# A light metric spanner

arXiv: https://arxiv.org/abs/1505.03681 · HTML: https://mlsanity.com/paper/1505.03681/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 May 2015.

## Built on by (most cited first, 1 of 1)

- [Randomized Dimensionality Reduction for Facility Location and Single-Linkage Clustering](https://mlsanity.com/paper/2107.01804/) (2021)

## Abstract (arXiv)

It has long been known that d-dimensional Euclidean point sets admit (1+ε)-stretch spanners with lightness WE = ε-O(d), that is total edge weight at most WE times the weight of the minimum spaning tree of the set [DHN93]. Whether or not a similar result holds for metric spaces with low doubling dimension has remained an important open problem, and has resisted numerous attempts at resolution. In this paper, we resolve the question in the affirmative, and show that doubling spaces admit (1+ε)-stretch spanners with lightness WD = (ddim/ε)O(ddim). Important in its own right, our result also implies a much faster polynomial-time approximation scheme for the traveling salesman problemin doubling metric spaces, improving upon the bound presented in [BGK-12].