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Next Generation Network Science

Office of Naval Research: Multi-University Research Initiative

Many current military as well as civilian technical visions convincingly suggest that net-centric technology can provide unprecedented levels of performance, robustness, and efficiency. Unfortunately, there is substantial confusion regarding the obstacles to achieving this vision, and our proposed program will clarify and address the central research challenges. Essentially what is needed is a deeper understanding of network structure and function, beyond naive graph-theoretic measures of large-scale connectivity, that incorporates the domain-specific drivers and constraints on system organization and dynamics. A crucial issue is architecture, by which we mean the most universal, high-level, persistent elements of this network organization, ideally consisting of well-defined protocols with principled, rigorous, theory-based design.

The most widely understood aspect of net-centric architecture is the need for layered, networked communication and control and a diversity of manned and unmanned platforms and sensors in addition to traditional assets of ships/planes/soldiers. However, the shift from networks that perform primarily sensing and communication to those that perform real-time, dynamic decision and control presents new challenges that are less well-understood. For example, the size and scope of modern networks means that there is rarely a single vantage point from which one can obtain a complete and accurate picture of network operations, much less compute and disseminate instructions for optimal behavior in a timely manner. Thus, there is a need to infer global network properties based on local or incomplete information. Moreover, one needs algorithms for real-time and dynamic sensing, decision, and control that are primarily local yet achieve provably global results, and our team has already created a broad foundation for this. Furthermore, we and our colleagues have developed a rigorous and practical theory for layered communication architectures based on optimization, duality, and games which has great potential for addressing these challenges.

Our team members have been pioneers in developing a mathematical and behavioral theory of networks, ranging from spectral graph theory to networked dynamical systems, and from information theory to interplay of communications theory, game theory, operations research and social sciences and economics, and statistical physics. These include development of a theory of network architecture that will provide new insights in the following topics:

  1. Tools for understanding the robustness and evolvability as well as fragilities of complex networks,
  2. New behavioral and mathematical models and methods for collective problem-solving over networks,
  3. Innovative paradigms and models for evolution of networks of dynamical systems,
  4. Real-time methods for exploiting network-based data and effective identity matching,
  5. New modelling paradigms for networks beyond graphs, and
  6. Novel approaches to an information theory of networks.