A group testing problem for hypergraphs of bounded rank

Suppose that a hypergraph H = (V, E) of rank r is given as well as a probability distribution p(e) (e ϵ E) on the edges. We show that in the usual group testing model the unknown edge can be found by less than — log p(e) + r tests. For the case of the uniform distribution, the result proves a conjecture of Du and Hwang.