English

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 GG and a subset TT of its vertices called terminals, and the goal is to compute a (weighted) graph HH on TT that is a minor of GG, such that the distance between every pair of terminals is preserved to within some small multiplicative factor, that is called the stretch of HH. It has been shown that on general graphs we can achieve stretch O(logT)O(\log |T|) [Filtser, 2018]. On the other hand, the best-known stretch lower bound is 88 [Chan-Xia-Konjevod-Richa, 2006], which holds even for trees. In this work, we show an improved lower bound of Ω~(logT)\tilde\Omega\big(\sqrt{\log |T|}\big).

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}
}