Before revision:  In addition to its inherent combinatorial interest---for instance, the t=3 case is connected to Tuza's famous conjecture on covering triangles of a graph with edges---variants of AHTP arise in recently proposed reductions to fundamental Euclidean clustering problems. AHTP admits a trivial factor t approximation algorithm as it can be cast as an instance of vertex cover on a structured t-uniform hypergraph that is a ``blown-up'' version of H. Our main result is an approximation algorithm with ratio \frac{t simple %DIFAUXCMD hypergraph with hyperedges intersecting in at most one element .
After revision:  In addition to its inherent combinatorial interest---for instance, the t=3 case is connected to Tuza's simple %DIFAUXCMD hypergraph with hyperedges intersecting in at most one element .