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I want to know if there is an algorithm which does the following:

Imagine you have a point cloud and the points affect each other but the action from each point to an other is only valid in some radius around this point (locally).

Now remove one point and the local configuration changes.

How is the cheapest way to determine which points are affected from this removement?

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    $\begingroup$ This seems to be known as range searching and is supported by data structures such as range trees and kd-trees. $\endgroup$
    – Yuval Filmus
    Commented Feb 16, 2015 at 17:47

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