On the Parallel Complexity of Struc- tural CSP Decomposition Methods

Constraint satisfaction problems are NP-complete in general, but they can be solved in polynomial time and also in parallel if their associated hypergraph is acyclic. It is often important for applications to solve also non-acyclic problems, thus finding larger tractable classes of CSPs is of high interest. Many structural decomposition methods have been suggested, which enable that the efficient techniques for acyclic hypergraphs can be applied to larger problem classes as well. For some of these classes, e.g. for bounded treewidth and bounded hypertreewidth also the recognition problem is in LogCFL, thus it is highly parallelizable. In this paper we show that all other tractable classes also posses this desirable property. In particular, we show, that recognizing hypergraphs with bounded biconnected width is in LogCFL. We also prove that recognizing hypergraphs with bounded cycle cutset width is feasible in L.