Sensor Redundancy Check Without Location Information

In this paper we study sufficient conditions for sensor redundancy that can be used without any coordinate or location 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), then any sensor with five neighbors that are pairwise non-neighbors is redundant, and this is best possible. In a slightly stronger model that sensors can distinguish close and distant neighbors, this sufficient condition can be fully generalized to the case where r(s) <= r(c): any sensor is redundant if it has in neighbors within distance alpha(m)r(s) that are pairwise farther than r(s), where m = 3, 4, 5 and alpha(3) approximate to 0.62, alpha(4) approximate to 0.81, alpha(5) = 1; or if it has g(alpha) neighbors within distance r(s) that are pairwise farther than alpha r(s), where alpha is an element of]0,1], g(1) = 5 and g((root 6 - root 2)/2) = 15.