Abstract
It is known that graphs of doubling dimension O(loglogn) can be augmented to become navigable. We show that for doubling dimension ≫loglogn, an infinite family of graphs cannot be augmented to become navigable. Our proof uses a counting argument which enable us to consider any kind of augmentations. In particular we do not restrict our analysis to the case of symmetric distributions, nor to distributions for which the choice of the long range link at a node must be independent from the choices of long range links at other nodes.
The complete version of this paper is available as: P. Fraigniaud, E. Lebhar, and Z. Lotker. A Doubling Dimension Threshold Θ(loglogn) for Augmented Graph Navigability. In 14th European Symp. on Algorithms (ESA), ETH Zürich, Switzerland, September 11-15, 2006.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fraigniaud, P., Lebhar, E., Lotker, Z. (2006). Brief Announcement: On Augmented Graph Navigability. In: Dolev, S. (eds) Distributed Computing. DISC 2006. Lecture Notes in Computer Science, vol 4167. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11864219_42
Download citation
DOI: https://doi.org/10.1007/11864219_42
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44624-8
Online ISBN: 978-3-540-44627-9
eBook Packages: Computer ScienceComputer Science (R0)