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Reporting Neighbors in High-Dimensional Euclidean Space

2014
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SIAM journal on computing (Print)
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We consider the following problem, which arises in many database and web-based applications: Given a set P of n points in a high-dimensional space R d and a distance r, we want to report all pairs of points of P at Euclidean distance at most r. We present two randomized algorithms, one based on randomly shifted grids, and the other on randomly shifted and rotated grids. The running time of both algorithms is of the form C(d)(n + k) log n, where k is the output size and C(d) is a constant that

doi:10.1137/12089867x
fatcat:dl3adensandr3jg2hevpx3a4yq