What is the sqrt(n)-approximation algorithm for set packing problem
See Viggo Kann's page on set packing. Viggo mentions two $\sqrt{|U|}$ algorithms:


Unweighted case: Halldórsson, M. M., Kratochvíl, 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: Halldórsson, 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.