Algebraic and Geometric Models for Space Networking
- URL: http://arxiv.org/abs/2304.01150v2
- Date: Thu, 5 Oct 2023 15:09:05 GMT
- Title: Algebraic and Geometric Models for Space Networking
- Authors: William Bernardoni, Robert Cardona, Jacob Cleveland, Justin Curry,
Robert Green, Brian Heller, Alan Hylton, Tung Lam, Robert Kassouf-Short
- Abstract summary: We present a novel definition of a time-varying graph (TVG), defined in terms of a matrix with values in subsets of the real line P(R)
We leverage semi-ring properties of P(R) to model multi-hop communication in a TVG using matrix multiplication and a truncated Kleene star.
To better model networking scenarios between the Earth and Mars, we introduce various semi-rings capable of modeling propagation delay.
- Score: 1.1608974088441382
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: In this paper we introduce some new algebraic and geometric perspectives on
networked space communications. Our main contribution is a novel definition of
a time-varying graph (TVG), defined in terms of a matrix with values in subsets
of the real line P(R). We leverage semi-ring properties of P(R) to model
multi-hop communication in a TVG using matrix multiplication and a truncated
Kleene star. This leads to novel statistics on the communication capacity of
TVGs called lifetime curves, which we generate for large samples of randomly
chosen STARLINK satellites, whose connectivity is modeled over day-long
simulations. Determining when a large subsample of STARLINK is temporally
strongly connected is further analyzed using novel metrics introduced here that
are inspired by topological data analysis (TDA). To better model networking
scenarios between the Earth and Mars, we introduce various semi-rings capable
of modeling propagation delay as well as protocols common to Delay Tolerant
Networking (DTN), such as store-and-forward. Finally, we illustrate the
applicability of zigzag persistence for featurizing different space networks
and demonstrate the efficacy of K-Nearest Neighbors (KNN) classification for
distinguishing Earth-Mars and Earth-Moon satellite systems using time-varying
topology alone.
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