Choosing subsets of a set such that the subsets satisfy a global constraint
From my answer at math.stackexchange: https://math.stackexchange.com/questions/3205/choosing-subsets-of-a-set-such-that-the-subsets-satisfy-a-global-constraint/3207#3207

Assuming $m$ is an input, your problem is NP-Complete.

Subset sum can be reduced to it.

Given $A = \\{x_{1}, ..., x_{n}\\}$ for which we need to find a subset of sum $S$, we can create $n$ inputs to your algorithm, with input $A$, $m$ and $p_{L} = p_{U} = \frac{S}{m}$, for $1 \leq m \leq n$.

If $m$ is fixed then the brute force algorithm (which you don't want) is $O(n^m)$ and so has a polynomial time algorithm.

If this does not answer your question, can you please clarify exactly what you need?