Topological Fidelity in Sensor Networks

Abstract: Sensor Networks are inherently complex networks, and many of their associated problems require analysis of some of their global characteristics. These are primarily affected by the topology of the network. We present in this paper, a general framework for a topological analysis of a network, and develop distributed algorithms in a generalized combinatorial setting in order to solve two seemingly unrelated problems, 1) Coverage hole detection and Localization and 2) Worm hole attack detection and Localization. We also note these solutions remain coordinate free as no priori localization information of the nodes is assumed. For the coverage hole problem, we follow a "divide and conquer approach", by strategically dissecting the network so that the overall topology is preserved, while efficiently pursuing the detection and localization of failures. The detection of holes, is enabled by first attributing a combinatorial object called a "Rips Complex" to each network segment, and by subsequently checking the existence/non-existence of holes by way of triviality of the first homology class of this complex. Our estimate exponentially approaches the location of potential holes with each iteration, yielding a very fast convergence coupled with optimal usage of valuable resources such as power and memory. We then show a simple extension of the above problem to address a well known problem in networks, namely the localization of a worm hole attack. We demonstrate the effectiveness of the presented algorithm with several substantiating examples.