If we pick n random points uniformly in [0, 1]d and connect each point to its k−nearest neighbors, then it is well known that there exists a giant connected component with high probability. We prove that in [0, 1]d it suffices to connect every point to cd,1 log logn points chosen randomly among its cd,2 logn−nearest neighbors to ensure a giant component of size n− o(n) with high probability. Th...