The friend-of-a-friend nearest neighbor heuristic needs about n^2/(2K^2) rounds on generic metric-derived rankings, while a range-query variant finishes in O(n log n) for a Poisson process on a torus.
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K-Nearest Neighbor Approximation Via the Friend-of-a-Friend Principle
The friend-of-a-friend nearest neighbor heuristic needs about n^2/(2K^2) rounds on generic metric-derived rankings, while a range-query variant finishes in O(n log n) for a Poisson process on a torus.