Range-Free Ranking in Sensors Networks and Its Applications to Localization

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.

• Type: Conference
• Year: 2004
• Where: ADHOCNOW
• Authors: Zvi Lotker, Marc Martinez de Albeniz, Stephane Perennes
• Keywords: ADHOCNOW 2004, Anchor Sensors, Sensors, Usual Localization Problem, Wireless Networks