An Ω (√log|T|) Lower Bound for Steiner Point Removal

In the Steiner point removal (SPR) problem, we are given a (weighted) graph G and a subset T of its vertices called terminals, and the goal is to compute a (weighted) graph H on T that is a minor of G, such that the distance between every pair of terminals is preserved to within some small multiplicative factor, that is called the stretch of H.