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

Abstract

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