Probabilistic k-Weighted Coverage Placement in Wireless Sensor Networks

In this paper, we study a new problem called probabilistic k-weighted coverage placement, which is a generalization of the Q-coverage placement. Q-coverage placement assumes that the monitored area has uniform coverage requirement: events within the monitored area should be detected with probability Q x 100% (i.e., detected by Q sensors), while probabilistic k-weighted coverage placement assumes that the monitored area has k-degrees of coverage requirement (i.e., k kinds of detection probability): events within distinct region of the monitored area are detected with distinct detection ability, i.e., one of the k kinds of detection probability. Besides, Q-coverage placement requires that the coverage requirement is integer multiple of 100% detection probability, while probabilistic k-weighted coverage placement allows coverage requirement to be non-integer multiple of 100% detection probability. We derive a lower bound on the number of sensors needed to satisfy the coverage requirement of a probabilistic k-weighted monitored area, and introduce a greedy algorithm to solve the problem.