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 Hebert,...
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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 Hebert, Bretto, and Cremilleux [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.
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