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

本课题针对形状复杂的大型多跳无线传感器网络，开发高效的路由方案。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给网络留下漏洞。有效的布线变得困难，因为需要一些如何“绕过”孔的知识。这个项目的新颖之处在于使用共形几何来计算网络的适当嵌入，从而使简单的分布式贪婪路由方案获得理想的属性。共形几何表明，任何表面都可以变形成三种典型形状：球面、平面和圆盘。因此，人们可以“调节”任何传感器场的形状，使其具有规范的、简单的形式。路由问题的复杂性和领域细节被封装在嵌入中，使得路由决策变得微不足道。利用Ricci曲率流计算传感器网络的保角映射，Ricci曲率流是一种本质上分布式的计算程序，可以很容易地包含无线链路的动态变化。该项目专注于保角映射和伴随的贪婪路由解决方案，这些解决方案保证了交付，实现了良好的负载平衡，促进了网络内存储和以数据为中心的路由，对网络故障具有弹性，并且可以推广到2D和3D网络。该项目探索无线网络和微分几何的独特跨学科领域。虽然该提案的主要推力是理论上的，但预计该项目也可以为大规模传感器网络提供实用的路由解决方案。

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.