year={1999}
}
+@BOOK{AMPL,
+ AUTHOR = "Robert Fourer and David M. Gay and Brian W. Kernighan",
+ TITLE = "AMPL: A Modeling Language for Mathematical Programming",
+ PUBLISHER = "Cengage Learning",
+ YEAR = "November 12, 2002",
+ edition = "2nd",
+
+}
+
+@article{Deng2012,
+ title={Transforming Area Coverage to Target Coverage to Maintain Coverage and Connectivity for Wireless Sensor Networks},
+ author={Xiu Deng and Jiguo Yu, Dongxiao Yu and Congcong Chen},
+ journal={International Journal of Distributed Sensor Networks},
+ volume={2012},
+ year={2012},
+ ee = {http://dx.doi.org/10.1155/2012/254318}
+}
+
+@inproceedings{jaggi2006,
+ title={Energy-efficient Connected Covereage in Wireless Sensor Networks},
+ author={N. Jaggi and A.A. Abouzeid},
+ booktitle={Proceeding of 4th Asian International Mobile Computing Conference AMOC2006},
+ year={2006}
+}
+
+@inproceedings{yangnovel,
+ title={A Novel Distributed Algorithm for Complete Targets Coverage in Energy Harvesting Wireless Sensor Networks },
+ author={Yang, Changlin and Chin, Kwan-Wu},
+ booktitle={IEEE ICC 2014- Ad-hoc and Sensor Networking Symposium},
+ pages={361--366},
+ year={2014},
+ organization={IEEE}
+}
+
+@INPROCEEDINGS{5714480,
+author={Xiaofei Xing and Jie Li and Guojun Wang},
+booktitle={Mobile Ad-hoc and Sensor Networks (MSN), 2010 Sixth International Conference on},
+title={Integer Programming Scheme for Target Coverage in Heterogeneous Wireless Sensor Networks},
+year={2010},
+month={Dec},
+pages={79-84},
+keywords={energy conservation;integer programming;wireless sensor networks;ETCA;clustered configurations;clusterheads;energy first algorithm;energy-efficient target coverage algorithm;heterogeneous wireless sensor networks;integer programming;network lifetime;polytype target coverage;sensor node;Algorithm design and analysis;Clustering algorithms;Energy consumption;Logic gates;Sensors;Simulation;Wireless sensor networks;Heterogeneous wireless sensor networks;network lifetime;optimization;target coverage},
+doi={10.1109/MSN.2010.18},}
+
+@article{Yang2014,
+ title={A Maximum Lifetime Coverage Algorithm Based on Linear Programming},
+ author={Mengmeng Yang and Jie Liu},
+ journal={Journal of Information Hiding an dMultimedia Signal Processing, Ubiquitous International},
+ volume={5},
+ number={2},
+ pages={296-301},
+ year={2014}
+}
+
+@article{rossi2012exact,
+ title={An exact approach for maximizing the lifetime of sensor networks with adjustable sensing ranges},
+ author={Rossi, Andr{\'e} and Singh, Alok and Sevaux, Marc},
+ journal={Computers \& Operations Research},
+ volume={39},
+ number={12},
+ pages={3166--3176},
+ year={2012},
+ publisher={Elsevier}
+}
+
+@ARTICLE{glpk,
+author = {Andrew Makhorin},
+title = {The GLPK (GNU Linear Programming Kit)},
+journal = {Available: https://www.gnu.org/software/glpk/},
+year = {2012},
+}
+
+@article{deschinkel2012column,
+ title={A Column Generation based Heuristic to Extend Lifetime in Wireless Sensor Network.},
+ author={Deschinkel, Karine},
+ journal={Sensors \& Transducers Journal},
+ volume={14-2},
+ pages={242--253},
+ year={2012}
+}
\ No newline at end of file
\begin{abstract}
- One fundamental issue in Wireless Sensor Networks (WSNs) is the lifetime coverage optimization, which reflects how well a WSN is covered so that the network lifetime can be maximized. In this paper, a Lifetime Coverage Optimization Protocol (LiCO) in WSNs is proposed. The surveillance region is divided into subregions and LiCO protocol is distributed among sensor nodes in each subregion. LiC0 protocols works into periods, each period is divided into four stages: Information exchange, Leader Election, Optimization Decision, and Sensing. Schedules node activities (wakeup and sleep of sensors) is performed in each subregion by a leader whose selection is the result of cooperation between nodes within the same subregion. The novelty of the approach lies essentially in the formulation of a new mathematical optimization model based on perimeter coverage level to schedule sensors activities. Extensive simulation experiments have been performed using OMNeT++, the discrete event simulator, to demonstrate that LiCO is capable to extend the lifetime coverage of WSN as longer time as possible in comparison with some other protocols.
+ One fundamental issue in Wireless Sensor Networks (WSNs) is the lifetime coverage optimization, which reflects how well a WSN is covered so that the network lifetime can be maximized. In this paper, a Lifetime Coverage Optimization Protocol (LiCO) in WSNs is proposed. The surveillance region is divided into subregions and LiCO protocol is distributed among sensor nodes in each subregion. LiCO protocols works with periods, each period is divided into four stages: Information exchange, Leader Election, Optimization Decision, and Sensing. Schedules node activities (wakeup and sleep of sensors) is performed in each subregion by a leader whose selection is the result of cooperation between nodes within the same subregion. The novelty of approach lies essentially in the formulation of a new mathematical optimization model based on perimeter coverage level to schedule sensors activities. Extensive simulation experiments have been performed using OMNeT++, the discrete event simulator, to demonstrate that LiCO is capable to extend the lifetime coverage of WSN as longer time as possible in comparison with some other protocols.
\end{abstract}
\section{\uppercase{Introduction}}
\label{sec:introduction}
-\noindent The great development in Micro Electro-Mechanical Systems (MEMS) and wireless communication hardware are being led to emerge networks of tiny distributed sensors called WSN~\cite{akyildiz2002wireless,puccinelli2005wireless}. WSN comprises of small, low-powered sensors working together for perform a typical mission by communicating with one another through multihop wireless connections. They can send the sensed measurements based on local decisions to the user by means of sink nodes. WSN has been used in many applications such as Military, Habitat, Environment, Health, industrial, and Business~\cite{yick2008wireless}.Typically, a sensor node contains three main parts~\cite{anastasi2009energy}: a sensing subsystem, for sense, measure, and gather the measurements from the real environment; processing subsystem, for measurements processing and storage; a communication subsystem, for data transmission and receiving. Moreover, the energy needed by the sensor node is supplied by a power supply, to accomplish the scheduled task. This power supply is composed of a battery with a limited lifetime. And it maybe be unsuitable or impossible to replace or recharge the batteries in most applications. It is then necessary to deploy the WSN with high density so as to increase the reliability and to exploit redundancy by using energy-efficient activity scheduling approaches. So, the main question is: how to extend the lifetime coverage of WSN as long time as possible while ensuring a high level of coverage? Many energy-efficient mechanisms have been suggested to retain energy and extend the lifetime of the WSNs~\cite{rault2014energy}. \\
+\noindent The great development in Micro Electro-Mechanical Systems (MEMS) and wireless communication hardware are being led to emerge networks of tiny distributed sensors called WSN~\cite{akyildiz2002wireless,puccinelli2005wireless}. WSN comprises of small, low-powered sensors working together for perform a typical mission by communicating with one another through multihop wireless connections. They can send the sensed measurements based on local decisions to the user by means of sink nodes. WSN has been used in many applications such as Military, Habitat, Environment, Health, industrial, and Business~\cite{yick2008wireless}. Typically, a sensor node contains three main parts~\cite{anastasi2009energy}: a sensing subsystem, for sense, measure, and gather the measurements from the real environment; processing subsystem, for measurements processing and storage; a communication subsystem, for data transmission and receiving. Moreover, the energy needed by the sensor node is supplied by a power supply, to accomplish the scheduled task. This power supply is composed of a battery with a limited lifetime. And it maybe be unsuitable or impossible to replace or recharge the batteries in most applications. It is then necessary to deploy the WSN with high density so as to increase the reliability and to exploit redundancy by using energy-efficient activity scheduling approaches. So, the main question is: how to extend the lifetime coverage of WSN as long time as possible while ensuring a high level of coverage? Many energy-efficient mechanisms have been suggested to retain energy and extend the lifetime of the WSNs~\cite{rault2014energy}. \\
%The sensor system ought to have a lifetime long enough to satisfy the application necessities. The lifetime coverage maximization is one of the fundamental requirements of any area coverage protocol in WSN implementation~\cite{nayak2010wireless}. In order to increase the reliability and prevent the possession of coverage holes (some parts are not covered in the area of interest) in the WSN, it is necessary to deploy the WSN with high density so as to increase the reliability and to exploit redundancy by using energy-efficient activity scheduling approaches.
\begin{enumerate}
\item We devise a framework to schedules nodes to be activated alternatively, such that the network lifetime may be prolonged ans certain coverage requirement can still be met.
This framework is based on the division of the area of interest into several smaller subregions; on the division of timeline into periods of equal length.
-One leader is elected for each subregion in an independent, distributed, and simultaneous way by the cooperation among the sensor nodes within each subregion, and this similar to cluster architecture
+One leader is elected for each subregion in an independent, distributed, and simultaneous way by the cooperation among the sensor nodes within each subregion, and this is similar to cluster architecture
\item We propose a new mathematical optimization model. Instead of trying to cover a set of specified points/targets as in most of the methods proposed in the literature,
we formulate an integer program based on perimeter coverage of each sensor. The model involves integer variables to capture the deviations between the
actual level of coverage and the required level. And a weighted sum of these deviations is minimized.
-\item We conducted extensive simulation experiments using the discrete event simulator OMNeT++, to demonstrate the efficiency of our protocol, compared to two approaches found in the literature, DESK \ref{} and GAF \ref{}, and compared to our previous work using another optimization model for sensor scheduling.
+\item We conducted extensive simulation experiments using the discrete event simulator OMNeT++, to demonstrate the efficiency of our protocol, compared to two approaches found in the literature, DESK \cite{ChinhVu} and GAF \cite{xu2001geography}, and compared to our previous work using another optimization model for sensor scheduling \cite{Idrees2}.
\end{enumerate}
the literature.
The most discussed coverage problems in literature can be classified into three
-types \cite{li2013survey}: area coverage \cite{Misra} where every point inside
+types \cite{li2013survey}: area coverage \cite{Misra} where every point inside
an area is to be monitored, target coverage \cite{yang2014novel} where the main
objective is to cover only a finite number of discrete points called targets,
-and barrier coverage \cite{Kumar:2005}\cite{kim2013maximum} to prevent intruders
+and barrier coverage \cite{HeShibo}\cite{kim2013maximum} to prevent intruders
from entering into the region of interest. In \cite{Deng2012} authors transform
the area coverage problem to the target coverage problem taking into account the
intersection points among disks of sensors nodes or between disk of sensor nodes
-and boundaries. In \cite{Huang:2003:CPW:941350.941367} authors prove that if the perimeters of sensors are sufficiently covered, the whole area is sufficiently covered and they provide an algorithm in $O(n d log d)$ time to compute the perimeter-coverage of each sensor ($d$ the maximum number of sensors that are neighboring to a sensor, $n$ the total number of sensors in the network). {\it In LiCO protocol, rather than determining the level of coverage of a set of discrete points, our optimization model is based on checking the perimeter-coverage of each sensor to activate a minimal number of sensors.}
+and boundaries. In \cite{Huang:2003:CPW:941350.941367} authors prove that if the perimeters of sensors are sufficiently covered, the whole area is sufficiently covered and they provide an algorithm in $O(nd~log~d)$ time to compute the perimeter-coverage of each sensor ($d$ the maximum number of sensors that are neighboring to a sensor, $n$ the total number of sensors in the network). {\it In LiCO protocol, instead of determining the level of coverage of a set of discrete points, our optimization model is based on checking the perimeter-coverage of each sensor to activate a minimal number of sensors.}
The major approach to extend network lifetime while preserving coverage is to
divide/organize the sensors into a suitable number of set covers (disjoint or
\begin{figure}[ht!]
\centering
-\includegraphics[width=75mm]{pcm.pdf}
+\includegraphics[width=75mm]{pcm.jpg}
\caption{Perimeter coverage of sensor node 0}
\label{pcmfig}
\end{figure}
Figure~\ref{twosensors} demonstrates the way of locating the left and right points of a segment for a sensor node $u$ covered by a sensor node $v$. This figure assumes that the neighbor sensor node $v$ is located on the west of a sensor $u$. It is assumed that the two sensor nodes $v$ and $u$ are located in the positions $(v_x,v_y)$ and $(u_x,u_y)$, respectively. The distance between $v$ and $u$ is computed by $Dist(u,v) = \sqrt{\vert u_x - v_x \vert^2 + \vert u_y - v_y \vert^2}$. The angle $\alpha$ is computed through the formula $\alpha = arccos \left(\dfrac{Dist(u,v)}{2R_s} \right)$. So, the arch of sensor $u$ falling in the angle $[\pi - \alpha,\pi + \alpha]$, is said to be perimeter-covered by sensor node $v$.
-The left and right points of each segment are placed on the line segment $[0,2\pi]$. Figure~\ref{pcmfig} illustrates the segments for the 9 neighbors of sensor $0$. The points reported on the line segment $[0,2\pi]$ separates it in intervals. 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. The table in figure~\ref{expcm} summarizes the level of coverage for each interval and the sensors involved in.
+The left and right points of each segment are placed on the line segment $[0,2\pi]$. Figure~\ref{pcmfig} illustrates the segments for the 9 neighbors of sensor $0$. 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{pcmfig}.
% to determine the level of the perimeter coverage for each left and right point of a segment.
\begin{figure}[ht!]
\centering
\label{twosensors}
\end{figure}
+
\begin{figure}[ht!]
\centering
\includegraphics[width=75mm]{expcm.pdf}
\label{expcm}
\end{figure}
+
+
+
+
+
+
+
+
%For example, consider the sensor node $0$ in figure~\ref{pcmfig}, which has 9 neighbors. Figure~\ref{expcm} shows the perimeter coverage level for all left and right points of a segment that covered by a neighboring sensor nodes. Based on the figure~\ref{expcm}, the set of sensors for each left and right point of the segments illustrated in figure~\ref{ex2pcm} for the sensor node 0.
+\iffalse
+
\begin{figure}[ht!]
\centering
\includegraphics[width=90mm]{ex2pcm.jpg}
\label{ex2pcm}
\end{figure}
+\fi
+
+ \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
+\begin{tabular}[c]{@{}c@{}}The angle \\ $\alpha$ \end{tabular} & \begin{tabular}[c]{@{}c@{}}Segment \\ Left (L) or\\ Right (R)\end{tabular} & \begin{tabular}[c]{@{}c@{}}Sensor \\ Node Id\end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ Coverage\\ Level\end{tabular} & \multicolumn{5}{c|}{\begin{tabular}[c]{@{}c@{}}The Set of Sensors\\ Involved in Interval \\ Coverage\end{tabular}} \\ \hline
+0.0291 & L & 1 & 4 & 0 & 1 & 3 & 4 & \\ \hline
+0.104 & L & 2 & 5 & 0 & 1 & 3 & 4 & 2 \\ \hline
+0.3168 & R & 3 & 4 & 0 & 1 & 4 & 2 & \\ \hline
+0.6752 & R & 4 & 3 & 0 & 1 & 2 & & \\ \hline
+1.8127 & R & 1 & 2 & 0 & 2 & & & \\ \hline
+1.9228 & L & 5 & 3 & 0 & 2 & 5 & & \\ \hline
+2.3959 & L & 6 & 4 & 0 & 2 & 5 & 6 & \\ \hline
+2.4258 & R & 2 & 3 & 0 & 5 & 6 & & \\ \hline
+2.7868 & L & 7 & 4 & 0 & 5 & 6 & 7 & \\ \hline
+2.8358 & L & 8 & 5 & 0 & 5 & 6 & 7 & 8 \\ \hline
+2.9184 & R & 5 & 4 & 0 & 6 & 7 & 8 & \\ \hline
+3.3301 & R & 7 & 3 & 0 & 6 & 8 & & \\ \hline
+3.9464 & L & 9 & 4 & 0 & 6 & 8 & 9 & \\ \hline
+4.767 & R & 6 & 3 & 0 & 8 & 9 & & \\ \hline
+4.8425 & L & 3 & 4 & 0 & 3 & 8 & 9 & \\ \hline
+4.9072 & R & 8 & 3 & 0 & 3 & 9 & & \\ \hline
+5.3804 & L & 4 & 4 & 0 & 3 & 4 & 9 & \\ \hline
+5.9157 & R & 9 & 3 & 0 & 3 & 4 & & \\ \hline
+\end{tabular}
+
+\label{my-label}
+\end{table}
+
+
%The optimization algorithm that used by LiCO protocol based on the perimeter coverage levels of the left and right points of the segments and worked to minimize the number of sensor nodes for each left or right point of the segments within each sensor node. The algorithm minimize the perimeter coverage level of the left and right points of the segments, while, it assures that every perimeter coverage level of the left and right points of the segments greater than or equal to 1.
In LiCO protocol, scheduling of sensor nodes'activities is formulated with an integer program based on coverage intervals and is detailed in section~\ref{cp}.
level of coverage. For example, weights associated with coverage intervals of a specified part of a region
may be given a relatively
larger magnitude than weights associated
-with another region. This kind of integer program is inspired from the model developed for brachytherapy treatment planning for optimizing dose distribution \ref{0031-9155-44-1-012}. The integer program must be solved by the leader in each subregion at the beginning of each sensing phase, whenever the environment has changed (new leader, death of some sensors). Note that the number of constraints in the model is constant (constraints of coverage expressed for all sensors), whereas the number of variables $X_k$ decreases over periods, since we consider only alive sensors (sensors with enough energy to be alive during one sensing phase) in the model.
+with another region. This kind of integer program is inspired from the model developed for brachytherapy treatment planning for optimizing dose distribution \cite{0031-9155-44-1-012}. The integer program must be solved by the leader in each subregion at the beginning of each sensing phase, whenever the environment has changed (new leader, death of some sensors). Note that the number of constraints in the model is constant (constraints of coverage expressed for all sensors), whereas the number of variables $X_k$ decreases over periods, since we consider only alive sensors (sensors with enough energy to be alive during one sensing phase) in the model.
\section{\uppercase{PERFORMANCE EVALUATION AND ANALYSIS}}
According to the interval of initial energy, a sensor may be active during at
most 20 rounds.
+The values of $\alpha^j_i$ and $\beta^j_i$ have been chosen in a way that ensuring a good network coverage and for a longer time during the lifetime of the WSN. We have given a higher priority for the undercoverage ( by setting the $\alpha^j_i$ with a larger value than $\beta^j_i$) so as to prevent the non-coverage for the interval i of the sensor j. On the other hand, we have given a little bit lower value for $\beta^j_i$ so as to minimize the number of active sensor nodes that contribute in covering the interval i in sensor j.
+
In the simulations, we introduce the following performance metrics to evaluate
the efficiency of our approach:
%\end{enumerate}
\subsection{Simulation Results}
-In this section, we present the simulation results of LiCO protocol and the other protocols using a discrete event simulator OMNeT++ \cite{varga} to run different series of simulations. We implemented all protocols precisely on a laptop DELL with Intel Core~i3~2370~M (2.4 GHz) processor (2 cores) and the MIPS (Million Instructions Per Second) rate equal to 35330. To be consistent with the use of a sensor node with Atmels AVR ATmega103L microcontroller (6 MHz) and a MIPS rate equal to 6, the original execution time on the laptop is multiplied by 2944.2 $\left(\frac{35330}{2} \times \frac{1}{6} \right)$ so as to use it by the energy consumption model especially, after the computation and listening. Employing the modeling language ????\ref{}, the associated integer program instance is generated in a standard format, which is then read and solved by the optimization solver GLPK (GNU linear Programming Kit available in the public domain) \cite{glpk} through a Branch-and-Bound method.
+In this section, we present the simulation results of LiCO protocol and the other protocols using a discrete event simulator OMNeT++ \cite{varga} to run different series of simulations. We implemented all protocols precisely on a laptop DELL with Intel Core~i3~2370~M (2.4 GHz) processor (2 cores) and the MIPS (Million Instructions Per Second) rate equal to 35330. To be consistent with the use of a sensor node with Atmels AVR ATmega103L microcontroller (6 MHz) and a MIPS rate equal to 6, the original execution time on the laptop is multiplied by 2944.2 $\left(\frac{35330}{2} \times \frac{1}{6} \right)$ so as to use it by the energy consumption model especially, after the computation and listening. Employing the modeling language for Mathematical Programming (AMPL)~\cite{AMPL}, the associated integer program instance is generated in a standard format, which is then read and solved by the optimization solver GLPK (GNU linear Programming Kit available in the public domain) \cite{glpk} through a Branch-and-Bound method.
We compared LiCO protocol to three other approaches: the first, called DESK and proposed by ~\cite{ChinhVu} is a fully distributed coverage algorithm; the second, called GAF ~\cite{xu2001geography}, consists in dividing the region
into fixed squares. During the decision phase, in each square, one sensor is
-chosen to remain active during the sensing phase; the third, DiLCO protocol~\cite{Idrees2} is an improved version on the work presented in ~\cite{idrees2014coverage}. Note that the LiCO protocol is based on the same framework as that of DiLCO. For these two protocols, the division of the region of interest in 16 subregions was chosen since it produces the best results. The difference between the two protocols relies on the use of the integer programming to provide the set of sensors that have to be actived in each sensing phase. Whereas DilCO protocol tries to satisfy the coverage of a set of primary points, LiCO protocol tries to reach a desired level of coverage $l$ for each sensor's perimeter. In the experimentations, we chose a level of coverage equal to 1 ($l=1$).
+chosen to remain active during the sensing phase; the third, DiLCO protocol~\cite{Idrees2} is an improved version on the work presented in ~\cite{idrees2014coverage}. Note that the LiCO protocol is based on the same framework as that of DiLCO. For these two protocols, the division of the region of interest in 16 subregions was chosen since it produces the best results. The difference between the two protocols relies on the use of the integer programming to provide the set of sensors that have to be activated in each sensing phase. Whereas DiLCO protocol tries to satisfy the coverage of a set of primary points, LiCO protocol tries to reach a desired level of coverage $l$ for each sensor's perimeter. In the experimentations, we chose a level of coverage equal to 1 ($l=1$).
\subsubsection{\textbf{Coverage Ratio}}
Figure~\ref{fig333} shows the average coverage ratio for 200 deployed nodes obtained with the four methods.
\label{fig333}
\end{figure}
-DESK, GAF, and DiLCO provides a little better coverage ratio with 99.99\%, 99.91\%, and 99.02\% against 98.76\% produced by LiCO for the first periods. This is due to the fact that DiLCO protocol put in sleep mode redundant sensors using optimization (which lightly decreases the coverage ratio) while there are more active nodes in the case of others methods. But when the number of periods exceeds 70 periods, it clearly appears that LiCO provides a better coverage ratio and keeps a coverage ratio greater than 50\% for longer periods (15 more compared to DiLCO, 40 more compared to DESK).
+DESK, GAF, and DiLCO provide a little better coverage ratio with 99.99\%, 99.91\%, and 99.02\% against 98.76\% produced by LiCO for the first periods. This is due to the fact that DiLCO protocol put in sleep mode redundant sensors using optimization (which lightly decreases the coverage ratio) while there are more active nodes in the case of others methods. But when the number of periods exceeds 70 periods, it clearly appears that LiCO provides a better coverage ratio and keeps a coverage ratio greater than 50\% for longer periods (15 more compared to DiLCO, 40 more compared to DESK).
%When the number of periods increases, coverage ratio produced by DESK and GAF protocols decreases. This is due to dead nodes. However, DiLCO protocol maintains almost a good coverage from the round 31 to the round 63 and it is close to LiCO protocol. The coverage ratio of LiCO protocol is better than other approaches from the period 64.
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