%\title{Lifetime Coverage Optimization Protocol \\
% in Wireless Sensor Networks}
-\title{Perimeter-based Coverage Optimization Protocol \\
- to Improve Lifetime in Wireless Sensor Networks}
+\title{Perimeter-based Coverage Optimization to Improve \\
+ Lifetime in Wireless Sensor Networks}
\author{Ali Kadhum Idrees,~\IEEEmembership{}
Karine Deschinkel,~\IEEEmembership{}
proved that if the transmission range fulfills the previous hypothesis, a
complete coverage of a convex area implies connectivity among active nodes.
-\indent LiCO protocol uses the same perimeter-coverage model than Huang and
+LiCO protocol uses the same perimeter-coverage model than Huang and
Tseng in~\cite{huang2005coverage}. It can be expressed as follows: a sensor is
said to be perimeter covered if all the points on its perimeter are covered by
at least one sensor other than itself. They proved that a network area is
\begin{figure}[ht!]
\centering
\begin{tabular}{@{}cr@{}}
- \includegraphics[width=75mm]{pcm.jpg} & \raisebox{3.25cm}{(a)}
- \\ \includegraphics[width=75mm]{twosensors.jpg} & \raisebox{2.75cm}{(b)}
+ \includegraphics[width=75mm]{pcm.jpg} & \raisebox{3.25cm}{(a)} \\
+ \includegraphics[width=75mm]{twosensors.jpg} & \raisebox{2.75cm}{(b)}
\end{tabular}
\caption{(a) Perimeter coverage of sensor node 0 and (b) finding the arc of
$u$'s perimeter covered by $v$.}
sensing area~: $(v_x,v_y)$ and $(u_x,u_y)$. From the previous coordinates we can
compute the euclidean distance between nodes~$u$ and $v$: $Dist(u,v)=\sqrt{\vert
u_x - v_x \vert^2 + \vert u_y-v_y \vert^2}$, while the angle~$\alpha$ is
-obtained through the formula $\alpha = arccos \left(\dfrac{Dist(u,v)}{2R_s}
-\right)$. So, the arc on the perimeter of node~$u$ defined by the angular
-interval $[\pi - \alpha,\pi + \alpha]$ is said to be perimeter-covered by sensor
-node $v$.
+obtained through the formula: $$\alpha = \arccos \left(\dfrac{Dist(u,v)}{2R_s}
+\right).$$ The arc on the perimeter of~$u$ defined by the angular interval $[\pi
+ - \alpha,\pi + \alpha]$ is said to be perimeter-covered by sensor~$v$.
Every couple of intersection points is placed on the angular interval $[0,2\pi]$
in a counterclockwise manner, leading to a partitioning of the interval.
%The points reported on the line segment $[0,2\pi]$ separates it in intervals as shown in figure~\ref{expcm}. For example, for each neighboring sensor of sensor 0, place the points $\alpha^ 1_L$, $\alpha^ 1_R$, $\alpha^ 2_L$, $\alpha^ 2_R$, $\alpha^ 3_L$, $\alpha^ 3_R$, $\alpha^ 4_L$, $\alpha^ 4_R$, $\alpha^ 5_L$, $\alpha^ 5_R$, $\alpha^ 6_L$, $\alpha^ 6_R$, $\alpha^ 7_L$, $\alpha^ 7_R$, $\alpha^ 8_L$, $\alpha^ 8_R$, $\alpha^ 9_L$, and $\alpha^ 9_R$; on the line segment $[0,2\pi]$, and then sort all these points in an ascending order into a list. Traverse the line segment $[0,2\pi]$ by visiting each point in the sorted list from left to right and determine the coverage level of each interval of the sensor 0 (see figure \ref{expcm}). For each interval, we sum up the number of parts of segments, and we deduce a level of coverage for each interval. For instance, the interval delimited by the points $5L$ and $6L$ contains three parts of segments. That means that this part of the perimeter of the sensor $0$ may be covered by three sensors, sensor $0$ itself and sensors $2$ and $5$. The level of coverage of this interval may reach $3$ if all previously mentioned sensors are active. Let say that sensors $0$, $2$ and $5$ are involved in the coverage of this interval. Table~\ref{my-label} summarizes the level of coverage for each interval and the sensors involved in for sensor node 0 in figure~\ref{pcm2sensors}(a).
% to determine the level of the perimeter coverage for each left and right point of a segment.
-\begin{figure*}[ht!]
+\begin{figure*}[t!]
\centering
-\includegraphics[width=137.5mm]{expcm2.jpg}
+\includegraphics[width=127.5mm]{expcm2.jpg}
\caption{Maximum coverage levels for perimeter of sensor node $0$.}
\label{expcm}
\end{figure*}
\fi
- \begin{table}[h]
+ \begin{table}[h!]
\caption{Coverage intervals and contributing sensors for sensor node 0.}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
\hline
and the corresponding interval will not be taken into account by the
optimization algorithm.
-\begin{figure}[t!]
+\begin{figure}[h!]
\centering
\includegraphics[width=62.5mm]{ex4pcm.jpg}
\caption{Sensing range outside the WSN's area of interest.}
