Enumerating all minimal hitting sets in polynomial total time

Abstract

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 $O(R{h}^2{w}^2)$.

There is a mistake in Case 1 of claim (4), which annihilates the proof of polynomial total time. This was pointed out independently by Arnaud Mary, then Endre Boros, then Martin Schirnek. My apologies for waiting so long with the withdrawal