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Unformatted text preview: University of Pennsylvania ScholarlyCommons Departmental Papers (ESE) Department of Electrical & Systems Engineering 12-9-2008 Distributed coverage verification in sensor networks without location information Alireza Tahbaz-Salehi University of Pennsylvania , atahbaz@seas.upenn.edu Ali Jadbabaie University of Pennsylvania , jadbabai@seas.upenn.edu 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. This paper is posted at ScholarlyCommons. http://repository.upenn.edu/ese_papers/481 For more information, please contact repository@pobox.upenn.edu . Distributed Coverage Verification in Sensor Networks Without Location Information Alireza Tahbaz-Salehi and Ali Jadbabaie Abstract 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. I. INTRODUCTION Recent advances in computing, communication, sensing and actuation technologies have brought networks composed of hundreds or even thousands of inexpensive mobile sensing platforms closer to reality. This has induced a significant amount of interest in development of analytical tools for pre- dicting the behavior, as well as controlling the complexities...
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