From: Michel Salomon Date: Wed, 14 Jan 2015 10:02:08 +0000 (+0100) Subject: Michel : some minor modifications X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/LiCO.git/commitdiff_plain/95096147988f0732c4e9796ebd0f7cae5f03576a?ds=inline;hp=--cc Michel : some minor modifications --- 95096147988f0732c4e9796ebd0f7cae5f03576a diff --git a/LiCO_Journal.tex b/LiCO_Journal.tex index a714974..4571961 100644 --- a/LiCO_Journal.tex +++ b/LiCO_Journal.tex @@ -38,8 +38,8 @@ %\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{} @@ -317,7 +317,7 @@ $R_c$ satisfies $R_c \geq 2 \cdot R_s$. In fact, Zhang and Zhou~\cite{Zhang05} 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 @@ -335,8 +335,8 @@ arcs. \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 $v$.} @@ -350,10 +350,9 @@ west side of sensor~$u$, with the following respective coordinates in the 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. @@ -376,9 +375,9 @@ above is thus given by the sixth line of the table. %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*} @@ -396,7 +395,7 @@ above is thus given by the sixth line of the table. \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 @@ -435,7 +434,7 @@ figure~\ref{ex4pcm}, the maximum coverage level for this arc is set to $\infty$ 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.}