An $\tilde\Omega\big(\sqrt{\log |T|}\big)$ Lower Bound for Steiner Point Removal
Data Structures and Algorithms
2023-10-13 v1
Abstract
In the Steiner point removal (SPR) problem, we are given a (weighted) graph and a subset of its vertices called terminals, and the goal is to compute a (weighted) graph on that is a minor of , such that the distance between every pair of terminals is preserved to within some small multiplicative factor, that is called the stretch of . It has been shown that on general graphs we can achieve stretch [Filtser, 2018]. On the other hand, the best-known stretch lower bound is [Chan-Xia-Konjevod-Richa, 2006], which holds even for trees. In this work, we show an improved lower bound of .
Keywords
Cite
@article{arxiv.2310.07862,
title = {An $\tilde\Omega\big(\sqrt{\log |T|}\big)$ Lower Bound for Steiner Point Removal},
author = {Yu Chen and Zihan Tan},
journal= {arXiv preprint arXiv:2310.07862},
year = {2023}
}