Steiner Point Removal with Distortion $O(\log k)$

Abstract

In the Steiner point removal (SPR) problem, we are given a weighted graph $G=(V,E)$ and a set of terminals $K\subset V$ 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 $O({\log }^{5}k)$. Cheung [Che17] improved the analysis of the same algorithm, bounding the distortion by $O({\log }^{2}k)$. We improve the analysis of this ball-growing algorithm even further, bounding the distortion by $O(\log k)$.

References in corpus (1)

• Steiner Point Removal --- Distant Terminals Don't (Really) Bother