Divide and Conquer: Localizing Coverage Holes in Sensor Networks

Sensor Networks are inherently complex networks, and associated problems where analysis of some global features becomes more important than local ones, often arise. Localizing the holes in the overall coverage is one such problem. We present here, a distributed algorithm in a generalized combinatorial setting to localize holes in the coverage, with no a priori localization information for the nodes. We follow a divide and conquer approach, strategically dissecting the network so that the overall topology is preserved, while simultaneously minimizing the computational complexity. The detection of holes is enabled by first attributing a combinatorial object called a "Rips Complex" to each network segment, and by then checking for the triviality of the first homology class of this complex. Our estimate approaches the location of the holes exponentially with each iteration leading to a very fast convergence coupled with optimal usage of valuable resources such as power and memory. We demonstrate the effectiveness of the presented algorithm with simulations.