Suppose I have a set of vectors $A_{i}$ and another set $B_{j}$ where $A_{i}$ and $B_{j}$ do not necessarily contain the same number of elements. What is the optimal pairing of vector $A_{i},B_{j}$ such that you produce the largest sum of dot products?
The vectors are the same length and of course once a pair is used, neither vector in that pair can be re-used in another pair. You could solve this by enumerating all the combinations - in each combination performing the dot products, summing for each pair in the combination and picking the combination with the maximum sum - but I assume there is a more efficient way.
