Distributed coverage verification in sensor networks without location information

In this paper, we present a series of 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 computational homology can be used in providing valuable information on the properties of the cover. Our approach is based on computation of certain generators of the first homology of the Rips complex corresponding to the sensor network. We first 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 to compute the sparsest generator of the first homology classes of the Rips complex. Furthermore, we show that one can detect redundancies in the sensor network by finding the sparsest generator of the second homology of the cover relative to its boundary. We also demonstrate how subgradient method...

• Type: Conference
• Year: 2008
• Where: CDC
• Authors: Alireza Tahbaz-Salehi, Ali Jadbabaie
• Keywords: CDC 2008, Control Systems, Coverage Holes, Rips Complex, Sensor Network