an oracle that can return in time the probability of a query point falling into a polygonal region of constant complexity. We can maintain a convex subdivision with vertices such that each query is answered in expected time, where OPT is the minimum expected time of the best linear decision tree for point location in . The space and construction time are . An update of as a mixed sequence of edge insertions and deletions takes amortized time. As a corollary, the randomized incremental construction of the Voronoi diagram of sites can be performed in expected time so that, during the incremental construction, a nearest neighbor query at any time can be answered optimally with respect to the intermediate Voronoi diagram at that time.

Publisher URL: http://arxiv.org/abs/2003.08288

DOI: arXiv:2003.08288v1

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