-In~\cite{DESK}, the author design a novel distributed heuristic, called Distributed Energy-efficient Scheduling for k-coverage (DESK), which ensures that the energy consumption among the sensors is balanced and the lifetime maximized while the coverage requirement is maintained. This heuristic works in rounds, requires only one-hop neighbor information, and each sensor decides its status (active or sleep) based on the perimeter coverage model from~\cite{ref133}. Figure~\ref{desk} shows the DESK network time line.
+% The authors in~\cite{DESK} design a novel distributed heuristic, called Distributed Energy-efficient Scheduling for K-coverage (DESK), which
+DESK is a novel distributed heuristic to ensure that the energy consumption among the sensors is balanced and the lifetime maximized while the coverage requirement is satisfied~\cite{DESK}. This heuristic works in rounds, requires only one-hop neighbor information, and each sensor decides its status (Active or Sleep) based on the perimeter coverage model from~\cite{ref133}.
+
+%DESK is based on the result from \cite{ref133}.
+In DESK \cite{ref133}, the whole area is K-covered if and only if the perimeters of all sensors are K-covered. The coverage level of a sensor $s_i$ is determined by calculating the angle corresponding to the arc that each of its neighbors covers its perimeter. Figure~\ref{figp}~(a) illuminates such arcs whilst figure~\ref{figp}~(b) shows the angles corresponding with those arcs in the range [0,2$ \pi $]. According to figure~\ref{figp}~(a) and (b), the coverage level of sensor $s_i$ can be calculated as follows.
+%via traversing the range from 0 to 2$ \pi $.
+For each sensor $s_j$ such that $d(s_i,s_j)$ $<$ $2R_s$, calculate the angle of $s_i$'s arc, denoted by [$\alpha_{j,L}$, $\alpha_{j,R}$], which is perimeter covered by $s_j$, where $\alpha= arccos(d(s_i, s_j)/2R_s)$ and $d(s_i,s_j)$ is the Euclidean distance between $s_i$ and $s_j$. After that, locate the points $\alpha_{j,L}$ and $\alpha_{j,R}$ of each neighboring sensor $s_j$ of $s_i$ on the line segment $[0, 2\pi]$. These points are sorted in ascending order into a list L. Traverse the line segment from 0 to $2\pi$ by visiting each element in the sorted list L from the left to the right and determine the perimeter coverage of $s_i$. Whenever an element $\alpha_{j,L}$ is traversed, the level of perimeter coverage should be increased by one. Whenever an element $\alpha_{j,R}$ is traversed, the level of perimeter coverage should be decreased by one.
+
+
+\begin{figure}[h!]
+ \centering
+ \begin{tabular}{@{}cr@{}}
+ \includegraphics[scale=0.8]{Figures/ch2/P22.jpg} & \raisebox{3cm}{(a)} \\
+ \includegraphics[scale=0.8]{Figures/ch2/P11.jpg} & \raisebox{3cm}{(b)}
+ \end{tabular}
+ \caption{Determining the perimeter-coverage of $s_i$’s perimeter.}
+ \label{figp}
+\end{figure}
+
+
