\label{ch4}
-\iffalse
-\section{Summary}
-\label{ch4:sec:01}
-In this chapter, a Distributed Lifetime Coverage Optimization protocol (DiLCO) to maintain
-the coverage and to improve the lifetime in wireless sensor networks is
-proposed. The area of interest is first divided into subregions using a
-divide-and-conquer method and then the DiLCO protocol is distributed on the
-sensor nodes in each subregion. The DiLCO combines two efficient techniques:
-leader election for each subregion, followed by an optimization-based planning
-of activity scheduling decisions for each subregion. The proposed DiLCO works
-into rounds during which a small number of nodes, remaining active for sensing,
-is selected to ensure coverage so as to maximize the lifetime of wireless sensor
-network. Each round consists of four phases: (i)~Information Exchange,
-(ii)~Leader Election, (iii)~Decision, and (iv)~Sensing. The decision process is
-carried out by a leader node, which solves an integer program. Compared with
-some existing protocols, simulation results show that the proposed protocol can
-prolong the network lifetime and improve the coverage performance effectively.
-
-\fi
\section{Introduction}
\label{ch4:sec:01}
\subsection{Primary Point Coverage Model}
\label{ch4:sec:02:02}
\indent Instead of working with the coverage area, we consider for each sensor a set of points called primary points. 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 $R_s$, 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.
-
-\indent We can calculate the positions of the selected primary
+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:\\
$X_{24}=( p_x + R_s * (\frac{- 1}{2}), p_y + R_s * (\frac{-\sqrt{3}}{2})) $\\
$X_{25}=( p_x + R_s * (\frac{1}{2}), p_y + R_s * (\frac{-\sqrt{3}}{2})) $.
-\begin{figure}[h!]
+
+
+\begin{figure} %[h!]
\centering
- \begin{multicols}{3}
+ \begin{multicols}{2}
\centering
-\includegraphics[scale=0.20]{Figures/ch4/fig21.pdf}\\~ ~ ~ ~ ~(a)
-\includegraphics[scale=0.20]{Figures/ch4/fig22.pdf}\\~ ~ ~ ~ ~(b)
-\includegraphics[scale=0.20]{Figures/ch4/principles13.pdf}\\~ ~ ~ ~ ~(c)
-\hfill
-\includegraphics[scale=0.20]{Figures/ch4/fig24.pdf}\\~ ~ ~(d)
-\includegraphics[scale=0.20]{Figures/ch4/fig25.pdf}\\~ ~ ~(e)
-\includegraphics[scale=0.20]{Figures/ch4/fig26.pdf}\\~ ~ ~(f)
+\includegraphics[scale=0.33]{Figures/ch4/fig21.pdf}\\~ ~ ~ ~ ~ ~ ~ ~(a)
+\includegraphics[scale=0.33]{Figures/ch4/principles13.pdf}\\~ ~ ~ ~ ~ ~(c)
+\hfill \hfill
+\includegraphics[scale=0.33]{Figures/ch4/fig25.pdf}\\~ ~ ~ ~ ~ ~(e)
+\includegraphics[scale=0.33]{Figures/ch4/fig22.pdf}\\~ ~ ~ ~ ~ ~ ~ ~ ~(b)
+\hfill \hfill
+\includegraphics[scale=0.33]{Figures/ch4/fig24.pdf}\\~ ~ ~ ~ ~ ~ ~(d)
+\includegraphics[scale=0.33]{Figures/ch4/fig26.pdf}\\~ ~ ~ ~ ~ ~ ~(f)
\end{multicols}
\caption{Wireless Sensor Node represented by (a)5, (b)9, (c)13, (d)17, (e)21 and (f)25 primary points respectively}
\label{fig1}
\end{figure}
-
+
+
\subsection{Main Idea}
% is used to refer this table in the text
\end{table}
-Simulations with five different node densities going from 50 to 250~nodes were
+Simulations with five different node densities going from 50 to 250~nodes were
performed considering each time 25~randomly generated networks, to obtain
experimental results which are relevant. The nodes are deployed on a field of
interest of $(50 \times 25)~m^2 $ in such a way that they cover the field with a
