“Who Are Your Friends?” — A Simple Mechanism that achieves perfect network formation

A fundamental challenge in peer-to-peer and online social networks is the design of a simple, distributed algorithm that allows users to discover, and connect to, peers who closely match their interests or preferences. In this paper, we consider an algorithm that is based on simple, local comparisons, and analyze it to provide insights into why similar peer discovery algorithms work well in practice. To do so, we use a mathematical framework to characterize the closeness of individual interests, and formally introduce the notion of a “perfect network formation” under the framework. Our analysis shows that the proposed algorithm indeeds achieves perfect network formation. Our analysis uses bounding techniques based on Chernoff bounds.