Local edge-connectivity augmentation in hypergraphs is NP-complete

We consider a local edge-connectivity hypergraph augmentation problem. Specifically, we are given a hypergraph G=(V,E)G=(V,E) and a subpartition of VV. We are asked to find the smallest possible integer γγ, for which there exists a set of size-two edges FF, with |F|=γ|F|=γ, such that in G′=(V,E∪F)G′=(V,E∪F), the local edge-connectivity between any pair of vertices lying in the same part of the subpartition is at least a given value kk. Using a transformation from the bin-packing problem, we show that the associated decision problem is NP-complete, even when k=2k=2.