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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${(7.875+\varepsilon)}$$</EquationSource> </InlineEquation>-approximations for any <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$${\varepsilon >0 }$$</EquationSource> </InlineEquation> when all targets and sensors lie in the Euclidean plane and all sensors have the same sensing radius R <Subscript> s </Subscript> and the same communication radius R <Subscript> c </Subscript> with R <Subscript> c </Subscript> ≥ 2R <Subscript> s </Subscript>. Copyright Springer Science+Business Media, LLC. 2013