+In this experiment, Figure~\ref{Figures/ch4/R1/CR} shows the average coverage ratio for 150 deployed nodes.
+\parskip 0pt
+\begin{figure}[h!]
+\centering
+ \includegraphics[scale=0.8] {Figures/ch4/R1/CR.pdf}
+\caption{Coverage ratio for 150 deployed nodes}
+\label{Figures/ch4/R1/CR}
+\end{figure}
+It can be seen that DiLCO protocol (with 4, 8, 16 and 32 subregions) gives nearly similar coverage ratios during the first thirty rounds.
+DiLCO-2 protocol gives near similar coverage ratio with other ones for first 10 rounds and then decreased until the died of the network in the round $18^{th}$. In case of only 2 subregions, the energy consumption is high and the network is rapidly disconnected.
+As shown in the Figure ~\ref{Figures/ch4/R1/CR}, as the number of subregions increases, the coverage preservation for the area of interest increases for a larger number of rounds. Coverage ratio decreases when the number of rounds increases due to dead nodes. Although some nodes are dead, thanks to DiLCO-8, DiLCO-16, and DiLCO-32 protocols, other nodes are preserved to ensure the coverage. Moreover, when we have a dense sensor network, it leads to maintain the coverage for a larger number of rounds. DiLCO-8, DiLCO-16, and DiLCO-32 protocols are slightly more efficient than other protocols, because they subdivide the area of interest into 8, 16 and 32~subregions; if one of the subregions becomes disconnected, the coverage may be still ensured in the remaining subregions.
+
+\item {{\bf Active Sensors Ratio}}
+%\subsubsection{Active Sensors Ratio}
+
+Figure~\ref{Figures/ch4/R1/ASR} shows the average active nodes ratio for 150 deployed nodes.
+\begin{figure}[h!]
+\centering
+\includegraphics[scale=0.8]{Figures/ch4/R1/ASR.pdf}
+\caption{Active sensors ratio for 150 deployed nodes }
+\label{Figures/ch4/R1/ASR}
+\end{figure}
+
+The results presented in Figure~\ref{Figures/ch4/R1/ASR} show the increase of the number of subregions lead to the increase of the number of active nodes. The DiLCO-16 and DiLCO-32 protocols have a larger number of active nodes, but it preserve the coverage for a larger number of rounds. The advantage of the DiLCO-16 and DiLCO-32 protocols are that even if a network is disconnected in one subregion, the other ones usually continues the optimization process, and this extends the lifetime of the network.
+
+\item {{\bf The percentage of stopped simulation runs}}
+%\subsubsection{The percentage of stopped simulation runs}
+
+Figure~\ref{Figures/ch4/R1/SR} illustrates the percentage of stopped simulation runs per round for 150 deployed nodes.
+\begin{figure}[h!]
+\centering
+\includegraphics[scale=0.8]{Figures/ch4/R1/SR.pdf}
+\caption{Percentage of stopped simulation runs for 150 deployed nodes }
+\label{Figures/ch4/R1/SR}
+\end{figure}
+
+DiLCO-2 is the approach which stops first because it applies the optimization on only two subregions and the high energy consumption accelerate the network disconnection.
+Thus, as explained previously, in case of the DiLCO-16 and DiLCO-32 with several subregions, the optimization effectively continues as long as a network in a subregion is still connected. This longer partial coverage optimization participates in extending the network lifetime.
+
+\item {{\bf The Energy Consumption}}
+%\subsubsection{The Energy Consumption}
+
+We measure the energy consumed by the sensors during the communication, listening, computation, active, and sleep modes for different network densities and compare it for different subregions. Figures~\ref{Figures/ch4/R1/EC95} and ~\ref{Figures/ch4/R1/EC50} illustrate the energy consumption for different network sizes for $Lifetime95$ and $Lifetime50$.
+
+\begin{figure}[h!]
+\centering
+\includegraphics[scale=0.8]{Figures/ch4/R1/EC95.pdf}
+\caption{Energy Consumption for Lifetime95}
+\label{Figures/ch4/R1/EC95}
+\end{figure}
+
+The results show that DiLCO-16 and DiLCO-32 are the most competitive from the energy consumption point of view. The other approaches have a high energy consumption due to the energy consumed during the different modes of the sensor node.\\
+
+As shown in Figures~\ref{Figures/ch4/R1/EC95} and ~\ref{Figures/ch4/R1/EC50}, DiLCO-2 consumes more energy than the other versions of DiLCO, especially for large sizes of network. This is easy to understand since the bigger the number of sensors involved in the integer program, the larger the time computation to solve the optimization problem, as well as the higher energy consumed during the communication.
+\begin{figure}[h!]
+\centering
+\includegraphics[scale=0.8]{Figures/ch4/R1/EC50.pdf}
+\caption{Energy Consumption for Lifetime50}
+\label{Figures/ch4/R1/EC50}
+\end{figure}
+In fact, the distribution of the computation over many subregions greatly reduces the number of communications, the time of listening and computation so thanks to the partitioning of the initial network in several independent subnetworks.
+
+\item {{\bf Execution Time}}
+%\subsubsection{Execution Time}
+
+In this experiment, the execution time of the our distributed optimization approach has been studied. Figure~\ref{Figures/ch4/R1/T} gives the average execution times in seconds for the decision phase (solving of the optimization problem) during one round. They are given for the different approaches and various numbers of sensors. The original execution time is computed as described in section \ref{ch4:sec:04:04}.
+%The original execution time is computed on a laptop DELL with intel Core i3 2370 M (2.4 GHz) processor (2 cores) and the MIPS (Million Instructions Per Second) rate equal to 35330. To be consistent with the use of a sensor node with Atmels AVR ATmega103L microcontroller (6 MHz) and a MIPS rate equal to 6 to run the optimization resolution, this time is multiplied by 2944.2 $\left( \frac{35330}{2} \times 6\right)$ and reported on Figure~\ref{fig8} for different network sizes.
+
+\begin{figure}[h!]
+\centering
+\includegraphics[scale=0.8]{Figures/ch4/R1/T.pdf}
+\caption{Execution Time (in seconds)}
+\label{Figures/ch4/R1/T}
+\end{figure}
+
+We can see from Figure~\ref{Figures/ch4/R1/T}, that the DiLCO-32 has very low execution times in comparison with other DiLCO versions because it is distributed on larger number of small subregions. Conversely, DiLCO-2 requires to solve an optimization problem considering half the nodes in each subregion presents high execution times.
+
+We think that in distributed fashion the solving of the optimization problem in a subregion can be tackled by sensor nodes. Overall, to be able to deal with very large networks, a distributed method is clearly required.
+
+\item {{\bf The Network Lifetime}}
+%\subsubsection{The Network Lifetime}
+
+In Figure~\ref{Figures/ch4/R1/LT95} and \ref{Figures/ch4/R1/LT50}, network lifetime, $Lifetime95$ and $Lifetime50$ respectively, are illustrated for different network sizes.
+
+\begin{figure}[h!]
+\centering
+\includegraphics[scale=0.8]{Figures/ch4/R1/LT95.pdf}
+\caption{Network Lifetime for $Lifetime95$}
+\label{Figures/ch4/R1/LT95}
+\end{figure}
+For DiLCO-2 protocol results, execution times quickly become unsuitable for a sensor network, and the energy consumed during the communication, seems to be huge because it is distributed over only two subregions.
+
+As highlighted by figures~\ref{Figures/ch4/R1/LT95} and \ref{Figures/ch4/R1/LT50}, the network lifetime obviously increases when the size of the network increases. DiLCO-16 protocol leads to the larger lifetime improvement. DiLCO-16 protocol efficiently extends the network lifetime because the benefit from the optimization with 16 subregions is better than DiLCO-32 protocol with 32 subregions. in fact, DilCO-32 protocol puts in active mode a larger number of sensor nodes especially near the borders of the subdivisions.
+
+Comparison shows that DiLCO-16 protocol, which uses 16 leaders, is the best one because it uses less number of active nodes during the network lifetime compared with DiLCO-32 protocol. It also means that distributing the protocol in each node and subdividing the sensing field into many subregions, which are managed independently and simultaneously, is a relevant way to maximize the lifetime of a network.
+
+\begin{figure}[h!]
+\centering
+\includegraphics[scale=0.8]{Figures/ch4/R1/LT50.pdf}
+\caption{Network Lifetime for $Lifetime50$}
+\label{Figures/ch4/R1/LT50}
+\end{figure}
