I am trying to solve this problem, and I cannot believe I do not find it already solved in the literature: I must be looking with the wrong keywords in the wrong place, so thanks in advance to all that will take the time to give me an answer.
Let P be a set of N points in the 3d euclidean space (x_i,y_i,z_i), and d_ij the distance of point P_i to point P_j for j not equal to i. Let H_P be the distribution (say the histogram) of d_ij.
Problem: given a histogram H_P, find a set of points Q (of arbitrary size) such that norm(H_Q-H_P)< eps in some norm.
Question: does this problem has a name at all? can somebody point me to the relevant literature/existing software?
Thanks again and sorry if the question is so stupid, but I am banging my head on this one for a couple of weeks already trying to find an efficient solution and am still at a loss.