Incremental complexity of a bi-objective hypergraph transversal problem

The hypergraph transversal problem has been intensively studied, from both a theoretical and a practical point of view. In particular , its incremental complexity is known to be quasi-polynomial in general and polynomial for bounded hypergraphs. Recent applications in computational biology however require to solve a generalization of this problem, that we call bi-objective transversal problem. The instance is in this case composed of a pair of hypergraphs (A, B), and the aim is to find minimal sets which hit all the hyperedges of A while intersecting a minimal set of hyperedges of B. In this paper, we formalize this problem, link it to a problem on monotone boolean $\land$ -- $\lor$ formulae of depth 3 and study its incremental complexity

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