Before revision:  Our algorithm is faster than existing algorithms when the  connectivity \lambda is \Omega(n^{(r-2)/2 . At the heart of our algorithm is a structural result regarding min-cuts in simple hypergraphs.
After revision:  Our algorithm is faster than existing algorithms when the connectivity \lambda is \omega(1) . At the heart of our algorithm is a structural result regarding min-cuts in simple hypergraphs.