Suppose we have a finite set S and a list of subsets of S. Then, the set packing problem asks if some k subsets in the list are pairwise disjoint . The optimization version of the problem, maximum set packing, asks for the maximum number of pairwise disjoint sets in the list.

http://en.wikipedia.org/wiki/Set_packing

So, Let S = {1,2,3,4,5,6,7,8,9,10}

and `Sa = {1,2,3,4}`
and `Sb = {4,5,6}`
and `Sc = {5,6,7,8}`
and `Sd = {9,10}`

Then the maximum number of pairwise disjoint sets are 3 ( Sa, Sc, Sd )

I could not find any articles about the algorithm involved. Can you shed some light on the same?

My approach:

Sort the sets according to the size. Start from the set of the smallest size. If no element of the next set intersects with the current set, then we unite the set and increase the count of maximum sets. Does this sound good to you? Any better ideas?