Distributed coverage verification in sensor networks without location information

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General Robotics, Automation, Sensing and Perception Laboratory
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In this paper, we present a distributed algorithm for detecting coverage holes in a sensor network 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. In particular, we capture the combinatorial relationships among the sensors by the means of the Rips complex, which is the generalization of the proximity graph of the network to higher dimensions. Our approach is based on computation of a certain generator of the first homology of the Rips complex of the network. We formulate the problem of localizing coverage holes as an optimization problem to compute the sparsest generator of the first homology classes. We also demonstrate how subgradient methods can be used in solving this optimization problem in a distributed manner. Finally, non-trivial simulations are provided that illustrate the performance of our algorithm.

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Tahbaz-Salehi, A.; Jadbabaie, A., "Distributed coverage verification in sensor networks without location information," Decision and Control, 2008. CDC 2008. 47th IEEE Conference on , vol., no., pp.4170-4176, 9-11 Dec. 2008 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=4738751&isnumber=4738560 Copyright 2008 IEEE. Reprinted from Proceedings of the 47th IEEE Conference on Decision and Control, 2008 (CDC 2008), vol., no., pp.4170-4176, 9-11 Dec. 2008 This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
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