Let $U = [1..n]$ be the universe of $n$ elements and $C$ be a  collection of subsets of $U$, $C= S_1, \dots, S_m$, where $S_i \subset U$. Then the problem is to find as many partitions of $C$, such that each partition covers the universe U. The hardness results can be  derived for this problem, but are there any approximation algorithms known for this ? I gather that the geometric version of this problem has some approximation algorithms, but is there any thing known in the general case ?
Finding maximum number of disjoint set covers
ds.algorithms;approximation