@inbook{29dcaf85e5bf44ae8f9296aacf36f020,
title = "Range-Free ranking in sensors networks and its applications to localization",
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 ranki 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.",
author = "Zvi Lotker and {De Albeniz}, {Marc Martinez} and St{\'e}phane P{\'e}r{\'e}nnes",
year = "2004",
month = jan,
day = "1",
doi = "10.1007/978-3-540-28634-9_13",
language = "English",
isbn = "9783540286349",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "158--171",
editor = "Ioanis Nikolaidis and Michel Barbeau and Evangelos Kranakis",
booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
address = "Germany",
}