Maximum lifetime connected coverage with two active‐phase sensors

A sensor with two active phrases means that active mode has two phases, the full‐active phase and the semi‐active phase, which require different energy consumptions. A full‐active sensor can sense data packets, transmit, receive, and relay the data packets. A semi‐active sensor cannot sense data packets, but it can transmit, receive, and relay data packets. Given a set of targets and a set of sensors with two active phrases, find a sleep/active schedule of sensors to maximize the time period during which active sensors form a connected coverage set. In this paper, this problem is showed to have polynomial‐time $(7.875+\epsilon )$ ‐approximations for any $\epsilon >0$ when all targets and sensors lie in the Euclidean plane and all sensors have the same sensing radius R s and the same communication radius R c with R c ≥ 2R s .