Let's say, for the sake of the question, I have 3 sets of real numbers of variate length:
$\{7,5,\tfrac{8}{5},\tfrac{1}{9}\},\qquad\{\tfrac{2}{7},4,\tfrac{1}{3}\},\qquad\{1,2,7,\tfrac{4}{10},\tfrac{5}{16},\tfrac{7}{8},\tfrac{9}{11}\}$
Is there a way to calculate the overall distance these sets have from one another? Again, there are only 3 sets for the sake of the example, but in practice there could be $N$ sets as such:
$\{A_1,B_1,C_1,\ldots,N_1\},\qquad \{A_2,B_2,C_2\ldots,N_2\},\;\ldots \quad\{A_n,B_n,C_n,\ldots,N_n\}$
These sets of reals can be considered to be sets in a metric space. The distance needed is the shortest overall distance between these sets, similar to the Hausdorff distance, except rather then finding the longest distance between 2 sets of points, I am trying to find the shortest distance between N sets of points.