Resolution based algorithms for the transversal hypergraph generation problem.

We study the problem, given a hypergraph H, how to generate its transversal (or dual) hypergraph G, using tools from Boolean resolution. We show how to compute the residual dual of H given a subset E of its minimal transversals. This is the hypergraph whose minimal transversals are exactly those missing from E to become the dual of H. We give a novel algorithm for the problem based on the notion of subtransversal. Though its complexity is superpolynomial, it gives new insight to the problem of hypergraph duality. Another variant of the algorithm seems also promising to efficiently test hypergraph duality in practice.