Geometry helps in routing scalability

TL;DR

This paper introduces a geometric approach to routing in Delay Tolerant Networks, demonstrating polynomial bounds and improved recomputation efficiency over traditional graph-based methods, with real-world satellite data applications.

Contribution

It establishes a polynomial upper bound on critical events in satellite networks and shows geometric routing reduces recomputation compared to classical algorithms.

Findings

Polynomial bound on topological critical events in satellite networks.

Geometric routing requires fewer recomputations than graph-based methods.

Existence of metric spanner properties in real-world satellite-derived graphs.

Abstract

Delay Tolerant Networking (DTN) aims to address a myriad of significant networking challenges that appear in time-varying settings, such as mobile and satellite networks, wherein changes in network topology are frequent and often subject to environmental constraints. Within this paradigm, routing problems are often solved by extending classical graph-theoretic path finding algorithms, such as the Bellman-Ford or Floyd-Warshall algorithms, to the time-varying setting; such extensions are simple to understand, but they have strict optimality criteria and can exhibit non-polynomial scaling. Acknowledging this, we study time-varying shortest path problems on metric graphs whose vertices are traced by semi-algebraic curves. As an exemplary application, we establish a polynomial upper bound on the number of topological critical events encountered by a set of $n$ satellites moving along elliptic curves in low Earth orbit (per orbital period). Experimental evaluations on networks derived from STARLINK satellite TLE's demonstrate that not only does this geometric framework allow for routing schemes between satellites requiring recomputation an order of magnitude less than graph-based methods, but it also demonstrates metric spanner properties exist in metric graphs derived from real-world data, opening the door for broader applications of geometric DTN routing.