For well-distributed points, nearest neighbor search is often near O(logn)O(\log n)O(logn) in practice. In the worst case (all points clustered tightly or along a line), it can degrade to O(n)O(n)O(n), but this is uncommon with typical spatial data.
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A notable resource on the topic of ordered dithering using arbitrary palettes is Joel Yliluoma’s Arbitrary-Palette Positional Dithering Algorithm. One key difference of Yliluoma’s approach is in the use of error metrics beyond the minimisation of . Yliluoma notes that the perceptual or psychovisual quality of the dither must be taken into account in addition to its mathematical accuracy. This is determined by use of some cost function which considers the relationship between a set of candidate colours. The number of candidates, the particular cost function, and the thoroughness of the selection process itself give rise to a number of possible implementations, each offering varying degrees of quality and time complexity.