Approximating fractional hypertree width

Fractional hypertree width is a hypergraph measure similar to tree width and hypertree width. Its algorithmic importance comes from the fact that, as shown in previous work [14], constraint satisfaction problems (CSP) and various problems in database theory are polynomial-time solvable if the input contains a bounded-width fractional hypertree decomposition of the hypergraph of the constraints. In this paper, we show that for every w ≥ 1, there is a polynomial-time algorithm that, given a hypergraph H with fractional hypertree width at most w, computes a fractional hypertree decomposition of width O(w3 ) for H. This means that polynomialtime algorithms relying on bounded-width fractional hypertree decompositions no longer need to be given a decomposition explicitly in the input, since an appropriate decomposition can be computed in polynomial time. Therefore, if H is a class of hypergraphs with bounded fractional hypertree width, then CSP restricted to instances whose structure is i...

• Type: Journal
• Year: 2010
• Where: TALG
• Authors: Dániel Marx
• Keywords: Fractional Hypertree, Fractional Hypertree Decomposition, Fractional Hypertree Width, TALG 2010