Threshold Treewidth and Hypertree Width

Treewidth and Hypertree Width

The chapter covers methods for identifying islands of tractability for NP-hard combinatorial problems by exploiting suitable properties of their graphical structure. Acyclic structures are considered, as well as nearly acyclic ones identified by means of so-called structural decomposition methods. In particular, the chapter focuses on the tree decomposition method, which is the most powerful de...

Minor-matching hypertree width

In this paper we present a new width measure for a tree decomposition, minor-matching hypertree width, μ-tw, for graphs and hypergraphs, such that bounding the width guarantees that set of maximal independent sets has a polynomially-sized restriction to each decomposition bag. The relaxed conditions of the decomposition allow a much wider class of graphs and hypergraphs of bounded width compare...

On Tractability and Hypertree Width

We investigate in this paper the notion of hypertree width as a parameter for bounding the complexity of CSPs, especially those whose constraints can be represented compactly, such as SAT problems. We first identify a simple condition which is necessary for hypertree width to provide better complexity bounds than treewidth. We then observe that SAT problems do not satisfy this condition and, he...

Width Functions for Hypertree Decompositions

Hypertree width and related hypergraph invariants

Tree-width of graphs is a well studied notion, which plays an important role in structural graph theory and has many algorithmic applications. Various other graph invariants are known to be the same or within a constant factor of tree-width, for example, the bramble number or tangle number of a graph [4, 5], the branch-width [5], the linkedness [4], and the number of cops required to win the ro...