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.
What is the sqrt(n)-approximation algorithm for set packing problem
approximation;packing
See Viggo Kann's page on set packing. Viggo mentions two $\sqrt{|U|}$ algorithms:Unweighted case: Halldrsson, M. M., Kratochvl, J., and Telle, J. A. (1998), Independent sets with domination constraints, Proc. 25th Int. Colloquium on Automata, Languages and Programming, Lecture Notes in Comput. Sci. 1443, Springer-Verlag, 176-185. Weighted case: Halldrsson, M. M. (1999a), Approximations of weighted independent set and hereditary subset problems, Proc. 5th Ann. Int. Conf. on Computing and Combinatorics, Lecture Notes in Comput. Sci., Springer-Verlag, 261-270. I found this link on the first page of the Google search set packing approximation algorithm. I suggest that next time you spend some quality time with your favorite search engine, looking at all links in the first few pages.