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Robert Short

Publications and source records attributed to Robert Short.

On the Current State of Sheaf Theoretic Networking

Advancing the Delay Tolerant Networking (DTN) effort has proven to be a unique and difficult challenge. In the journey to implementing space networking, NASA has considered several strategies. From direct translations of Internet Protocol (IP) to satellite networks to pre-planned routing structures in Contact Graph Routing (CGR), each potential solution for DTN has come with its fair share of setbacks and challenges. Frequently, these challenges can be traced back to specific assumptions made in the development of each protocol that do not carry over from ground networks to space networks. To address these fundamental assumptions, a more general and foundational networking theory is required. In this paper, we survey a novel mathematical foundation for networking using the theory of cellular sheaves. Sheaves form a mathematical tool for modeling local phenomenon that leads to global effects. Sheaves have been introduced a number of times, and our goal here is to summarize the applications and point towards important future work that must be done to build a stronger, cohesive theory for networking.

Sheaves↗

Towards the Development of a Multi-Agent Cognitive Networking System for the Lunar Environment

This paper details the development of a multi-agent cognitive system intended to optimize networking performance in the lunar environment. One concept of the future of lunar communication, LunaNet, outlines a complex network of networks. Challenges such as scalability, interoperability, and reliability must first be addressed to successfully fulfill this vision. Machine intelligence can greatly reduce the reliance on human operators and enable efficient operations for tasks such as scheduling and network management. Machine learning, artificial intelligence, and other automated decision-making techniques can be used to allow network nodes to intelligently sense and adapt to changes in the environment such as link disruptions, new nodes joining the network, and support for a diverse range of protocols. Cognitive networking seeks to evolve these technologies into an autonomous system with improved science data return, reliability, and scalability. In this paper, we study four main areas as a means to further develop cognitive networking capabilities: networking protocol development, analysis of wireless data for modeling and simulation, development of algorithms for a multi-agent system, and spectrum sensing technology.

cognitive networking↗

A Survey of Mathematical Structures for Lunar Networks

To 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.

Delay tolerant networking↗

Planting a Flag in the Tropics: The Essential Tropical Geometric Background for Networking Applications

This Technical Memorandum serves to guide future NASA researchers and the public at large in terms of how Tropical Geometry can be applied to optimization problems, namely in networking. We give a basic overview of Tropical Geometry through a collection of resources we have summarized. Lastly, we include a discussion of power diagrams viewed as stratified spaces which may be a useful tool to study tropical varieties.

Tropical Geometry↗

Applying the Cognitive Space Gateway to Swarm Topologies

NASA's future vision for interplanetary networking includes a lunar network, Cube Satellite (CubeSat) constellations, and deep space robotic missions, comprising what could be viewed as a network of networks. Delay-tolerant networking (DTN) architecture and protocols provide a standard network layer among these varying scenarios and mitigate many challenges of the space environment, such as long delays, unplanned service interruptions, and asymmetric links. The Cognitive Space Gateway (CSG) is a routing method in a DTN architecture that uses spiking neural networks as the learning element to optimize routing decisions in a complex environment. This work aims to further develop cognitive networking technologies in several critical areas, including DTN, the CSG algorithm, CubeSat swarm topologies, and cloud services. To test the algorithm in a realistic scenario, the emulated network topology is based on a CubeSat swarm. The swarm may function as a mesh of nodes or as a hub-and-spoke network. An emulation environment will be built upon a commercial cloud service, such as Amazon Web Services (AWS) Elastic Compute Cloud. The cloud environment may enable a flexible, lower maintenance approach versus a multi-hop network based in a physical laboratory. The cloud platform will provide a secure environment allowing for collaboration among government and academic entities.

Ricardo Lent↗

A Mathematical Analysis of an Example Delay Tolerant Network using the Theory of Sheaves

NASA’s High-Data Rate Architecture (HiDRA) project is working towards a general yet practical toolkit and knowledge base to help usher in the era of new technologies for space systems communications, such as optical links. The High-Rate Delay Tolerant Networking (HDTN) implementation falls under the umbrellas of both the toolkit and the knowledge base, as its advancements illuminate more general areas of Delay Tolerant Networking (DTN) that need growth. The goal of this paper is to explore the usage of particular mathematical machineries, namely temporal flow networks and sheaves, to identify fundamental, underlying structures in DTN for space systems. Satellites, space assets, ground stations, etc. give rise to a disconnected network, and it is the goal of DTN to glue disparate links together into a cohesive system, that is, a network. Depending on a given link, the latencies might be beyond that which the Transmission Control Protocol (TCP) can handle, and contact times might have one-way light times in excess of minute (sometimes significantly longer). Some links might be periodic (say, due to orbital mechanics) or they might not be. This diversity has made it difficult to probe the underlying structure. An immediate consequence is that DTNs in practice today are controlled by globally distributed contact plans (schedules), which are the input to the contact graph routing (CGR) algorithm. While this is effective for smaller networks, it will be very difficult to scale for future networks. Deeper and more rigorous theory is needed to bring DTN to the next evolutionary step. To this end, this paper introduces and suggests a mathematical framework for DTN, and applies it to a space network that is simulated using an orbital analysis toolkit. The tag-line for the structure known as sheaves is that they are the mathematically precise way of gluing local data together into unique, global data. If we consider routing, we see that networking is a “sheafy” science. We then discuss a simplified sheaf model, known as the cellular sheaf. The sheaf-theoretic analysis is presented and discussed, as it is hoped that this and related papers will help form the primordial ooze of DTN theory. Finally there is a section of future work suggesting follow-on research.

Delay Tolerant Networking↗

Tuning the Performance of a Computational Persistent Homology Package

In recent years, persistent homology has become an attractive method for data analysis. It captures topological features, such as connected components, holes, and voids from point cloud data and summarizes the way in which these features appear and disappear in a filtration sequence. In this project, we focus on improving the performanceof Eirene, a computational package for persistent homology. Eirene is a 5000-line open-source software library implemented in the dynamic programming language Julia. We use the Julia profiling tools to identify performance bottlenecks and develop novel methods to manage them, including the parallelization of some time-consuming functions on multicore/manycore hardware. Empirical results show that performance can be greatly improved.

Persistent Homology↗

Towards Sheaf Theoretic Analyses for Delay Tolerant Networking

The goal of Delay Tolerant Networking (DTN) is to take a collection of heterogeneous, disparate connections between satellites, space assets, ground stations, and ground infrastructure and bring it together into a cohesive, functioning overlay network. Depending on the systems being considered, one can find links with a one-way light time exceeding minutes (and hours),periodic links which can sometimes be predicted by orbital mechanics, and restrictions based on the variety of capabilities built into these systems. These characteristics preclude traditional network models and routing techniques and have classically led to either rigid routing tables or purely probabilistic models. As the deeper underlying structures remain unknown, development of more DTN-optimized algorithms has lacked the necessary foundation. In a continuation of previous work, the goal of this paper is to identify and study these fundamental structures that exist in delay tolerant networks (DTN), with a focus on space networks. The current routing methodology has been to use contact graph routing (CGR) algorithms. CGR models a series of known contacts as a static graph. For CGR to work, this graph must be globally consistent and must have an accurate picture of the network. Because this is a globally controlled structure, there is little room for flexibility in the event of changes to the network which would naturally occur as the network grows. As a response to the desire for flexibility as the network changes, we introduced the mathematical structure known as sheaves to DTNs last year. The tag-line for sheaves is that they are a mathematically precise way of gluing local data together into unique global data. Thus, sheaves lend extra power to traditional models(and routing algorithms) by taking additional information and merging it, in as consistent a manner as possible, with the representation itself. The clearest example of how Earth-bound networks exhibit behavior that is “sheafy” is link state routers, which build a local-to-global picture of their network by gluing local information together into a global network, exactly as a sheaf would do. For routing within delay tolerant networks to truly exploit this structure, a deeper structure than a graph is required. In this paper, we develop sheaves that can work over directed graphs such as temporal flow networks, we construct a sheaf representation for Dijkstra’s algorithm, and we outline a construction for routing sheaves capable of modeling multicast scenarios. Finally, there is a section of future work suggesting follow-on research.

Robert Short↗

Dude Where's My Stars: A Novel Topologically Justified Approach to Star Tracking

In this paper, we consider two novel approaches to celestial navigation for spacecraft. Determining attitude without any prior knowledge using star tracking is known to be a difficult task, particularly given the computational complexity and the many potential sources of misinformation. We consider localization by optimizing matching parameters without explicit star identification in a computationally tractable manner. This is achieved using the mathematical tools of topological data analysis (TDA) and cellular sheaves to study the geometry and distribution of cataloged stars. A framework is gained that enhances the statistical approach to noise handling and false star detection, and heterogeneous sensor fusion. Finally, we discuss confidence bounds and minimum information requirements for successful operation.

Sheaf theory↗

Sheaf Theoretic Models for Routing in Delay Tolerant Networks

One 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.

Robert Short↗

New Horizons for a Practical and Performance-Optimized Solar System Internet

The High-rate Delay Tolerant Networking (HDTN) project at the NASA Glenn Research Center (GRC) is developing a performance-optimized Delay Tolerant Networking (DTN) implementation using the Bundle Protocol (BP) both for infusion in modern, distributed spacecraft systems and for foundational network research purposes. While one purpose of networking is to enable a returns-to-scale with communicating assets, it is recognized that neither the protocol nor its implementations may impose a bottleneck on data delivery if expected to be implemented. With this in mind, this paper explores the current status of the HDTN software, including its capabilities and also various performance metrics at the bundle layer, the convergence layers (e.g. performance-optimized Licklider Transmission Protocol, or LTP), and bundle storage and retrieval. This includes goals of software implementations that support multi-gigabit per second communications regardless of payload size. A discussion on the current software architecture and internal scheduling and routing is included. Interoperability with such extant DTN implementations as Interplanetary Overlay Network (ION) and DTN Marshall Enterprise Implementation (DTNME) are included. The research goals of the project are also listed, including Software-Defined Networking (SDN) and the theory of DTNs. A table-based filtration system for the Bundle Protocol (BP), called BP Filter, is also explored: this addition enables table-based policies within the context of a DTN for management purposes. Infusion begins with systems testing in the Johnson Space Center (JSC) Software Development and Integration Laboratory (SDIL), which supports International Space Station (ISS) Flight Software development, integration, and verification. Observations made from the results of testing in the SDIL and in flight testing are also discussed, pointing to a path for infusion into high data return low-earth orbit (LEO) missions. The paper concludes with areas for future work.

Delay Tolerant Networking↗

Introducing Tropical Geometric Approaches to Delay Tolerant Networking Optimization

Delay Tolerant Networking (DTN) is the standard approach to the networking of space systems with the goal of supporting the Solar System Internet (SSI). Current space networks have a small scale and often depend on rigorously scheduled (pre-determined) contact opportunities; this manual approach inhibits scalability. The goal of this paper is to recast these scheduling problems in order to apply the optimization machinery of tropical geometry. Contact opportunities in space are dependent on such factors as orbital mechanics and asset availability, which induce time-varying connectivity; indeed, end-to-end connectivity might never occur. Routing optimization within this structure is classically difficult and typically utilizes Dijkstra's algorithm as applied to contact graphs. Alternatively, we follow the successes of tropical geometry in train schedule optimization, job assignments, and even traditional networking, by extending this approach to this more general (i.e. disconnected) problem space. These successes imply tropical geometry provides a useful framework in the context of DTNs, starting with applications to queuing theory and long-haul links. Recently, tropical geometry has been applied to parametric path optimization on graphs with variable edge weights. In this work, we extend these advances to account for the problem of routing in a space network, and find that tropical geometry is well-suited to the challenges offered by this new setting, including contact schedules featuring probabilities. Our approach leverages the combinatorial nature of the problem to give feasible shortest path trees in the presence of variable channel conditions and latency, evolving topologies, and uncertainty inherent in space routing. We discuss our tropical approach to DTN for two Python implementations, a Verilog Tropical ALU implementation, tropical frameworks for other parametric graph problems, and solution stability. Lastly, a program for future work is included to illuminate the path ahead.

Delay Tolerant Networking↗