Polynomially Solvable Cases of Hypergraph Transversal and Related Problems

We also study the readability of a monotone Boolean function which is defined as the minimum integer r such that it can be represented by an AND-OR-formula with every variable occurrence is bounded by r. We prove that it is NP-hard to approximate the readability of even a depth three Boolean formula. We also give tight sublinear upper bounds on the readability of a monotone Boolean function given in CNF (or DNF) form, parameterized by the number of terms in the CNF and the maximum number of variables in the intersection of any constant number of terms. For interval DNF's we give much tighter logarithmic bounds on the readability.

Finally, we discuss an implementation of a quasi-polynomial algorithm for the hypergraph transversal problem that runs in polynomial space. We found our implementation to be competitive with all but one previous implementation on various datasets.