\title{{\itshape Perimeter-based Coverage Optimization to Improve Lifetime \\
in Wireless Sensor Networks}}
-\author{Ali Kadhum Idrees$^{a, b}$, Karine Deschinkel$^{a}$$^{\ast}$\thanks{$^\ast$Corresponding author. Email: karine.deschinkel@univ-fcomte.fr}, Michel Salomon$^{a}$ and Rapha\"el Couturier $^{a}$
-$^{a}${\em{FEMTO-ST Institute, UMR 6174 CNRS, University of Franche-Comt\'e,
- Belfort, France}}
-$^{b}${\em{Department of Computer Science, University of Babylon, Babylon, Iraq}} }
-
-
-
+\author{Ali Kadhum Idrees$^{a,b}$, Karine Deschinkel$^{a}$$^{\ast}$\thanks{$^\ast$Corresponding author. Email: karine.deschinkel@univ-fcomte.fr}, Michel Salomon$^{a}$ and Rapha\"el Couturier $^{a}$
+ $^{a}${\em{FEMTO-ST Institute, UMR 6174 CNRS, \\
+ University Bourgogne Franche-Comt\'e (UBFC), Belfort, France}} \\
+ $^{b}${\em{Department of Computer Science, University of Babylon, Babylon, Iraq}}
+}
+
\maketitle
\begin{abstract}
\begin{figure*}[t!]
\centering
-\includegraphics[width=0.95\linewidth]{figure2.eps}
+\includegraphics[width=0.9\linewidth]{figure2.eps}
\caption{Maximum coverage levels for perimeter of sensor node $0$.}
\label{figure2}
\end{figure*}
\begin{figure}[t!]
\centering
-\includegraphics[width=85mm]{figure4.eps}
+\includegraphics[width=80mm]{figure4.eps}
\caption{PeCO protocol.}
\label{figure4}
\end{figure}
obtained by multiplying the energy consumed in the active state (9.72 mW) with
the time in seconds for one period (3600 seconds), and adding the energy for the
pre-sensing phases. According to the interval of initial energy, a sensor may
-be active during at most 20 periods.
+be active during at most 20 periods. Here information exchange is executed every hour but the length of the sensing period could be reduced and adapted dynamically. On the one hand a small sensing period would allow to be more reliable but would have higher communication costs. On the other hand the choice of a long duration may cause problems in case of nodes failure during the sensing period.
The values of $\alpha^j_i$ and $\beta^j_i$ have been chosen to ensure a good
network coverage and a longer WSN lifetime. Higher priority is given to the
The modeling language for Mathematical Programming (AMPL)~\citep{AMPL} is used
to generate the integer program instance in a standard format, which is then
read and solved by the optimization solver GLPK (GNU linear Programming Kit
-available in the public domain) \citep{glpk} through a Branch-and-Bound method.
+available in the public domain) \citep{glpk} through a Branch-and-Bound method.
+Obviously executing GLPK in practice on a sensor node is usually untractable due to
+the huge memory use. Fortunately, to solve the optimization problem we could use
+commercial solvers like CPLEX which are less memory consuming and more efficient, or
+implement a lightweight heuristic. For example, for a WSN of 200 sensor nodes, a leader
+node has to deal with constraints induced by about 12 sensor nodes. In that case, to solve the optimization problem a
+memory consumption of more than 1 MB can be observed with GLPK, whereas with CPLEX less than 300 kB would be needed.
% No discussion about the execution of GLPK on a sensor ?
in~\citep{idrees2014coverage}. Let us notice that PeCO and DiLCO protocols are
based on the same framework. In particular, the choice for the simulations of a
partitioning in 16~subregions was made because it corresponds to the
-configuration producing the best results for DiLCO. The protocols are
+configuration producing the best results for DiLCO. Of course, this number of subregions sould be adapted according to the size of the area of interest and the number of sensors.
+
+ The protocols are
distinguished from one another by the formulation of the integer program
providing the set of sensors which have to be activated in each sensing
phase. DiLCO protocol tries to satisfy the coverage of a set of primary points,
