J. Aspnes, T. Eren, D. K. Goldenberg, A. S. Morse, W. Whiteley, Y. R. Yang, B. D. O. Anderson, and P. N. Belhumeur. A theory of network localization. IEEE Transactions on Mobile Computing, 12(5):1663–1678, December 2006.
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.
@article(AspnesEGMWYAB2006,
title="A theory of network localization",
author="J. Aspnes and T. Eren and D. K. Goldenberg and A. S. Morse and W. Whiteley and Y. R. Yang and B. D. O. Anderson and P. N. Belhumeur",
journal="IEEE Transactions on Mobile Computing",
volume=5,
number=12,
pages={1663--1678},
month=dec,
year=2006
)