Embeddings to Rectilinear Space and Gromov-Hausdorff Distances

TL;DR

This paper explores the relationship between embedding finite metric spaces into rectilinear space and Gromov-Hausdorff distances, providing a new perspective on the problem.

Contribution

It reformulates the embedding problem into rectilinear space using Gromov-Hausdorff distances, offering a novel approach to understanding metric space embeddings.

Findings

Reformulation of embedding problem via Gromov-Hausdorff distance

New theoretical connection between metric embeddings and Gromov-Hausdorff metric

Potential implications for metric space analysis and embedding algorithms

Abstract

We show that the problem whether a given finite metric space can be embedded into $m$-dimensional rectilinear space can be reformulated in terms of the Gromov--Hausdorff distance between some special finite metric spaces.