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

Compactly generating all satisfying truth assignments of a Horn formula

As instance of an overarching principle of exclusion an algorithm is presented that compactly (thus not one by one) generates all models of a Horn formula. The principle of exclusion can be adapted to generate only the models of weight $k$. We compare and contrast it with constraint programming, $0,1$ integer programming, and binary decision diagrams.Comment: Considerably improves upon the readibility of the previous versio

Compression with wildcards: All exact, or all minimal hitting sets

Our main objective is the COMPRESSED enumeration (based on wildcards) of all minimal hitting sets of general hypergraphs. To the author's best knowledge the only previous attempt towards compression, due to Toda [T], is based on BDD's and much different from our techniques. Numerical experiments show that traditional one-by-one enumeration schemes cannot compete against compressed enumeration when the degree of compression is high. Our method works particularly well in these two cases: Either compressing all exact hitting sets, or all minimum-cardinality hitting sets. It also supports parallelization and cut-off (i.e. restriction to all minimal hitting sets of cardinality at most m).Comment: 30 pages, many Table