Stochastic Closest-Pair Problem and Most-Likely Nearest-Neighbor Search in Tree Spaces

  • Jie Xue
  • Yuan LiEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10389)


Let \(\mathcal {T}\) be a tree space represented by a weighted tree with t vertices, and S be a set of n stochastic points in \(\mathcal {T}\), 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 \(\ell \)-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.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.University of Minnesota — Twin CitiesMinneapolisUSA

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