Covering metric spaces by few trees

Yair Bartal, Ora Nova Fandina, Ofer Neiman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

A tree cover of a metric space (X,d) is a collection of trees, so that every pair x,y∈X has a low distortion path in one of the trees. If it has the stronger property that every point x∈X has a single tree with low distortion paths to all other points, we call this a Ramsey tree cover. In this paper we devise efficient algorithms to construct tree covers and Ramsey tree covers for general, planar and doubling metrics. We pay particular attention to the desirable case of distortion close to 1, and study what can be achieved when the number of trees is small. In particular, our work shows a large separation between what can be achieved by tree covers vs. Ramsey tree covers.

Original languageAmerican English
Pages (from-to)26-42
Number of pages17
JournalJournal of Computer and System Sciences
Volume130
DOIs
StatePublished - Dec 2022

Bibliographical note

Publisher Copyright:
© 2022 Elsevier Inc.

Keywords

  • Metric embedding
  • Spanners
  • Tree covers

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