Lower Bounds for Three Algorithms for the Transversal Hypergraph Generation

The computation of all minimal transversals of a given hypergraph in output-polynomial time is a long standing open question known as the transversal hypergraph generation. One of the first attempts on this problem—the sequential method of Berge [Ber89]—is not output-polynomial as shown by Takata [Tak02]. In recent years, three new algorithms designed to improve the sequential method were published and experimentally shown to perform well on practically relevant cases [BMR03, DL05, KS05]. Nevertheless, a theoretical analysis was still pending. We close this gap by proving lower bounds for all three algorithms. Our lower bounds show that none of the algorithms is outputpolynomial.