One of the most important structural parameters of graphs is treewidth, a measure for the " tree-likeness " and thus in many cases an indicator for the hardness of problem instances. The smaller the treewidth, the closer the graph is to a tree and the more efficiently the underlying instance often can be solved. However , computing the treewidth of a graph… (More)
We present algorithms for the propositional model counting problem #SAT. The algorithms utilize tree decompositions of certain graphs associated with the given CNF formula; in particular we consider primal, dual, and incidence graphs. We describe the algorithms coherently for a direct comparison and with sufficient detail for making an actual implementation… (More)
We study the consistency problem for extended global cardinality (EGC) constraints. An EGC constraint consists of a set X of variables, a set D of values, a domain D(x) ⊆ D for each variable x, and a " car-dinality set " K(d) of non-negative integers for each value d. The problem is to instantiate each variable x with a value in D(x) such that for each… (More)
Hypertree decompositions of hypergraphs are a generalization of tree decompositions of graphs. The corresponding hypertree-width is a measure for the cyclicity and therefore tractability of the encoded computation problem. Many NP-hard decision and computation problems are known to be tractable on instances whose structure corresponds to hypergraphs of… (More)
We consider the constraint satisfaction problem (CSP) parameterized by the tree-width of primal, dual, and incidence graphs, combined with several other basic parameters such as domain size and arity. We determine all combinations of the considered parameters that admit fixed-parameter tractability.
The literature provides several structural decomposition methods for identifying tractable subclasses of the constraint satisfaction problem. Generalized hypertree decomposition is the most general of such decomposition methods. Although the relationship to other structural decomposition methods has been thoroughly investigated, only little research has… (More)
We generalize the notion of backdoor sets from propositional formulas to quantified Boolean formulas (QBF). This allows us to obtain hierarchies of tractable classes of quantified Boolean formulas with the classes of quantified Horn and quantified 2CNF formulas, respectively, at their first level, thus gradually generalizing these two important tractable… (More)
We review the concepts of hypertree decomposition and hypertree width from a graph theoretical perspective and report on a number of recent results related to these concepts. We also show – as a new result – that computing hypertree decompositions is fixed-parameter intractable. This paper reports about the recently introduced concept of hypertree… (More)