Stochastic closest-pair problem and most-likely nearest-neighbor search in tree spaces

Abstract

Let T be a tree space represented by a weighted tree with t vertices, and S be a set of n stochastic points in T , each of which has a fixed location with an independent existence probability. We investigate two fundamental problems under such a stochastic setting, the closest-pair problem and the nearest-neighbor search. For the former, we propose the first algorithm of computing the ℓ-threshold probability and the expectation of the closest-pair distance of a realization of S. For the latter, we study the k most-likely nearest-neighbor search (k-LNN) via a notion called the k most-likely Voronoi Diagram (k-LVD), where we show the combinatorial complexity of k-LVD is O(nk) under two reasonable assumptions, leading to a logarithmic query time for k-LNN.