The set packing problem is : Given a universe $U$ and a family $S$ of subsets of $U$, a packing is a subfamily $C\subseteq S$ of sets such that all sets in $C$ are pairwise disjoint, and the size of the packing is $|C|$. The goal is to find the $C$ where $|C|$ is maximum.
According to Wikipedia, there exists a $\sqrt{|U|}$-approximation algorithm for this problem. But it doesn't give a way to approach that, it seems that the way cannot be found on google as well.