Quadtrees and related structures are 2-Presortable, admitting expected O(n sqrt(log n)) algorithms given presorts along both axes.
28 Drago Krznaric and Christos Levcopoulos
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The Presort Hierarchy for Geometric Problems
Quadtrees and related structures are 2-Presortable, admitting expected O(n sqrt(log n)) algorithms given presorts along both axes.