Affiliations: Masdar Institute of Science and Technology, Abu Dhabi, UAE. [email protected] | Bauhaus-Universität Weimar, D–99423 Weimar, Germany. [email protected] | National University of Computer and Emerging Sciences, Karachi, Pakistan. [email protected]
Note: [] Address for correspondence: Bauhaus-Universität Weimar, D–99423 Weimar, Germany.
Abstract: The computation of transversal hypergraphs in output-polynomial time is a long standing open question. An Apriori-like level-wise approach (referred to as the HBC-algorithm or MTminer) was published in 2007 by Hébert, Bretto, and Crémilleux [A Data Mining Formalization to Improve Hypergraph Minimal Transversal Computation, Fundamenta Informaticae, 80(4), 2007, 415–433] and was experimentally demonstrated to have very good performance on hypergraphs with small transversals. In this short note extending the paper by Hagen [Lower bounds for three algorithms for transversal hypergraph generation, Discrete Applied Mathematics, 157(7), 2009, 1460–1469], we prove a superpolynomial lower bound for the HBC-algorithm. This lower bound also shows that the originally claimed upper bound on the HBC-algorithm's running time is wrong.
