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.
Friedman, Jon Louis Bentley, and Raphael A
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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.