When dimension d is at least polylogarithmic in n, k-d tree defeatist search returns the nearest neighbor with probability no better than random guessing and comprehensive search visits every cell with high probability.
An improved algorithm finding nearest neighbor using kd-trees
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Performance bounds for nearest neighbor search with k-d trees
When dimension d is at least polylogarithmic in n, k-d tree defeatist search returns the nearest neighbor with probability no better than random guessing and comprehensive search visits every cell with high probability.