Sensor redundancy check without geometric information
Peter Braß, Hyeon-Suk Na · 2011
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 rs around his position, and can communicate with other sensors up to a distance rc. We prove that if rs ≥ rc, 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 rs ≤ rc in several ways: any sensor is redundant if it has m neighbors within distance αmrs, being pairwise farther than rs, where m = 3, 4, 5 and α3 ≈ 0.62, α4 ≈ 0.81, α5 = 1; or if it has g(α) neighbors within distance rs that are pairwise farther than αrs, where α ∈]0, 1], g(1) = 5 and 15 ≤ g((√6 -- √2)/2) ≤ 16.