A set packing in a collection of finite sets is a subcollection
such that any two members are disjoint sets. The
set packing problem asks whether
contains a set packing with at least
members. It 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.