New upper bounds for neighbor searching

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Abstract

This paper investigates the circular retrieval problem and the k-nearest neighbor problem, for sets of n points in the Euclidean plane. Two similar data structures each solve both problems. A deterministic structure uses space O(n(log n log log n)2), and a probabilistic structure uses space O(n log2 n). For both problems, these two structures answer a query that returns k points in O(k + log n) time. © 1986 Academic Press, Inc.

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Chazelle, B., Cole, R., Preparata, F. P., & Yap, C. (1986). New upper bounds for neighbor searching. Information and Control, 68(1–3), 105–124. https://doi.org/10.1016/S0019-9958(86)80030-4

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