Covering metric spaces by few trees

Yair Bartal, Nova Fandina, Ofer Neiman

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

11 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. Tree covers and Ramsey tree covers have been studied by [15, 31, 19, 30, 38], and have found several important algorithmic applications, e.g. routing and distance oracles. The union of trees in a tree cover also serves as a special type of spanner, that can be decomposed into a few trees with low distortion paths contained in a single tree; Such spanners for Euclidean pointsets were presented by [8]. 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 languageEnglish
Title of host publication46th International Colloquium on Automata, Languages, and Programming, ICALP 2019
EditorsChristel Baier, Ioannis Chatzigiannakis, Paola Flocchini, Stefano Leonardi
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771092
DOIs
StatePublished - 1 Jul 2019
Event46th International Colloquium on Automata, Languages, and Programming, ICALP 2019 - Patras, Greece
Duration: 9 Jul 201912 Jul 2019

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume132
ISSN (Print)1868-8969

Conference

Conference46th International Colloquium on Automata, Languages, and Programming, ICALP 2019
Country/TerritoryGreece
CityPatras
Period9/07/1912/07/19

Keywords

  • Probabilistic hierarchical family
  • Ramsey tree cover
  • Tree cover

ASJC Scopus subject areas

  • Software

Cite this