Lower Bounds for Three Algorithms for the Transversal Hypergraph Generation

Abstract. 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 [Ber89]—is not outputpolynomial as was shown by Takata [Tak02]. Recently, three new algorithms improving the sequential method were published and experimentally shown to perform very well in practice [BMR03, DL05, KS05]. Nevertheless, a theoretical worst-case analysis has been pending. We close this gap by proving lower bounds for all three algorithms. Thereby, we show that none of them is output-polynomial.

• Type: Conference
• Year: 2007
• Where: WG
• Authors: Matthias Hagen
• Keywords: Computer Science, Problem—the Sequential Method, Sequential Method, Transversal Hypergraph Generation, WG 2007