Sensor redundancy check without geometric information

Abstract

In this paper we study sufficient conditions for sensor redundancy that can be used without any coordinate or geometric information. We assume boolean sensing model: each sensor observes a disc of radius r s around his position, and can communicate with other sensors up to a distance r c. We prove that if r s ≥ r c, any sensor with five neighbors that are pairwise not neighbors is redundant, and this is best possible. With a slightly stronger model that sensors can distinguish close and distant neighbors, we generalizes to the case where r s ≤ r c in several ways: any sensor is redundant if it has m neighbors within distance α mr s, being pairwise farther than r s, where m = 3, 4, 5 and α 3 ≈ 0.62, α 4 ≈ 0.81, α 5 = 1; or if it has g(α) neighbors within distance r s that are pairwise farther than αr s, where α ε]0, 1], g(1) = 5 and 15 ≤ g((√6 - √2)/2) ≤ 16. © 2011 ACM.