Holes Detection in Anisotropic Sensornets: Topological Methods

Abstract

Wireless sensor networks (WSNs) are tightly linked with the practical environment in which the sensors are deployed. Sensor positioning is a pivotal part of main location-dependent applications that utilize sensornets. The global topology of the network is important to both sensor network applications and the implementation of networking functionalities. This paper studies the topology discovery with an emphasis on boundary recognition in a sensor network. A large mass of sensor nodes are supposed to scatter in a geometric region, with nearby nodes communicating with each other directly. This paper is thus designed to detect the holes in the topological architecture of sensornets only by connectivity information. Existent edges determination methods hold the high costs as assumptions. Without the help of a large amount of uniformly deployed seed nodes, those schemes fail in anisotropic WSNs with possible holes. To address this issue, we propose a solution, named PPA based on Poincare-Perelman Theorem, to judge whether there are holes in WSNs-monitored areas. Our solution can properly detect holes on the topological surfaces and connect them into meaningful boundary cycles. The judging method has also been rigorously proved to be appropriate for continuous geometric domains as well as discrete domains. Extensive simulations have been shown that the algorithm even enables networks with low density to produce good results.