  In a constraint satisfaction problem (CSP) the goal is to find an assignment
of a given set of variables subject to specified constraints. A global
cardinality constraint is an additional requirement that prescribes how many
variables must be assigned a certain value. We study the complexity of the
problem CCSP(G), the constraint satisfaction problem with global cardinality
constraints that allows only relations from the set G. The main result of this
paper characterizes sets G that give rise to problems solvable in polynomial
time, and states that the remaining such problems are NP-complete.
