Let A and B be two sets of points in R^d, where |A|=|B|=n and the distance between them is defined by some bipartite measure dist(A,B). We study several problems in which the goal is to translate the set B, so that dist(A, B) is minimized. The main measures that we consider are (i) the diameter in two and three dimensions, that is diam(A,B) = max {d(a,b) : a in A, b in B}, where d(a,b) is the Euclidean distance between $a$ and $b$,