Consider the vertices of an n-dimensional cube. Distance between two vertices is measured as the minimum number of edges between the two vertices. Now consider a subset of these vertices. If we call the total set of vertices as 'T' and the subset as 'S' then our objective is to partition 'S' into two sets 'A' and 'B' and for both of these sets find vertices $x_A$ and $x_B$ from T such that the sum total of the distance between $x_A$ and the vertices of A and $x_B$ and the vertices of B should be a minimum.

How to approach this question?

Given that we know the distance relation for every pair of vertex, is it possible to know the minimum distance through some simple calculation?