NeTS: Small: Large Scale Sensor Network Routing Using Conformal Geometry

This project develops efficient routing schemes for large scale multi-hop wireless sensor networks with a complex shape. As sensor networks grow large in size, terrain features or non-uniform energy usage may leave the network with holes. Efficient routing becomes difficult as some knowledge of how to "get around" the holes is needed. The novelty of this project is to use conformal geometry to compute a proper embedding of the network such that simple, distributed greedy routing schemes achieve desirable properties. Conformal geometry shows that any surface can be deformed to three canonical shapes: the sphere, the plane and the disk. Thus, one can "regulate" any sensor field shape to be of a canonical, simple form. The complexity of the routing problem and the domain specifics are encapsulated in the embedding such that routing decision becomes trivial. The conformal mapping of a sensor network is computed using Ricci curvature flow, an intrinsically distributed computation routine that can easily incorporate the dynamic changes of wireless links. This project focuses on conformal mapping and the companion greedy routing solutions that guarantee delivery, achieve good load balancing, facilitate in-network storage and data-centric routing, are resilient to network failures, and generalize to both 2D and 3D networks. This project explores the unique cross-disciplinary area of wireless networking and differential geometry. Although the main thrust of this proposal is theoretical, it is expected that the project can also provide practical routing solutions for large scale sensor networks.