K-coverage in regular deterministic sensor deployments

An area is k-covered if every point of the area is covered by at least k sensors. K-coverage is necessary for many applications, such as intrusion detection, data gathering, and object tracking. It is also desirable in situations where a stronger environmental monitoring capability is desired, such as military applications. In this paper, we study the problem of k-coverage in deterministic homogeneous deployments of sensors. We examine the three regular sensor deployments - triangular, square and hexagonal deployments - for k-coverage of the deployment area, for k ≥ 1. We compare the three regular deployments in terms of sensor density. For each deployment, we compute an upper bound and a lower bound on the optimal distance of sensors from each other that ensure k-coverage of the area. We present the results for each k from 1 to 20 and show that the required number of sensors to k-cover the area using uniform random deployment is approximately 3-10 times higher than regular deployments.