Let $S$ be a set of $n$ integers. Consider the following weighted permutations problem.
Let $m<n$ be an integer. What is an efficient algorithm to enumerate all subsets of $m$ integers of $S$ such that they are listed in order of the sum of the integers in each subset?
Each subset is a permutation, and each permutation has a total weight that is the sum of the integers in the permutation.
The idea is to come up with an algorithm that is not the trivial algorithm of enumerating all subsets, and then sorting them, i.e. more of a "streaming" type algorithm. That is, efficiency in terms not so much of time but of "small" space.
Maybe this is published somewhere in the literature although I have not seen it.