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- At root (assuming there is a vertical split), either the left subtree or the right subtree is traversed
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- The next level children have splits on y-dimension
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- Hence, both subtrees may be traversed
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- This yields the recurrence
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![](images/img328.png) |
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- Solving the above recurrence (with
),
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![](images/img330.png) |
- Same time for horizontal lines
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- Time for T points in the answer set is linear
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- Worst-case searching time in 2 dimensions is
![](images/img331.png)
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