Abstract
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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Xue, J., Li, Y. (2017). Stochastic Closest-Pair Problem and Most-Likely Nearest-Neighbor Search in Tree Spaces. In: Ellen, F., Kolokolova, A., Sack, JR. (eds) Algorithms and Data Structures. WADS 2017. Lecture Notes in Computer Science(), vol 10389. Springer, Cham. https://doi.org/10.1007/978-3-319-62127-2_48
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DOI: https://doi.org/10.1007/978-3-319-62127-2_48
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