Navigability is a Robust Property
Social and Information Networks
2015-01-21 v1 Data Structures and Algorithms
Abstract
The Small World phenomenon has inspired researchers across a number of fields. A breakthrough in its understanding was made by Kleinberg who introduced Rank Based Augmentation (RBA): add to each vertex independently an arc to a random destination selected from a carefully crafted probability distribution. Kleinberg proved that RBA makes many networks navigable, i.e., it allows greedy routing to successfully deliver messages between any two vertices in a polylogarithmic number of steps. We prove that navigability is an inherent property of many random networks, arising without coordination, or even independence assumptions.
Cite
@article{arxiv.1501.04931,
title = {Navigability is a Robust Property},
author = {Dimitris Achlioptas and Paris Siminelakis},
journal= {arXiv preprint arXiv:1501.04931},
year = {2015}
}