In the Steiner point removal (SPR) problem, we are given a weighted graph
G=(V,E) and a set of terminals KβV of size k. The objective is to
find a minor M of G with only the terminals as its vertex set, such that
the distance between the terminals will be preserved up to a small
multiplicative distortion. Kamma, Krauthgamer and Nguyen [KKN15] used a
ball-growing algorithm with exponential distributions to show that the
distortion is at most O(log5k). Cheung [Che17] improved the analysis of
the same algorithm, bounding the distortion by O(log2k). We improve the
analysis of this ball-growing algorithm even further, bounding the distortion
by O(logk)