The exact cover problem asks whether a finite set 
has an exact cover by a given collection 
of its subsets. An exact cover
is a subcollection 
in which every element of 
occurs in exactly one member. Thus the members of 
are disjoint sets whose union is 
.
The decision problem is NP-complete (Karp 1972). The restricted exact cover by 3-sets problem,
abbreviated X3C, requires every member of 
to have cardinality 3 and is also NP-complete.
