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, 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 article, we show that for every fixed 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 polynomial-time 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 a CSP restricted to instances whose structure is in H is polynomial-time solvable. This makes bounded fractional hypertree width the most general known hypergraph property that makes CSP, Boolean conjunctive queries, and conjunctive query containment polynomial-time solvable.