Given $n$ sets $r_1, r_2, \cdots, r_n$ and a number $\delta$ where $0 \le \delta \le 1$. Let $T=\cup_{i=1}^{n}r_i=\{t_1,t_2,\cdots,t_m\}$. Each $t$ has a value $v(t)$, which is given to us.  The task is to find a subset $S$ of $T$ that minimize the total value $\sum_{t\in S}v(t)$ while guaranteeing $\sum_{i=1}^{n}\frac{|r_i \cap S|}{|r_i|}>\delta n$.Is this problem NP-complete? If so, which problem should I reduce from?I've tried reduce it from the knapsack problem. One of the steps is not in P time and the attempt failed.
Knapsack and set cover-like problem
np complete;proof techniques;knapsack problems