%Instead of working with a continuous coverage area, we make it discrete by considering for each sensor a set of points called primary points. Consequently, we assume that the sensing disk defined by a sensor is covered if all of its primary points are covered. The choice of number and locations of primary points is the subject of another study not presented here.
-\indent Instead of working with the coverage area, we consider for each sensor a set of points called primary points~\cite{idrees2014coverage}. We also assume that the sensing disk defined by a sensor is covered if all the primary points of this sensor are covered. By knowing the position (point center: ($p_x,p_y$)) of a wireless sensor node and it's sensing range $R_s$, we calculate the primary points directly based on the proposed model. We use these primary points (that can be increased or decreased if necessary) as references to ensure that the monitored region of interest is covered by the selected set of sensors, instead of using all the points in the area.
-We can calculate the positions of the selected primary
-points in the circle disk of the sensing range of a wireless sensor
-node (see Figure~\ref{fig1}) as follows:\\
-Assuming that the point center of a wireless sensor node is located at $(p_x,p_y)$, we can define up to 25 primary points $X_1$ to $X_{25}$.\\
+\indent Instead of working with the coverage area, we consider for each sensor a set of points called primary points~\cite{idrees2014coverage}. We assume that the sensing disk defined by a sensor is covered if all the primary points of this sensor are covered. By knowing the position (point center: ($p_x,p_y$)) of a wireless sensor node and it's sensing range $R_s$, we define up to 25 primary points $X_1$ to $X_{25}$ as decribed on Figure~\ref{fig1}. The coordinates of the primary points are the following :\\
%$(p_x,p_y)$ = point center of wireless sensor node\\
$X_1=(p_x,p_y)$ \\
$X_2=( p_x + R_s * (1), p_y + R_s * (0) )$\\
\textcolor{red}{Our first protocol based GLPK optimization solver is declined into four versions: MuDiLCO-1, MuDiLCO-3, MuDiLCO-5,
and MuDiLCO-7, corresponding respectively to $T=1,3,5,7$ ($T$ the number of rounds in one sensing period).
- The second protocol based based GLPK optimization solver with time limit is declined into four versions: TL-MuDiLCO-1, TL-MuDiLCO-3, TL-MuDiLCO-5, and TL-MuDiLCO-7. Table \ref{tl} shows time limit values for TL-MuDiLCO protocol versions. After extensive experiments, we chose the values that explained in Table \ref{tl} because they gave the best results. In Table \ref{tl}, "NO" refers to apply the GLPK solver without time limit because we did not find improvement on the results of MuDiLCO protocol with the time limit}.
+ The second protocol based based GLPK optimization solver with time limit is declined into four versions: TL-MuDiLCO-1, TL-MuDiLCO-3, TL-MuDiLCO-5, and TL-MuDiLCO-7. Table \ref{tl} shows time limit values for TL-MuDiLCO protocol versions. After extensive experiments, we chose the values that explained in Table \ref{tl} because they gave the best results. In these experiments, we started with the average execution time of the corresponding MuDiLCO version and network size divided by 3 as a time limit. After that, we increase these values until reaching the best results. In fact, selecting the optimal values for the time limits can be investigated in future. In Table \ref{tl}, "NO" refers to apply the GLPK solver without time limit because we did not find improvement on the results of MuDiLCO protocol with the time limit. }.
\begin{table}[ht]
\caption{Time limit values for TL-MuDiLCO protocol versions }
\hline
100 & NO & NO & NO & NO \\
\hline
- 150 & NO & 0.006 & NO & 0.03 \\
+ 150 & NO & NO & NO & 0.03 \\
\hline
- 200 & 0.0035 & 0.0094 & 0.020 & 0.06 \\
+ 200 & NO & 0.0094 & 0.020 & 0.06 \\
\hline
- 250 & 0.0055 & 0.013 & 0.03 & 0.08 \\
+ 250 & NO & 0.013 & 0.03 & 0.08 \\
\hline
\end{tabular}
