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Sheaf Theoretic Models for Routing in Delay Tolerant NetworksOne key to communications scalability is routing; as such the goal of this paper is to build upon successful efforts towards general routing for space-based networks. With the ever-increasing accessibility of space, the number of assets is increasing, which becomes a critical communications burden in terms of scheduling, spectrum allocation, and resource allocation. In order to mitigate these concerns, a true networking approach is necessary; a standard approach for space systems is Delay Tolerant Networking (DTN). For DTN to be a meaningful answer to the Solar System Internet (SSI) question, DTN must offer meaningful routing solutions that span the heterogeneous collection of links and nodes. This, in turn, depends on the general structure of these disconnected networks -- a structure that remains largely unknown.

In ground communications networks, routing decisions are made based on several pathfinding algorithms working in tandem. In previous work, we modeled Dijkstra's pathfinding algorithm using sheaves and provided a more general framework for determining paths using sheaves over graphs. Continuing our sheaf-theoretic approach, we introduce here an expansion of our pathfinding sheaf to handle more general information, and we expand on additional pathfinding algorithms that can be represented using sheaves. Moreover, we demonstrate means of combining multiple algorithms into a single sheaf structure so that changes of scale can be presented in the language of sheaves.

In addition, space communications networks rely upon radio transmitter antennas which can establish broadcast and multicast communications options, rather than the primarily unicast options available to wired networks. Last year, we also introduced a multicast routing sheaf for presenting broadcast, unicast, and multicast communications over a graph. Extending that work, we also introduce queuing sheaves so that we can blend these communications options together to simulate a variety of routing options across space networks. In addition, we include examples to illustrate the applicability of this abstract theory to routing in disconnected networks.
Document ID
Document Type
Conference Paper
Robert Short (Glenn Research Center Cleveland, Ohio, United States)
Alan Hylton (Glenn Research Center Cleveland, Ohio, United States)
Jacob Cleveland (Glenn Research Center Cleveland, Ohio, United States)
Michael Moy (Colorado State University Fort Collins, Colorado, 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 (University at Albany, State University of New York Albany, New York, United States)
Brendan Mallery (Tufts University Medford, Massachusetts, United States)
Gabriel Bainbridge (The Ohio State University Columbus, Ohio, United States)
Zander Memon (American University)
Date Acquired
February 10, 2022
Subject Category
Communications and Radar
Theoretical Mathematics
Meeting Information
IEEE Aerospace Conference 2022(Big Sky, MT)
Funding Number(s)
WBS: 278371.01.06
Distribution Limits
Use by or on behalf of the US Gov. Permitted.
Technical Review
Single Expert

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NameType AeroConf_2022___Sheaves_for_Routing_in_DTN -- 2022-02-25.pdf STI