Enumerating all minimal hitting sets in polynomial total time

Consider a hypergraph (=set system) $\mathbb{H}$ whose $h$ hyperedges are subsets of a set with w elements. We show that the $R$ minimal hitting sets of $\mathbb{H}$ can be enumerated in polynomial total time $O(Rh^2 w^2)$.Comment: 8 page

Coupon collecting and transversals of hypergraphs

Analysis of AlgorithmsThe classic Coupon-Collector Problem (CCP) is generalized. Only basic probability theory is used. Centerpiece rather is an algorithm that efficiently counts all k-element transversals of a set system