Before revision: We propose an algorithmic version of the hypergraph Tur\'{a}n problem (AHTP) : given a t-uniform hypergraph H=(V,E), the goal is to find the smallest collection of (t-1) -element subsets of V such that every hyperedge e \in E contains one of these subsets.
After revision: A famous conjecture of Tuza states that the minimum number of edges needed to cover all the triangles in a graph is at most twice the maximum number of edge-disjoint triangles. This conjecture was couched in a broader setting by Aharoni and Zerbib who proposed a hypergraph version of this conjecture, and also studied its implied fractional versions. We establish the fractional version of the Aharoni-Zerbib conjecture up to lower order terms. Specifically, we give a factor t/2+ O(\sqrt{t \log t an algorithmic version of the hypergraph Tur\'{a}n problem (AHTP) : given a t-uniform hypergraph H=(V,E), the goal is to find the smallest collection of (t-1) -element subsets of V such that every hyperedge e \in E contains one of these subsets.