Generalized hypertree decompositions: np-hardness and tractable variants

The generalized hypertree width GHW(H) of a hypergraph H is a measure of its cyclicity. Classes of conjunctive queries or constraint satisfaction problems whose associated hypergraphs have bounded GHW are known to be solvable in polynomial time. However, it has been an open problem for several years if for a fixed constant k and input hypergraph H it can be determined in polynomial time whether GHW(H) k. Here, this problem is settled by proving that even for k = 3 the problem is already NP-hard. On the way to this result, another long standing open problem, originally raised by Goodman and Shmueli in 1984 in the context of join optimization is solved. It is proven that determining whether a hypergraph H admits a tree projection with respect to a hypergraph G is NP-complete. Our intractability results on generalized hypertree width motivate further research on more restrictive tractable hypergraph decomposition methods that approximate general hypertree decomposition (GHD). We show th...

• Type: Conference
• Year: 2007
• Where: PODS
• Authors: Georg Gottlob, Thomas Schwentick, Zoltán Miklós
• Keywords: Database, Decomposition Method, Hypergraph Decomposition Methods, Input Hypergraph, PODS 2007