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A Theory of Network Localization
December 2006 (vol. 5 no. 12)
pp. 1663-1678
In this paper, we provide a theoretical foundation for the problem of network localization in which some nodes know their locations and other nodes determine their locations by measuring the distances to their neighbors. We construct grounded graphs to model network localization and apply graph rigidity theory to test the conditions for unique localizability and to construct uniquely localizable networks. We further study the computational complexity of network localization and investigate a subclass of grounded graphs where localization can be computed efficiently. We conclude with a discussion of localization in sensor networks where the sensors are placed randomly.

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Index Terms:
Computer systems organization, communication/networking and IT, mobile computing, algorithm/protocol design and analysis, architectures, theory of computation, analysis of algorithms and problem complexity, nonnumerical algorithms and problems, geometrical problems and computation, mathematics of computing, discrete mathematics, graph theory, network problems, computer applications, mobile applications, location-dependent and sensitive, wireless sensor networks.
James Aspnes, Tolga Eren, David K. Goldenberg, A. Stephen Morse, Walter Whiteley, Yang Richard Yang, Brian D.O. Anderson, Peter N. Belhumeur, "A Theory of Network Localization," IEEE Transactions on Mobile Computing, vol. 5, no. 12, pp. 1663-1678, Dec. 2006, doi:10.1109/TMC.2006.174
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