I am trying to show a decision problem is NP-complete, using a polynomial-time reduction. As this is a homework question I won't post the exact question but the gist is this:
"Let $k\in\mathbb{N}$. Let $S$ be a set of natural numbers, and $S^i \subset S$ a collection of subsets, each given by some rule. Does there exist an $S^i$ such that $\sum_{s \in S^i} s \leq k$?"
Is there an obvious choice of problem to reduce from? I've been trying to use CLIQUE but haven't had great success so far.
Apologies if this is too vague.