Distributed Coverage Verification in Sensor Networks Without Location Information

In this paper, we present three distributed algorithms for coverage verification in sensor networks with no location information. We demonstrate how, in the absence of localization devices, simplicial complexes and tools from algebraic topology can be used in providing valuable information about the properties of the cover. Our approach is based on computation of homologies of the Rips complex corresponding to the sensor network. First, we present a decentralized scheme based on Laplacian flows to compute a generator of the first homology, which represents coverage holes. Then, we formulate the problem of localizing coverage holes as an optimization problem for computing a sparse generator of the first homology. Furthermore, we show that one can detect redundancies in the sensor network by finding a sparse generator of the second homology of the cover relative to its boundary. We demonstrate how subgradient methods can be used in solving these optimization problems in a distributed manner. Finally, we provide simulations that illustrate the performance of our algorithms.