Update on fig. 2

[LiCO.git] / LiCO_Journal.tex

diff --git a/LiCO_Journal.tex b/LiCO_Journal.tex
index 98fc632a537f40d8005d471a6bb9b1ff6564b006..a71497461d5dfa53350c56917929e6b77a28af37 100644 (file)
--- a/LiCO_Journal.tex
+++ b/LiCO_Journal.tex
@@ -36,8 +36,10 @@
 \DeclareGraphicsRule{.ps}{pdf}{.pdf}{`ps2pdf -dEPSCrop -dNOSAFER #1 \noexpand\OutputFile}
 \begin{document}
 
 \DeclareGraphicsRule{.ps}{pdf}{.pdf}{`ps2pdf -dEPSCrop -dNOSAFER #1 \noexpand\OutputFile}
 \begin{document}
 

-\title{Lifetime Coverage Optimization Protocol \\
-  in Wireless Sensor Networks}  %LiCO Protocol 
+%\title{Lifetime Coverage Optimization Protocol \\
+%  in Wireless Sensor Networks}
+\title{Perimeter-based Coverage Optimization Protocol \\
+  to Improve Lifetime in Wireless Sensor Networks}

 
 \author{Ali Kadhum Idrees,~\IEEEmembership{}
         Karine Deschinkel,~\IEEEmembership{}
 
 \author{Ali Kadhum Idrees,~\IEEEmembership{}
         Karine Deschinkel,~\IEEEmembership{}


@@ -58,7 +60,7 @@ use of its limited energy provision, so  that it can fulfill its monitoring task
 as  long as  possible. Among  known  available approaches  that can  be used  to
 improve  power  management,  lifetime coverage  optimization  provides  activity
 scheduling which ensures  sensing coverage while minimizing the  energy cost. In
 as  long as  possible. Among  known  available approaches  that can  be used  to
 improve  power  management,  lifetime coverage  optimization  provides  activity
 scheduling which ensures  sensing coverage while minimizing the  energy cost. In

-this paper,  we propose  a such approach  called Lifetime  Coverage Optimization
+this paper,  we propose such an approach  called Lifetime  Coverage Optimization

 protocol (LiCO).   It is a  hybrid of  centralized and distributed  methods: the
 region of interest is first subdivided  into subregions and our protocol is then
 distributed among sensor nodes in each  subregion. A sensor node which runs LiCO
 protocol (LiCO).   It is a  hybrid of  centralized and distributed  methods: the
 region of interest is first subdivided  into subregions and our protocol is then
 distributed among sensor nodes in each  subregion. A sensor node which runs LiCO


@@ -66,11 +68,11 @@ protocol  repeats   periodically  four  stages:  information   exchange,  leader
 election, optimization decision, and sensing.  More precisely, the scheduling of
 nodes' activities (sleep/wake up duty cycles) is achieved in each subregion by a
 leader selected after  cooperation between nodes within the  same subregion. The
 election, optimization decision, and sensing.  More precisely, the scheduling of
 nodes' activities (sleep/wake up duty cycles) is achieved in each subregion by a
 leader selected after  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  offer
-longer lifetime coverage for WSNs in comparison with some other protocols.
+novelty  of  our  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
+offer longer lifetime coverage for WSNs in comparison with some other protocols.

 \end{abstract} 
 
 % Note that keywords are not normally used for peerreview papers.
 \end{abstract} 
 
 % Note that keywords are not normally used for peerreview papers.


@@ -92,7 +94,7 @@ communicating with one another through multi-hop radio communications. Each node
 can send the data  it collects in its environment, thanks to  its sensor, to the
 user by means of  sink nodes. The features of a WSN made  it suitable for a wide
 range of application  in areas such as business,  environment, health, industry,
 can send the data  it collects in its environment, thanks to  its sensor, to the
 user by means of  sink nodes. The features of a WSN made  it suitable for a wide
 range of application  in areas such as business,  environment, health, industry,

-military, and  son~\cite{yick2008wireless}.  Typically,  a sensor  node contains
+military, and so on~\cite{yick2008wireless}.   Typically, a sensor node contains

 three main components~\cite{anastasi2009energy}: a  sensing unit able to measure
 physical,  chemical, or  biological  phenomena observed  in  the environment;  a
 processing unit which will process and store the collected measurements; a radio
 three main components~\cite{anastasi2009energy}: a  sensing unit able to measure
 physical,  chemical, or  biological  phenomena observed  in  the environment;  a
 processing unit which will process and store the collected measurements; a radio


@@ -121,7 +123,7 @@ This paper makes the following contributions.
 \begin{enumerate}
 \item We devise a framework to schedule nodes to be activated alternatively such
   that the network lifetime is prolonged  while ensuring that a certain level of
 \begin{enumerate}
 \item We devise a framework to schedule nodes to be activated alternatively such
   that the network lifetime is prolonged  while ensuring that a certain level of

-  coverage is preserved.  A  key idea in our framework is  to exploit spatial an
+  coverage is preserved.  A key idea in  our framework is to exploit spatial and

   temporal subdivision.   On the one hand  the area of interest  if divided into
   several smaller subregions and on the other hand the time line is divided into
   periods of equal length. In each subregion the sensor nodes will cooperatively
   temporal subdivision.   On the one hand  the area of interest  if divided into
   several smaller subregions and on the other hand the time line is divided into
   periods of equal length. In each subregion the sensor nodes will cooperatively


@@ -203,13 +205,13 @@ each period.   {\it Motivated by  these works,  LiCO protocol works  in periods,
 
 Various centralized  and distributed approaches, or  even a mixing of  these two
 concepts, have  been proposed  to extend the  network lifetime.   In distributed
 
 Various centralized  and distributed approaches, or  even a mixing of  these two
 concepts, have  been proposed  to extend the  network lifetime.   In distributed

-algorithms~\cite{yangnovel,ChinhVu,qu2013distributed}  each  sensors decides  of
-its own  activity scheduling after  an information exchange with  its neighbors.
-The main interest of  a such approach is to avoid  long range communications and
-thus to reduce the energy dedicated to the communications.  Unfortunately, since
-each node has  only information on its immediate neighbors  (usually the one-hop
-ones)  it may  take a  bad  decision leading  to a  global suboptimal  solution.
-Conversely,                                                          centralized
+algorithms~\cite{yangnovel,ChinhVu,qu2013distributed} each sensor decides of its
+own activity scheduling  after an information exchange with  its neighbors.  The
+main interest of a such approach is  to avoid long range communications and thus
+to reduce the energy dedicated to the communications.  Unfortunately, since each
+node has only information on its  immediate neighbors (usually the one-hop ones)
+it may take a bad decision leading to a global suboptimal solution.  Conversely,
+centralized

 algorithms~\cite{cardei2005improving,zorbas2010solving,pujari2011high}    always
 provide nearly  or close to  optimal solution since  the algorithm has  a global
 view of the whole network. The disadvantage of a centralized method is obviously
 algorithms~\cite{cardei2005improving,zorbas2010solving,pujari2011high}    always
 provide nearly  or close to  optimal solution since  the algorithm has  a global
 view of the whole network. The disadvantage of a centralized method is obviously


@@ -319,7 +321,7 @@ complete coverage of a convex area implies connectivity among active nodes.
 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
 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

-$k$-covered if and only if each sensor in the network is $k$-perimeter-covered.
+$k$-covered if and only if each sensor in the network is $k$-perimeter-covered (perimeter covered by at least $k$ sensors).

 %According to this model, we named the intersections among the sensor nodes in the sensing field as intersection points. Instead of working with the coverage area, we consider for each sensor a set of intersection points which are determined by using perimeter-coverage model. 
 Figure~\ref{pcm2sensors}(a)  shows  the coverage  of  sensor  node~$0$. On  this
 figure, we can  see that sensor~$0$ has  nine neighbors and we  have reported on
 %According to this model, we named the intersections among the sensor nodes in the sensing field as intersection points. Instead of working with the coverage area, we consider for each sensor a set of intersection points which are determined by using perimeter-coverage model. 
 Figure~\ref{pcm2sensors}(a)  shows  the coverage  of  sensor  node~$0$. On  this
 figure, we can  see that sensor~$0$ has  nine neighbors and we  have reported on


@@ -343,7 +345,7 @@ arcs.
 
 Figure~\ref{pcm2sensors}(b) describes the geometric information used to find the
 locations of the  left and right points of  an arc on the perimeter  of a sensor
 
 Figure~\ref{pcm2sensors}(b) describes the geometric information used to find the
 locations of the  left and right points of  an arc on the perimeter  of a sensor

-node~$u$ covered by a sensor node~$v$. Node~$s$ is supposed to be located on the
+node~$u$ covered by a sensor node~$v$. Node~$v$ is supposed to be located on the

 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 $v$: $Dist(u,v)=\sqrt{\vert
 west  side of  sensor~$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


@@ -363,7 +365,8 @@ positions. The intersection points are  then visited one after another, starting
 from  first  intersection point  after  point~zero,  and  the maximum  level  of
 coverage is determined  for each interval defined by two  successive points. The
 maximum  level of  coverage is  equal to  the number  of overlapping  arcs.  For
 from  first  intersection point  after  point~zero,  and  the maximum  level  of
 coverage is determined  for each interval defined by two  successive points. The
 maximum  level of  coverage is  equal to  the number  of overlapping  arcs.  For

-example, between~$5L$  and~$6L$ the maximum  level of  coverage is equal  to $3$
+example, 
+between~$5L$  and~$6L$ the maximum  level of  coverage is equal  to $3$

 (the value is highlighted in yellow  at the bottom of figure~\ref{expcm}), which
 means that at most 2~neighbors can cover  the perimeter in addition to node $0$.
 Table~\ref{my-label} summarizes for each coverage  interval the maximum level of
 (the value is highlighted in yellow  at the bottom of figure~\ref{expcm}), which
 means that at most 2~neighbors can cover  the perimeter in addition to node $0$.
 Table~\ref{my-label} summarizes for each coverage  interval the maximum level of


@@ -375,7 +378,7 @@ above is thus given by the sixth line of the table.
 
 \begin{figure*}[ht!]
 \centering
 
 \begin{figure*}[ht!]
 \centering

-\includegraphics[width=137.5mm]{expcm.pdf}  
+\includegraphics[width=137.5mm]{expcm2.jpg}  

 \caption{Maximum coverage levels for perimeter of sensor node $0$.}
 \label{expcm}
 \end{figure*} 
 \caption{Maximum coverage levels for perimeter of sensor node $0$.}
 \label{expcm}
 \end{figure*} 


@@ -397,7 +400,7 @@ above is thus given by the sixth line of the table.
  \caption{Coverage intervals and contributing sensors for sensor node 0.}
 \begin{tabular}{|c|c|c|c|c|c|c|c|c|}
 \hline
  \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@{}}Left \\ point \\ angle~$\alpha$ \end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ left \\ point\end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ right \\ point\end{tabular} & \begin{tabular}[c]{@{}c@{}}Maximum \\ coverage\\  level\end{tabular} & \multicolumn{5}{c|}{\begin{tabular}[c]{@{}c@{}}Set of sensors\\ involved \\ in interval coverage\end{tabular}} \\ \hline
+\begin{tabular}[c]{@{}c@{}}Left \\ point \\ angle~$\alpha$ \end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ left \\ point\end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ right \\ point\end{tabular} & \begin{tabular}[c]{@{}c@{}}Maximum \\ coverage\\  level\end{tabular} & \multicolumn{5}{c|}{\begin{tabular}[c]{@{}c@{}}Set of sensors\\ involved \\ in coverage interval\end{tabular}} \\ \hline

 0.0291    & 1L                                                                        & 2L                                                        & 4                                                                     & 0                     & 1                     & 3                    & 4                    &                      \\ \hline
 0.104     & 2L                                                                        & 3R                                                        & 5                                                                     & 0                     & 1                     & 3                    & 4                    & 2                    \\ \hline
 0.3168    & 3R                                                                        & 4R                                                        & 4                                                                     & 0                     & 1                     & 4                    & 2                    &                      \\ \hline
 0.0291    & 1L                                                                        & 2L                                                        & 4                                                                     & 0                     & 1                     & 3                    & 4                    &                      \\ \hline
 0.104     & 2L                                                                        & 3R                                                        & 5                                                                     & 0                     & 1                     & 3                    & 4                    & 2                    \\ \hline
 0.3168    & 3R                                                                        & 4R                                                        & 4                                                                     & 0                     & 1                     & 4                    & 2                    &                      \\ \hline


@@ -474,7 +477,7 @@ the area.
 \begin{figure}[t!]
 \centering
 \includegraphics[width=80mm]{Model.pdf}  
 \begin{figure}[t!]
 \centering
 \includegraphics[width=80mm]{Model.pdf}  

-\caption{LiCO protocol}
+\caption{LiCO protocol.}

 \label{fig2}
 \end{figure} 
 
 \label{fig2}
 \end{figure} 
 


@@ -497,7 +500,7 @@ Five status are possible for a sensor node in the network:
   determine the activities scheduling;
 \item ACTIVE: node is sensing;
 \item SLEEP: node is turned off;
   determine the activities scheduling;
 \item ACTIVE: node is sensing;
 \item SLEEP: node is turned off;

-\item COMMUNICATION: transmits or recevives packets.
+\item COMMUNICATION: transmits or receives packets.

 \end{itemize}
 %\end{enumerate}
 %Below, we describe each phase in more details.
 \end{itemize}
 %\end{enumerate}
 %Below, we describe each phase in more details.


@@ -555,12 +558,12 @@ protocol applied by a sensor node $s_k$ where $k$ is the node index in the WSN.
 
 In this  algorithm, K.CurrentSize and  K.PreviousSize refer to the  current size
 and the  previous size of  the subnetwork  in the subregion  respectively.  That
 
 In this  algorithm, K.CurrentSize and  K.PreviousSize refer to the  current size
 and the  previous size of  the subnetwork  in the subregion  respectively.  That

-means the  number of sensor nodes  which are still alive.  Initially, the sensor
+means the number  of sensor nodes which are still  alive.  Initially, the sensor

 node checks its remaining energy $RE_k$,  which must be greater than a threshold
 node checks its remaining energy $RE_k$,  which must be greater than a threshold

-$E_{th}$  in order  to  participate  in the  current  period.  Each sensor  node
+$E_{th}$  in order  to  participate in  the current  period.   Each sensor  node

 determines its  position and its subregion  using an embedded GPS  or a location
 discovery algorithm. After  that, all the sensors  collect position coordinates,
 determines its  position and its subregion  using an embedded GPS  or a location
 discovery algorithm. After  that, all the sensors  collect position coordinates,

-remaining energy, sensor  node ID, and the number of  its one-hop live neighbors
+remaining energy, sensor node ID, and the number of their one-hop live neighbors

 during the information  exchange. The sensors inside a same  region cooperate to
 elect a  leader. The selection  criteria for the  leader, in order  of priority,
 are: larger  number of neighbors, larger  remaining energy, and then  in case of
 during the information  exchange. The sensors inside a same  region cooperate to
 elect a  leader. The selection  criteria for the  leader, in order  of priority,
 are: larger  number of neighbors, larger  remaining energy, and then  in case of


@@ -618,7 +621,7 @@ sensor $j$  is given by  $\sum_{k \in A} a^j_{ik}  X_k$.  To extend  the network
 lifetime,  the objective  is to  activate a  minimal number  of sensors  in each
 period to  ensure the  desired coverage  level. As the  number of  alive sensors
 decreases, it becomes impossible to reach  the desired level of coverage for all
 lifetime,  the objective  is to  activate a  minimal number  of sensors  in each
 period to  ensure the  desired coverage  level. As the  number of  alive sensors
 decreases, it becomes impossible to reach  the desired level of coverage for all

-coverage intervals. Therefore we uses variables $M^j_i$ and $V^j_i$ as a measure
+coverage intervals. Therefore we use variables  $M^j_i$ and $V^j_i$ as a measure

 of the  deviation between  the desired  number of active  sensors in  a coverage
 interval and  the effective  number. And  we try  to minimize  these deviations,
 first to  force the  activation of  a minimal  number of  sensors to  ensure the
 of the  deviation between  the desired  number of active  sensors in  a coverage
 interval and  the effective  number. And  we try  to minimize  these deviations,
 first to  force the  activation of  a minimal  number of  sensors to  ensure the


@@ -736,10 +739,10 @@ be active during at most 20 periods.
 The values  of $\alpha^j_i$ and  $\beta^j_i$ have been  chosen to ensure  a good
 network coverage and a longer WSN lifetime.  We have given a higher priority for
 the  undercoverage  (by  setting  the  $\alpha^j_i$ with  a  larger  value  than
 The values  of $\alpha^j_i$ and  $\beta^j_i$ have been  chosen to ensure  a good
 network coverage and a longer WSN lifetime.  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 which  contribute in covering
-the interval.
+$\beta^j_i$)  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 which contribute
+in covering the interval.

 
 We introduce the following performance metrics to evaluate the efficiency of our
 approach.
 
 We introduce the following performance metrics to evaluate the efficiency of our
 approach.


@@ -751,7 +754,7 @@ approach.
   $Lifetime_{50}$  denote, respectively,  the  amount of  time  during which  is
   guaranteed a  level of coverage  greater than $95\%$  and $50\%$. The  WSN can
   fulfill the expected  monitoring task until all its nodes  have depleted their
   $Lifetime_{50}$  denote, respectively,  the  amount of  time  during which  is
   guaranteed a  level of coverage  greater than $95\%$  and $50\%$. The  WSN can
   fulfill the expected  monitoring task until all its nodes  have depleted their

-  energy or if the network is not more connected. This last condition is crucial
+  energy or if the network is no  more connected. This last condition is crucial

   because without  network connectivity a  sensor may not be  able to send  to a
   base station an event it has sensed.
 \item {\bf  Coverage Ratio (CR)} : it  measures how  well the  WSN is  able to
   because without  network connectivity a  sensor may not be  able to send  to a
   base station an event it has sensed.
 \item {\bf  Coverage Ratio (CR)} : it  measures how  well the  WSN is  able to


@@ -771,7 +774,7 @@ approach.
   follows:
   \begin{equation*}
     \scriptsize
   follows:
   \begin{equation*}
     \scriptsize

-    \mbox{ASR}(\%) =  \frac{\sum\limits_{r=1}^R \mbox{$|A_r|$}}{\mbox{$|S|$}} \times 100
+    \mbox{ASR}(\%) =  \frac{\sum\limits_{r=1}^R \mbox{$|A_r^p|$}}{\mbox{$|S|$}} \times 100

   \end{equation*}
   where $|A_r^p|$ is  the number of active  sensors in the subregion  $r$ in the
   current sensing period~$p$, $|S|$ is the number of sensors in the network, and
   \end{equation*}
   where $|A_r^p|$ is  the number of active  sensors in the subregion  $r$ in the
   current sensing period~$p$, $|S|$ is the number of sensors in the network, and


@@ -827,7 +830,7 @@ it corresponds to the configuration producing  the better results for DiLCO. 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,
 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,

-whereas LICO protocol objectif is to reach a desired level of coverage for each
+whereas LiCO protocol objective is to reach a desired level of coverage for each

 sensor perimeter. In our experimentations, we chose a level of coverage equal to
 one ($l=1$).
 
 sensor perimeter. In our experimentations, we chose a level of coverage equal to
 one ($l=1$).
 


@@ -881,7 +884,7 @@ figure \ref{fig333}.
 
 We study the effect of the energy  consumed by the WSN during the communication,
 computation, listening, active, and sleep status for different network densities
 
 We study the effect of the energy  consumed by the WSN during the communication,
 computation, listening, active, and sleep status for different network densities

-and  compare  it for  the  fours  approaches.  Figures~\ref{fig3EC}(a)  and  (b)
+and  compare  it for  the  four  approaches.  Figures~\ref{fig3EC}(a)  and  (b)

 illustrate  the  energy   consumption  for  different  network   sizes  and  for
 $Lifetime95$ and  $Lifetime50$. The results show  that our LiCO protocol  is the
 most competitive  from the energy  consumption point of  view. As shown  in both
 illustrate  the  energy   consumption  for  different  network   sizes  and  for
 $Lifetime95$ and  $Lifetime50$. The results show  that our LiCO protocol  is the
 most competitive  from the energy  consumption point of  view. As shown  in both


@@ -912,16 +915,17 @@ while keeping a good coverage level.
 \subsubsection{\bf Network Lifetime}
 
 We observe the superiority of LiCO and DiLCO protocols in comparison against the
 \subsubsection{\bf Network Lifetime}
 
 We observe the superiority of LiCO and DiLCO protocols in comparison against the

-two other approaches  in prolonging the network  WSN. In figures~\ref{fig3LT}(a)
-and (b),  $Lifetime95$ and $Lifetime50$  are shown for different  network sizes.
-As highlighted  by these figures,  the lifetime increases  with the size  of the
-network,  and it  is  clearly the  larger  for DiLCO  and  LiCO protocols.   For
-instance, for a network of 300 sensors  and coverage ratio greater than 50\%, we
-can see  on figure~\ref{fig3LT}(b) that the  lifetime is about two  times longer
-with LiCO compared to DESK protocol.  The performance difference is more obvious
-in  figure~\ref{fig3LT}(b)  than  in  figure~\ref{fig3LT}(a)  because  the  gain
-induced  by our  protocols increases  with  the time,  and the  lifetime with  a
-coverage of 50\% is far more longer than with 95\%.
+two    other   approaches    in    prolonging   the    network   lifetime.    In
+figures~\ref{fig3LT}(a)  and (b),  $Lifetime95$ and  $Lifetime50$ are  shown for
+different  network  sizes.   As  highlighted  by  these  figures,  the  lifetime
+increases with the size  of the network, and it is clearly  the larger for DiLCO
+and LiCO  protocols.  For instance,  for a  network of 300~sensors  and coverage
+ratio greater than 50\%, we can  see on figure~\ref{fig3LT}(b) that the lifetime
+is about two times longer with  LiCO compared to DESK protocol.  The performance
+difference    is    more    obvious   in    figure~\ref{fig3LT}(b)    than    in
+figure~\ref{fig3LT}(a) because the gain induced  by our protocols increases with
+the time, and the lifetime with a coverage  of 50\% is far more longer than with
+95\%.

 
 \begin{figure}[h!]
   \centering
 
 \begin{figure}[h!]
   \centering


@@ -945,8 +949,8 @@ that do not require a 100\% coverage of  the area to be monitored. LiCO might be
 an interesting  method since  it achieves  a good balance  between a  high level
 coverage ratio and network lifetime. LiCO always outperforms DiLCO for the three
 lower  coverage  ratios,  moreover  the   improvements  grow  with  the  network
 an interesting  method since  it achieves  a good balance  between a  high level
 coverage ratio and network lifetime. LiCO always outperforms DiLCO for the three
 lower  coverage  ratios,  moreover  the   improvements  grow  with  the  network

-size. DiLCO is better for coverage ratios near 100\%, but LiCO is not so bad for
-the smallest network sizes.
+size. DiLCO is better  for coverage ratios near 100\%, but in  that case LiCO is
+not so bad for the smallest network sizes.

 
 \begin{figure}[h!]
 \centering \includegraphics[scale=0.5]{R/LTa.eps}
 
 \begin{figure}[h!]
 \centering \includegraphics[scale=0.5]{R/LTa.eps}


@@ -962,7 +966,7 @@ the smallest network sizes.
 
 In this paper  we have studied the problem of  lifetime coverage optimization in
 WSNs. We designed  a new protocol, called Lifetime  Coverage Optimization, which
 
 In this paper  we have studied the problem of  lifetime coverage optimization in
 WSNs. We designed  a new protocol, called Lifetime  Coverage Optimization, which

-schedules  node' activities  (wake up and  sleep  stages) with  the objective  of
+schedules nodes'  activities (wake up  and sleep  stages) with the  objective of

 maintaining a  good coverage ratio  while maximizing the network  lifetime. This
 protocol is  applied in a distributed  way in regular subregions  obtained after
 partitioning the area of interest in a preliminary step. It works in periods and
 maintaining a  good coverage ratio  while maximizing the network  lifetime. This
 protocol is  applied in a distributed  way in regular subregions  obtained after
 partitioning the area of interest in a preliminary step. It works in periods and