Abstract
We domonstrate that a resolution- r PR quadtree containing n points has, in the worst case, at most 8n(r− [log 4( n 2 ]) + 8n 3 − 1 3 nodes. This captures the fact that as n tends towards 4 r , the number of nodes in a PR quadtree quickly approaches O( n). This is a more precise estimation of the worst case space requirement of a PR quadtree then has been attempted before.
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