Greedy Forwarding in Dynamic Scale-Free Networks Embedded in Hyperbolic Metric Spaces

TL;DR

This paper demonstrates that hyperbolic geometry naturally leads to efficient, topology-oblivious greedy forwarding in dynamic scale-free networks, achieving near-optimal routing without complex protocols.

Contribution

It reveals how hyperbolic metric spaces enable highly efficient greedy forwarding in dynamic scale-free networks, with potential applications in Internet routing and overlay networks.

Findings

Greedy forwarding achieves 100% delivery probability

Routing paths are nearly optimal in length

Efficiency persists in highly dynamic network conditions

Abstract

We show that complex (scale-free) network topologies naturally emerge from hyperbolic metric spaces. Hyperbolic geometry facilitates maximally efficient greedy forwarding in these networks. Greedy forwarding is topology-oblivious. Nevertheless, greedy packets find their destinations with 100% probability following almost optimal shortest paths. This remarkable efficiency sustains even in highly dynamic networks. Our findings suggest that forwarding information through complex networks, such as the Internet, is possible without the overhead of existing routing protocols, and may also find practical applications in overlay networks for tasks such as application-level routing, information sharing, and data distribution.