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We obtain an explicit formula for the expected cost of a fixed partial match query in a random relaxed K-d tree, that is, the expected cost for a query of the form q = (q0 , q1 , . . . , qK-1 ) with 0 < s < K specified coordinates with values z0 , . . . , zs-1 ¿ (0, 1). This is a generalization of previous results in the literature for s = 1. Qualitatively similar results hold for standard K-d trees and we conjecture that this also holds for other multidimensional tree structures such as quadtrees and K-d tries.
CitationDuch, A.; Lau, G.; Martínez, C. On the average performance of fixed partial match queries in random relaxed K-d trees. A: International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms. "AoFA 2014: 25th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms: UPMC-Jussieu Paris, France, June 16–20, 2014: talks". Paris: 2014, p. 103-114.
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