“…Unfortunately, this Extension Dominating Set problem and many similar problems are NP-hard, see [6,12,14,15,37,38,45]. Even worse: when parameterized by the "pre-solution size," Extension Dominating Set is one of the few problems known to be complete for the parameterized complexity class W [3], as shown in [11]. This blocks any progress on the Hitting Set Transversal Problem by using extension test algorithms, which is the question whether all minimal hitting sets of a hypergraph can be enumerated with polynomial delay (or even output-polynomial) only.…”