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

本计画针对大规模多跳无线感测器网路的复杂形状，发展有效的路由机制。随着传感器网络规模的扩大，地形特征或不均匀的能量使用可能会使网络出现漏洞。有效的路由变得困难，因为一些知识，如何“绕过”的洞是needed.The新颖性，这个项目是使用保形几何计算一个适当的嵌入网络，使简单的，分布式贪婪路由方案实现理想的性能。保角几何表明，任何曲面都可以变形为三种标准形状：球面、平面和圆盘。因此，可以将任何传感器场形状“调节”为规范的简单形式。路由问题的复杂性和域的细节被封装在嵌入，使路由决策变得微不足道。传感器网络的共形映射计算使用Ricci曲率流，本质上是分布式的计算例程，可以很容易地将无线链路的动态变化。该项目的重点是保角映射和同伴贪婪路由解决方案，保证交付，实现良好的负载平衡，促进网络存储和以数据为中心的路由，对网络故障具有弹性，并推广到2D和3D网络。该项目探索了无线网络和微分几何的独特跨学科领域。虽然这个建议的主要推力是理论上的，预计该项目也可以提供实际的路由解决方案，为大规模的传感器网络。

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.