Hypertree Decompositions: Structure, Algorithms, and Applications

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. 1 Hypertree Decompositions: Definition and Basics This paper reports about the recently introduced concept of hypertree decomposition and the associated notion of hypertree-width. The latter is a cyclicity measure for hypergraphs, and constitutes a hypergraph invariant as it is preserved under hypergraph isomorphisms. Many interesting NP-hard problems are polynomially solvable for classes of instances associated with hypergraphs of bounded width. This is also true for other hypergraph invariants such as treewidth, cutset-width, and so on. However, the advantage of hypertree-width with respect to other known hypergraph invariants is that it is more general and covers larger classes of instances of bounded ...

• Type: Conference
• Year: 2005
• Where: WG
• Authors: Georg Gottlob, Martin Grohe, Nysret Musliu, Marko Samer, Francesco Scarcello
• Keywords: Computer Science, Hypergraph Invariants, Hypergraph Isomorphisms, Hypertree Decompositions, WG 2005