Robust proximity search for balls using sublinear space
Given a set of n disjoint balls b1, . . . , bn in ℝd, we provide a data structure, of near linear size, that can answer (1 ±ε)-approximate kth-nearest neighbor queries in O(log n + 1/εd) time, where k and ε are provided at query time. If k and ε are provided in advance, we provide a data structure to answer such queries, that requires (roughly) O(n/k) space; that is, the data structure has sublinear space requirement if k is sufficiently large.
Leibniz International Proceedings in Informatics, LIPIcs
Har-Peled, S., & Kumar, N. (2014). Robust proximity search for balls using sublinear space. Leibniz International Proceedings in Informatics, LIPIcs, 29, 315-326. https://doi.org/10.4230/LIPIcs.FSTTCS.2014.315