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Suppose I have a set $A=\{a_1,a_2,...,a_n\}$ and a metric $f$ on $A$. I want to extract a subset $B$ of size $k$ such that it maximizes the sum of the distances between every possible pair in B. i.e. to maximize:

$$\sum _{a_i,a_j\in B, a_i\neq a_j} f(a_i,a_j)$$

Is there any known algorithm to do this?

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    [Duplicate question](http://math.stackexchange.com/questions/2106489/maximizing-sum-of-metric-function-on-a-set-adaptation-of-hungarian-algorithm) – 2017-01-22

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