Dense packings of congruent circles in a circle
Discrete Mathematics
The broadcast storm problem in a mobile ad hoc network
Wireless Networks - Selected Papers from Mobicom'99
Analysis on the redundancy of wireless sensor networks
WSNA '03 Proceedings of the 2nd ACM international conference on Wireless sensor networks and applications
Integrated coverage and connectivity configuration for energy conservation in sensor networks
ACM Transactions on Sensor Networks (TOSN)
Redundancy and coverage detection in sensor networks
ACM Transactions on Sensor Networks (TOSN)
Location-unaware coverage in wireless sensor networks
Ad Hoc Networks
Localized Sensor Area Coverage with Low Communication Overhead
IEEE Transactions on Mobile Computing
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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.