How to code the maximum set packing algorithm?

Question

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

Answer 1

You can solve the set packing problem searching a Maximum independent set. You encode your problem as follows:

• for each set you put a vertex
• you put an edge between two vertex if they share a common number.

Then you wan't a maximum set of vertex without two having two related vertex. Unfortunately this is a NP-Hard problem. Any know algorithm is exponential.