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A Survey of Mathematical Structures for Lunar NetworksTo sustain the current and increasing accessibility of space, a scalable communications infrastructure (i.e. the Solar System Internet, SSI) is necessary. The goal of this paper is to begin the discovery of the fundamental underlying mathematical structure of space networks to help the research community harness these structures for algorithm development and optimization. To ensure the applicability of the research, the approaches are considered through the lens of simulated scenarios inspired by the Artemis Back-to-the-Moon mission set for 2024.

We note that any approach to an SSI must fit under the umbrella of Delay Tolerant Networking (DTN), due to celestial mobility, high link latencies, high variance in link latencies, disconnections, lack of end-to-end paths, and so on. These difficulties are exacerbated by the fact that the underlying structure of a space network is a time-evolving network and may experience multiple discontinuities in its topology.

In this paper we propose several novel approaches to a mathematical foundation for Delay Tolerant Networking Theory that fall outside the traditional scope of temporal network theory. These techniques include methods from Topological Data Analysis, Dynamic Graph Analysis, Applied Algebraic Geometry, Probability Theory, and Game Theory. Some of these methods include tools adapted to the study of dynamic metric spaces, such as zigzag persistent homology and their higher parameter analogs. We find that several of these methods target desired engineering outcomes such as discovery and automatic sub-netting. While each approach is theoretical, they are also algorithmic in nature and offer immediate practical applications. The paper concludes with comparisons of the various methods along with suggestions for future work.
Document ID
20220003566
Document Type
Conference Paper
Authors
Alan Hylton
(Glenn Research Center Cleveland, Ohio, United States)
Robert Short ORCID
(Glenn Research Center Cleveland, Ohio, United States)
Jacob Cleveland ORCID
(Glenn Research Center Cleveland, Ohio, United States)
Olivia Freides
(American University Washington D.C., District of Columbia, United States)
Zander Memon
(American University Washington D.C., District of Columbia, United States)
Robert Cardona
(University at Albany, State University of New York Albany, New York, United States)
Robert Green
(University at Albany, State University of New York Albany, New York, United States)
Justin Curry ORCID
(University at Albany, State University of New York Albany, New York, United States)
Sriram Gopalakrishnan
(University of Bordeaux Bordeaux, France)
Devavrat Vivek Dabke
(Princeton University Princeton, New Jersey, United States)
Brittany Story ORCID
(Colorado State University Fort Collins, Colorado, United States)
Michael Moy
(Colorado State University Fort Collins, Colorado, United States)
Brendan Mallery
(Tufts University Medford, Massachusetts, United States)
Date Acquired
February 28, 2022
Publication Date
March 9, 2022
Subject Category
Computer Systems
Theoretical Mathematics
Meeting Information
IEEE Aerospace Conference(Big Sky, MT)
Funding Number(s)
WBS: 278371.01.06
Distribution Limits
Public
Copyright
Use by or on behalf of the US Gov. Permitted.
Technical Review
Single Expert
Keywords
Delay tolerant networking
DTN
Topological data analysis
Persistent homology
Temporal graph theory
Algebraic geometry
Game theory
Simulation
Lunar

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