Before revision:  The blown-up hypergraph further has many forbidden structures, including a ``tent'' structure for the case t=3. Whether a generalization of Tuza's conjecture could also hold for tent-free 3-uniform hypergraphswas posed in a recent work. We answer this question in the negative by giving a construction based on combinatorial lines that is tent-free, and yet needs to include most of the vertices in a vertex cover .
After revision:  However, for set cover on simple n-vertex hypergraphs, the greedy algorithm achieves a factor (\ln n)/2, better than the optimal \ln n factor for general hypergraphs .