A doubling dimension threshold ⊖ (log log n) for augmented graph navigability

Pierre Fraigniaud, Emmanuelle Lebhar, Zvi Lotker

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

23 Scopus citations

Abstract

In his seminal work, Kleinberg showed how to augment meshes using random edges, so that they become navigable; that is, greedy routing computes paths of polylogarithmic expected length between any pairs of nodes. This yields the crucial question of determining wether such an augmentation is possible for all graphs. In this paper, we answer negatively to this question by exhibiting a threshold on the doubling dimension, above which an infinite family of graphs cannot be augmented to become navigable whatever the distribution of random edges is. Precisely, it was known that graphs of doubling dimension at most O(log log n) are navigable. We show that for doubling dimension ≫ log log n, an infinite family of graphs cannot be augmented to become navigable. Finally, we complete our result by studying the special case of square meshes, that we prove to always be augmentable to become navigable.

Original languageEnglish
Title of host publicationAlgorithms, ESA 2006 - 14th Annual European Symposium, Proceedings
PublisherSpringer Verlag
Pages376-386
Number of pages11
ISBN (Print)3540388753, 9783540388753
DOIs
StatePublished - 1 Jan 2006
Externally publishedYes
Event14th Annual European Symposium on Algorithms, ESA 2006 - Zurich, Switzerland
Duration: 11 Sep 200613 Sep 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4168 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference14th Annual European Symposium on Algorithms, ESA 2006
Country/TerritorySwitzerland
CityZurich
Period11/09/0613/09/06

Keywords

  • Doubling dimension
  • Greedy routing
  • Small world

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