\item We devise a framework to schedule nodes to be activated alternatively such that the network lifetime is prolonged while ensuring that a certain level of coverage is preserved. A key idea in our framework is to exploit spatial an temporal subdivision. On the one hand the area of interest if divided into several smaller subregions and on the other hand the time line is divided into periods of equal length. In each subregion the sensor nodes will cooperatively choose a leader which will schedule nodes' activities, and this grouping of sensors is similar to typical cluster architecture. We propose a new mathematical optimization model. Instead of trying to cover a set of specified points/targets as in most of the methods proposed in the literature, we formulate an integer program based on perimeter coverage of each sensor. The model involves integer variables to capture the deviations between the actual level of coverage and the required level. So that an optimal scheduling will be obtained by minimizing a weighted sum of these deviations. This contribution is demonstrated in Chapter 5.
-\item We add an improved model of energy consumption to assess the efficiency of our protocols as well as we conducted extensive simulation experiments, using the discrete event simulator OMNeT++, to demonstrate the efficiency of our protocols. We compared our proposed distributed optimization protocols to two approaches found in the literature: DESK~\cite{DESK} and GAF~\cite{GAF}, simulation results based on multiple criteria (energy consumption, coverage ratio, network lifetime and so on) show that the proposed protocols can prolong efficiently the network lifetime and improve the coverage performance.
+\item We add an improved model of energy consumption to assess the efficiency of our protocols as well as we conducted extensive simulation experiments, using the discrete event simulator OMNeT++, to demonstrate the efficiency of our protocols. We compared our proposed distributed optimization protocols to two approaches found in the literature: DESK~\cite{DESK} and GAF~\cite{GAF}, simulation results based on multiple criteria (energy consumption, coverage ratio, network lifetime and so on) show that the proposed protocols can prolong efficiently the network lifetime and improve the coverage performance.
\end{enumerate}
