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When another data point is inserted and the Voronoi diagram reconstructed, the newly created region displaces the area that once belonged to the old regions. Those points whose regions were displaced are considered natural neighbours to the new point. The weight of each natural neighbour is given by the area taken from the total area occupied by the new region. In 3D, we measure polyhedral volumes instead of areas.
，更多细节参见搜狗输入法2026
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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