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Alex Rivera
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Is there a known, efficient algorithm for finding the closest group of three points in a cloud? This is similar to the closest pair of points problem but I am looking for three points instead of two. Edit The definition of "closest" will affect the complexity of the algorithm. As Jack pointed out, finding the minimum area triangle is 3sum-hard and in any case not well suited to my application. I am hoping there is a more efficient algorithm for finding the minimum perimeter (i.e. |AB|+|AC|+|BC|) triangle or something similar (e.g. minimum |AB|²+|AC|²+|BC|².) I know of no reason why this should be 3sum-hard as the existence of 3 colinear points elsewhere would not affect the result. Note: my points have eight dimensions, so any algorithm that is restricted to fewer dimensions is not suitable.
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