The set packing problem asks whether a collection of finite sets contains a set packing
with at least
members. Here, a set packing is a subcollection
whose members are pairwise disjoint.
The problem is NP-complete (Karp 1972).
Set packing generalizes the independent set problem: associate a graph vertex with each member of and join two graph
vertices when the corresponding sets intersect. Set packings
then correspond exactly to independent sets in
the resulting intersection graph.