  Cardinality constraints or, more generally, weight constraints are well
recognized as an important extension of answer-set programming. Clearly, all
common algorithmic tasks related to programs with cardinality or weight
constraints - like checking the consistency of a program - are intractable.
Many intractable problems in the area of knowledge representation and reasoning
have been shown to become linear time tractable if the treewidth of the
programs or formulas under consideration is bounded by some constant. The goal
of this paper is to apply the notion of treewidth to programs with cardinality
or weight constraints and to identify tractable fragments. It will turn out
that the straightforward application of treewidth to such class of programs
does not suffice to obtain tractability. However, by imposing further
restrictions, tractability can be achieved.
