Abstract
We address the question of finding sensors’ coordinates, or at least an approximation of them, when the sensors’ abilities are very weak. In a d dimensional space, we define an extremely relaxed notion of coordinates along dimension i. The rank i of a sensor s is the number of sensors with ith-coordinate less than the i-coordinate of s. In this paper we provide a theoretical foundation for sensor ranking, when one assumes that a few anchor sensors know their locations and that the others determine their rank only by exchanging information. We show that the rank problem can be solved in linear time in ℝ and that it is NP-Hard in ℝ2. We also study the usual localization problem and show that in general one cannot solve it; unless one knows a priori information on the sensors distribution.
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Lotker, Z., de Albeniz, M.M., Pérénnes, S. (2004). Range-Free Ranking in Sensors Networks and Its Applications to Localization. In: Nikolaidis, I., Barbeau, M., Kranakis, E. (eds) Ad-Hoc, Mobile, and Wireless Networks. ADHOC-NOW 2004. Lecture Notes in Computer Science, vol 3158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28634-9_13
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DOI: https://doi.org/10.1007/978-3-540-28634-9_13
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