correction de quelques coquilles

[LiCO.git] / LiCO_Journal.tex

diff --git a/LiCO_Journal.tex b/LiCO_Journal.tex
index f18c11d59f815b8bcdeed5ff28ed673b841899f4..051f1116dd59e60d1a62b4649110a63b683c369b 100644 (file)
--- a/LiCO_Journal.tex
+++ b/LiCO_Journal.tex
@@ -56,12 +56,12 @@
 
 \begin{abstract}
 The most important problem in a Wireless Sensor Network (WSN) is to optimize the
 
 \begin{abstract}
 The most important problem in a Wireless Sensor Network (WSN) is to optimize the

-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
+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
 this paper,  we propose such an approach called Perimeter-based Coverage Optimization
 improve  power  management,  lifetime coverage  optimization  provides  activity
 scheduling which ensures sensing coverage while minimizing the energy cost. In
 this paper,  we propose such an approach called Perimeter-based Coverage Optimization

-protocol (PeCO).   It is a  hybrid of centralized and distributed methods: the
+protocol (PeCO). 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 repeats  periodically four  stages:
 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 repeats  periodically four  stages:


@@ -69,16 +69,16 @@ distributed among sensor nodes in each  subregion.
 %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.
 %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 our approach lies essentially in the formulation of a new
-mathematical optimization  model based on  perimeter coverage level  to schedule
+The novelty of our approach lies essentially in the formulation of a new
+mathematical optimization  model based on the  perimeter coverage level  to schedule

 sensors' activities.  Extensive simulation experiments have been performed using
 sensors' activities.  Extensive simulation experiments have been performed using

-OMNeT++, the  discrete event simulator, to  demonstrate that PeCO  is capable to
+OMNeT++, the  discrete event simulator, to  demonstrate that PeCO  can

 offer longer lifetime coverage for WSNs in comparison with some other protocols.
 \end{abstract} 
 
 % Note that keywords are not normally used for peerreview papers.
 \begin{IEEEkeywords}
 offer longer lifetime coverage for WSNs in comparison with some other protocols.
 \end{abstract} 
 
 % Note that keywords are not normally used for peerreview papers.
 \begin{IEEEkeywords}

-Wireless Sensor Networks, Area Coverage, Network lifetime, Optimization, Scheduling.
+Wireless Sensor Networks, Area Coverage, Network Lifetime, Optimization, Scheduling.

 \end{IEEEkeywords}
 
 \IEEEpeerreviewmaketitle
 \end{IEEEkeywords}
 
 \IEEEpeerreviewmaketitle


@@ -105,12 +105,12 @@ The energy needed  by an active sensor node to  perform sensing, processing, and
 communication is supplied by a power supply which is a battery. This battery has
 a limited energy provision and it may  be unsuitable or impossible to replace or
 recharge it in  most applications. Therefore it is necessary  to deploy WSN with
 communication is supplied by a power supply which is a battery. This battery has
 a limited energy provision and it may  be unsuitable or impossible to replace or
 recharge it in  most applications. Therefore it is necessary  to deploy WSN with

-high density in order to increase the reliability and to exploit node redundancy
+high density in order to increase  reliability and to exploit node redundancy

 thanks to energy-efficient activity  scheduling approaches.  Indeed, the overlap
 of sensing  areas can be exploited  to schedule alternatively some  sensors in a
 low power sleep mode and thus save  energy. Overall, the main question that must
 be answered is: how to extend the lifetime coverage of a WSN as long as possible
 thanks to energy-efficient activity  scheduling approaches.  Indeed, the overlap
 of sensing  areas can be exploited  to schedule alternatively some  sensors in a
 low power sleep mode and thus save  energy. Overall, the main question that must
 be answered is: how to extend the lifetime coverage of a WSN as long as possible

-while  ensuring   a  high  level  of   coverage?   So,  this  last   years  many
+while  ensuring   a  high  level  of   coverage?   These past few years  many

 energy-efficient mechanisms have been suggested  to retain energy and extend the
 lifetime of the WSNs~\cite{rault2014energy}.
 
 energy-efficient mechanisms have been suggested  to retain energy and extend the
 lifetime of the WSNs~\cite{rault2014energy}.
 


@@ -125,7 +125,7 @@ This paper makes the following contributions.
 \item We have devised 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 and
 \item We have devised 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 and

-  temporal subdivision.   On the one hand,  the area of interest  if divided into
+  temporal subdivision.   On the one hand,  the area of interest  is 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
   choose a  leader which will schedule  nodes' activities, and this  grouping of
   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
   choose a  leader which will schedule  nodes' activities, and this  grouping of


@@ -172,7 +172,7 @@ fixed area  must be monitored, while  target coverage~\cite{yang2014novel} refer
 to  the objective  of coverage  for a  finite number  of discrete  points called
 targets,  and  barrier coverage~\cite{HeShibo}\cite{kim2013maximum}  focuses  on
 preventing  intruders   from  entering   into  the   region  of   interest.   In
 to  the objective  of coverage  for a  finite number  of discrete  points called
 targets,  and  barrier coverage~\cite{HeShibo}\cite{kim2013maximum}  focuses  on
 preventing  intruders   from  entering   into  the   region  of   interest.   In

-\cite{Deng2012}  authors  transform the  area  coverage  problem to  the  target
+\cite{Deng2012}  authors  transform the  area  coverage  problem into  the  target

 coverage one 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
 coverage one 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


@@ -211,14 +211,14 @@ own activity scheduling  after an information exchange with  its neighbors.  The
 main interest of such an 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)
 main interest of such an 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,
+it may make 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
 its high  cost in communications needed to  transmit to a single  node, the base
 station which will globally schedule  nodes' activities, data from all the other
 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
 its high  cost in communications needed to  transmit to a single  node, the base
 station which will globally schedule  nodes' activities, data from all the other

-sensor nodes  in the area.  The price  in communications can be  very huge since
+sensor nodes  in the area.  The price  in communications can be  huge since

 long range  communications will be  needed. In fact  the larger the WNS  is, the
 higher the  communication and  thus the energy  cost are.   {\it In order  to be
   suitable for large-scale  networks, in the PeCO protocol,  the area of interest
 long range  communications will be  needed. In fact  the larger the WNS  is, the
 higher the  communication and  thus the energy  cost are.   {\it In order  to be
   suitable for large-scale  networks, in the PeCO protocol,  the area of interest


@@ -227,7 +227,7 @@ higher the  communication and  thus the energy  cost are.   {\it In order  to be
   period.  Thus our  protocol is  scalable  and is a  globally distributed  method,
   whereas it is centralized in each subregion.}
 
   period.  Thus our  protocol is  scalable  and is a  globally distributed  method,
   whereas it is centralized in each subregion.}
 

-Various  coverage scheduling  algorithms have  been developed  this last  years.
+Various  coverage scheduling  algorithms have  been developed  these past few years.

 Many of  them, dealing with  the maximization of the  number of cover  sets, are
 heuristics.   These  heuristics involve  the  construction  of  a cover  set  by
 including in priority the sensor nodes  which cover critical targets, that is to
 Many of  them, dealing with  the maximization of the  number of cover  sets, are
 heuristics.   These  heuristics involve  the  construction  of  a cover  set  by
 including in priority the sensor nodes  which cover critical targets, that is to


@@ -286,7 +286,7 @@ used~\cite{castano2013column,rossi2012exact,deschinkel2012column}. {\it  In the
 \section{ The PeCO Protocol Description}
 \label{sec:The PeCO Protocol Description}
 
 \section{ The PeCO Protocol Description}
 \label{sec:The PeCO Protocol Description}
 

-\noindent  In  this  section,  we  describe in  details  our  Lifetime  Coverage
+\noindent  In  this  section,  we  describe in  details  our Perimeter-based  Coverage

 Optimization protocol.  First we present the  assumptions we made and the models
 we considered (in particular the perimeter coverage one), second we describe the
 background idea of our protocol, and third  we give the outline of the algorithm
 Optimization protocol.  First we present the  assumptions we made and the models
 we considered (in particular the perimeter coverage one), second we describe the
 background idea of our protocol, and third  we give the outline of the algorithm


@@ -303,7 +303,7 @@ distributed in  a bounded sensor field  is considered. The wireless  sensors are
 deployed in high density  to ensure initially a high coverage  ratio of the area
 of interest.  We  assume that all the  sensor nodes are homogeneous  in terms of
 communication,  sensing,  and  processing capabilities  and  heterogeneous  from
 deployed in high density  to ensure initially a high coverage  ratio of the area
 of interest.  We  assume that all the  sensor nodes are homogeneous  in terms of
 communication,  sensing,  and  processing capabilities  and  heterogeneous  from

-energy provision  point of  view.  The  location information  is available  to a
+the energy provision  point of  view.  The  location information  is available  to a

 sensor node either  through hardware such as embedded GPS  or location discovery
 algorithms.   We  assume  that  each  sensor  node  can  directly  transmit  its
 measurements to  a mobile  sink node.  For  example, a sink  can be  an unmanned
 sensor node either  through hardware such as embedded GPS  or location discovery
 algorithms.   We  assume  that  each  sensor  node  can  directly  transmit  its
 measurements to  a mobile  sink node.  For  example, a sink  can be  an unmanned


@@ -315,7 +315,7 @@ sensor nodes  have a constant sensing  range $R_s$.  Thus, all  the space points
 within a disk centered at a sensor with  a radius equal to the sensing range are
 said to be covered  by this sensor. We also assume  that the communication range
 $R_c$ satisfies $R_c  \geq 2 \cdot R_s$. In fact,  Zhang and Zhou~\cite{Zhang05}
 within a disk centered at a sensor with  a radius equal to the sensing range are
 said to be covered  by this sensor. We also assume  that the communication range
 $R_c$ 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
+proved  that if  the  transmission  range fulfills  the  previous hypothesis,  the

 complete coverage of a convex area implies connectivity among active nodes.
 
 The PeCO protocol  uses the  same perimeter-coverage  model as  Huang and
 complete coverage of a convex area implies connectivity among active nodes.
 
 The PeCO protocol  uses the  same perimeter-coverage  model as  Huang and


@@ -327,9 +327,9 @@ $k$-covered if and only if each sensor in the network is $k$-perimeter-covered (
 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
 its  perimeter (the  perimeter  of the  disk  covered by  the  sensor) for  each
 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
 its  perimeter (the  perimeter  of the  disk  covered by  the  sensor) for  each

-neighbor  the  two  points  resulting  from  intersection  of  the  two  sensing
+neighbor  the  two  points  resulting  from the intersection  of  the  two  sensing

 areas. These points are denoted for  neighbor~$i$ by $iL$ and $iR$, respectively
 areas. These points are denoted for  neighbor~$i$ by $iL$ and $iR$, respectively

-for  left and  right from  neighbor  point of  view.  The  resulting couples  of
+for  left and  right from  a neighboing  point of  view.  The  resulting couples  of

 intersection points subdivide  the perimeter of sensor~$0$  into portions called
 arcs.
 
 intersection points subdivide  the perimeter of sensor~$0$  into portions called
 arcs.
 


@@ -427,7 +427,7 @@ above is thus given by the sixth line of the table.
 
 %The optimization algorithm that used by PeCO 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.
 
 
 %The optimization algorithm that used by PeCO 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 the PeCO  protocol, scheduling of sensor  nodes' activities is formulated  with an
+In the PeCO  protocol, the scheduling of the sensor  nodes' activities is formulated  with an

 integer program  based on  coverage intervals. The  formulation of  the coverage
 optimization problem is  detailed in~section~\ref{cp}.  Note that  when a sensor
 node  has a  part of  its sensing  range outside  the WSN  sensing field,  as in
 integer program  based on  coverage intervals. The  formulation of  the coverage
 optimization problem is  detailed in~section~\ref{cp}.  Note that  when a sensor
 node  has a  part of  its sensing  range outside  the WSN  sensing field,  as in


@@ -557,7 +557,7 @@ protocol applied by a sensor node $s_k$ where $k$ is the node index in the WSN.
 \end{algorithm}
 
 In this  algorithm, K.CurrentSize and K.PreviousSize  respectively represent the
 \end{algorithm}
 
 In this  algorithm, K.CurrentSize and K.PreviousSize  respectively represent the

-current number and  the previous number of alive nodes in  the subnetwork of the
+current number and  the previous number of living nodes in  the subnetwork of the

 subregion.  Initially, the sensor 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  determines its position  and its subregion  using an
 subregion.  Initially, the sensor 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  determines its position  and its subregion  using an


@@ -565,7 +565,7 @@ embedded  GPS or a  location discovery  algorithm. After  that, all  the sensors
 collect position coordinates,  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
 collect position coordinates,  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
+leader, in order of priority,  are: larger numbers of neighbors, larger remaining

 energy, and  then in case  of equality, larger  index.  Once chosen,  the leader
 collects information to formulate and  solve the integer program which allows to
 construct the set of active sensors in the sensing stage.
 energy, and  then in case  of equality, larger  index.  Once chosen,  the leader
 collects information to formulate and  solve the integer program which allows to
 construct the set of active sensors in the sensing stage.


@@ -574,11 +574,11 @@ construct the set of active sensors in the sensing stage.
 
 % The leader has the responsibility of applying the integer program algorithm (see section~\ref{cp}), which provides a set of sensors planned to be active in the sensing stage.  As leader, it will send an Active-Sleep packet to each sensor in the same subregion to inform it if it has to be active or not. On the contrary, if the sensor is not the leader, it will wait for the Active-Sleep packet to know its state for the sensing stage.
 
 
 % The leader has the responsibility of applying the integer program algorithm (see section~\ref{cp}), which provides a set of sensors planned to be active in the sensing stage.  As leader, it will send an Active-Sleep packet to each sensor in the same subregion to inform it if it has to be active or not. On the contrary, if the sensor is not the leader, it will wait for the Active-Sleep packet to know its state for the sensing stage.
 

-\section{Lifetime Coverage problem formulation}
+\section{Perimeter-based Coverage Problem Formulation}

 \label{cp}
 
 \noindent In this  section, the coverage model is  mathematically formulated. We
 \label{cp}
 
 \noindent In this  section, the coverage model is  mathematically formulated. We

-start  with a  description of  the notations  that will  be used  throughout the
+start  with a  description of the notations that will  be used  throughout the

 section.
 
 First, we have the following sets:
 section.
 
 First, we have the following sets:


@@ -670,7 +670,7 @@ relative importance of satisfying the associated level of coverage. For example,
 weights associated with  coverage intervals of a specified part  of a region may
 be  given by a  relatively larger  magnitude than  weights associated  with another
 region. This  kind of integer program  is inspired from the  model developed for
 weights associated with  coverage intervals of a specified part  of a region may
 be  given by 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
+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
 \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


@@ -736,11 +736,11 @@ pre-sensing phases.  According  to the interval of initial energy,  a sensor may
 be active during at most 20 periods.
 
 The values  of $\alpha^j_i$ and  $\beta^j_i$ have been  chosen to ensure  a good
 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
+network coverage and a longer WSN lifetime.  We have given a higher priority to

 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
 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
+sensor~$j$.  On the  other hand,  we have assigned to
+$\beta^j_i$ a value which is slightly lower 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
 in covering the interval.
 
 We introduce the following performance metrics to evaluate the efficiency of our


@@ -768,7 +768,7 @@ approach.
   points in  the sensing  field.  In  our simulations  we have  set a  layout of
   $N~=~51~\times~26~=~1326$~grid points.
 \item {\bf Active Sensors Ratio (ASR)}: a  major objective of our protocol is to
   points in  the sensing  field.  In  our simulations  we have  set a  layout of
   $N~=~51~\times~26~=~1326$~grid points.
 \item {\bf Active Sensors Ratio (ASR)}: a  major objective of our protocol is to

-  activate nodes  as few  as possible,  in order  to minimize  the communication
+  activate  as few nodes as possible,  in order  to minimize  the communication

   overhead and maximize the WSN lifetime. The active sensors ratio is defined as
   follows:
   \begin{equation*}
   overhead and maximize the WSN lifetime. The active sensors ratio is defined as
   follows:
   \begin{equation*}


@@ -805,7 +805,7 @@ approach.
 In  order  to  assess and  analyze  the  performance  of  our protocol  we  have
 implemented PeCO protocol in  OMNeT++~\cite{varga} simulator.  Besides PeCO, two
 other  protocols,  described  in  the  next paragraph,  will  be  evaluated  for
 In  order  to  assess and  analyze  the  performance  of  our protocol  we  have
 implemented PeCO protocol in  OMNeT++~\cite{varga} simulator.  Besides PeCO, two
 other  protocols,  described  in  the  next paragraph,  will  be  evaluated  for

-comparison purposes.   The simulations were run  on a laptop DELL  with an Intel
+comparison purposes.   The simulations were run  on a DELL laptop  with an Intel

 Core~i3~2370~M (2.4~GHz)  processor (2  cores) whose MIPS  (Million Instructions
 Per Second) rate  is equal to 35330. To  be consistent with the use  of a sensor
 node based on  Atmels AVR ATmega103L microcontroller (6~MHz) having  a MIPS rate
 Core~i3~2370~M (2.4~GHz)  processor (2  cores) whose MIPS  (Million Instructions
 Per Second) rate  is equal to 35330. To  be consistent with the use  of a sensor
 node based on  Atmels AVR ATmega103L microcontroller (6~MHz) having  a MIPS rate


@@ -816,7 +816,7 @@ 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) \cite{glpk} through a Branch-and-Bound method.
 
 optimization solver  GLPK (GNU  linear Programming Kit  available in  the public
 domain) \cite{glpk} through a Branch-and-Bound method.
 

-As said previously, the PeCO is  compared with three other approaches. The first
+As said previously, the PeCO is  compared to three other approaches. The first

 one,  called  DESK,  is  a  fully distributed  coverage  algorithm  proposed  by
 \cite{ChinhVu}. The second one,  called GAF~\cite{xu2001geography}, consists in
 dividing  the monitoring  area into  fixed  squares. Then,  during the  decision
 one,  called  DESK,  is  a  fully distributed  coverage  algorithm  proposed  by
 \cite{ChinhVu}. The second one,  called GAF~\cite{xu2001geography}, consists in
 dividing  the monitoring  area into  fixed  squares. Then,  during the  decision


@@ -824,22 +824,22 @@ phase, in each square, one sensor is  chosen to remain active during the sensing
 phase. The last  one, the DiLCO protocol~\cite{Idrees2}, is  an improved version
 of a research work we presented in~\cite{idrees2014coverage}. Let us notice that
 PeCO and  DiLCO protocols are  based on the  same framework. In  particular, the
 phase. The last  one, the DiLCO protocol~\cite{Idrees2}, is  an improved version
 of a research work we presented in~\cite{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 chosen because
-it corresponds to the configuration producing  the better results for DiLCO. 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 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 PeCO protocol objective is to reach a desired level of coverage for each
+whereas the PeCO 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 ($l=1$).
 
 \subsubsection{\bf Coverage Ratio}
 
 Figure~\ref{fig333}  shows the  average coverage  ratio for  200 deployed  nodes
 sensor perimeter. In our experimentations, we chose a level of coverage equal to
 one ($l=1$).
 
 \subsubsection{\bf Coverage Ratio}
 
 Figure~\ref{fig333}  shows the  average coverage  ratio for  200 deployed  nodes

-obtained with the  four protocols. DESK, GAF, and DiLCO  provide a little better
-coverage ratio with respectively 99.99\%,  99.91\%, and 99.02\%, against 98.76\%
+obtained with the  four protocols. DESK, GAF, and DiLCO  provide a slightly better
+coverage ratio with respectively 99.99\%,  99.91\%, and 99.02\%, compared to the 98.76\%

 produced by  PeCO for the  first periods. This  is due to  the fact that  at the
 produced by  PeCO for the  first periods. This  is due to  the fact that  at the

-beginning  DiLCO protocol  puts in  sleep status  more redundant  sensors (which
+beginning the DiLCO protocol  puts to  sleep status  more redundant  sensors (which

 slightly decreases the coverage ratio), while the three other protocols activate
 more sensor  nodes. Later, when the  number of periods is  beyond~70, it clearly
 appears that  PeCO provides a better  coverage ratio and keeps  a coverage ratio
 slightly decreases the coverage ratio), while the three other protocols activate
 more sensor  nodes. Later, when the  number of periods is  beyond~70, it clearly
 appears that  PeCO provides a better  coverage ratio and keeps  a coverage ratio


@@ -863,7 +863,7 @@ substantial increase of the coverage performance.
 \subsubsection{\bf Active Sensors Ratio}
 
 Having the less active sensor nodes in  each period is essential to minimize the
 \subsubsection{\bf Active Sensors Ratio}
 
 Having the less active sensor nodes in  each period is essential to minimize the

-energy consumption  and so  maximize the network  lifetime.  Figure~\ref{fig444}
+energy consumption  and thus to  maximize the network  lifetime.  Figure~\ref{fig444}

 shows the  average active nodes ratio  for 200 deployed nodes.   We observe that
 DESK and  GAF have 30.36  \% and  34.96 \% active  nodes for the  first fourteen
 rounds and  DiLCO and PeCO  protocols compete perfectly  with only 17.92  \% and
 shows the  average active nodes ratio  for 200 deployed nodes.   We observe that
 DESK and  GAF have 30.36  \% and  34.96 \% active  nodes for the  first fourteen
 rounds and  DiLCO and PeCO  protocols compete perfectly  with only 17.92  \% and


@@ -881,9 +881,9 @@ Figure \ref{fig333}.
 
 \subsubsection{\bf Energy Consumption}
 
 
 \subsubsection{\bf Energy Consumption}
 

-We study the effect of the energy  consumed by the WSN during the communication,
+We studied the effect of the energy  consumed by the WSN during the communication,

 computation, listening, active, and sleep status for different network densities
 computation, listening, active, and sleep status for different network densities

-and  compare  it for  the  four  approaches.  Figures~\ref{fig3EC}(a)  and  (b)
+and  compared  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 PeCO 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 PeCO protocol  is the
 most competitive  from the energy  consumption point of  view. As shown  in both


@@ -913,17 +913,17 @@ while keeping a good coverage level.
 
 \subsubsection{\bf Network Lifetime}
 
 
 \subsubsection{\bf Network Lifetime}
 

-We observe the superiority of PeCO and DiLCO protocols in comparison against the
+We observe the superiority of PeCO and DiLCO protocols in comparison with the

 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
 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
+increases with the size  of the network, and it is clearly   largest for DiLCO

 and PeCO  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 twice longer with  PeCO 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
 and PeCO  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 twice longer with  PeCO 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
+ time, and the lifetime with a coverage  of 50\% is far  longer than with

 95\%.
 
 \begin{figure}[h!]
 95\%.
 
 \begin{figure}[h!]


@@ -943,13 +943,13 @@ Figure~\ref{figLTALL}  compares  the  lifetime  coverage of  our  protocols  for
 different coverage  ratios. We denote by  Protocol/50, Protocol/80, Protocol/85,
 Protocol/90, and  Protocol/95 the amount  of time  during which the  network can
 satisfy an area coverage greater than $50\%$, $80\%$, $85\%$, $90\%$, and $95\%$
 different coverage  ratios. We denote by  Protocol/50, Protocol/80, Protocol/85,
 Protocol/90, and  Protocol/95 the amount  of time  during which the  network can
 satisfy an area coverage greater than $50\%$, $80\%$, $85\%$, $90\%$, and $95\%$

-respectively, where  Protocol is DiLCO  or PeCO.  Indeed there  are applications
+respectively, where the term Protocol refers to  DiLCO  or PeCO.  Indeed there  are applications

 that do not require a 100\% coverage of  the area to be monitored. PeCO might be
 an interesting  method since  it achieves  a good balance  between a  high level
 coverage ratio and network lifetime. PeCO 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 in  that case PeCO is
 that do not require a 100\% coverage of  the area to be monitored. PeCO might be
 an interesting  method since  it achieves  a good balance  between a  high level
 coverage ratio and network lifetime. PeCO 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 in  that case PeCO is

-not so bad for the smallest network sizes.
+not ineffective 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}


@@ -963,8 +963,8 @@ not so bad for the smallest network sizes.
 \section{Conclusion and Future Works}
 \label{sec:Conclusion and Future Works}
 
 \section{Conclusion and Future Works}
 \label{sec:Conclusion and Future Works}
 

-In this paper  we have studied the problem of  lifetime coverage optimization in
-WSNs. We have designed  a new protocol, called Lifetime  Coverage Optimization, which
+In this paper  we have studied the problem of  Perimeter-based Coverage Optimization in
+WSNs. We have designed  a new protocol, called Perimeter-based  Coverage Optimization, which

 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
 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


@@ -987,7 +987,7 @@ simulation  results  show   that  PeCO  is  more   energy-efficient  than  other
 approaches, with respect to lifetime,  coverage ratio, active sensors ratio, and
 energy consumption.
 %Indeed, when dealing with large and dense WSNs, a distributed optimization approach on the subregions of WSN like the one we are proposed allows to reduce the difficulty of a single global optimization problem by partitioning it in many smaller problems, one per subregion, that can be solved more easily. We have  identified different  research directions  that arise  out of  the work presented here.
 approaches, with respect to lifetime,  coverage ratio, active sensors ratio, and
 energy consumption.
 %Indeed, when dealing with large and dense WSNs, a distributed optimization approach on the subregions of WSN like the one we are proposed allows to reduce the difficulty of a single global optimization problem by partitioning it in many smaller problems, one per subregion, that can be solved more easily. We have  identified different  research directions  that arise  out of  the work presented here.

-We plan to extend our framework such that the schedules are planned for multiple
+We plan to extend our framework so that the schedules are planned for multiple

 sensing periods.
 %in order to compute all active sensor schedules in only one step for many periods;
 We also want  to improve our integer program to  take into account heterogeneous
 sensing periods.
 %in order to compute all active sensor schedules in only one step for many periods;
 We also want  to improve our integer program to  take into account heterogeneous


@@ -998,7 +998,7 @@ sensor-testbed to evaluate it in real world applications.
 
 \section*{Acknowledgments}
 
 
 \section*{Acknowledgments}
 

-\noindent  As a  Ph.D.   student, Ali  Kadhum IDREES  would  like to  gratefully
+\noindent  As a  Ph.D.   student, Ali Kadhum IDREES  would  like to  gratefully

 acknowledge the  University of Babylon -  IRAQ for financial support  and Campus
 France for the  received support. This work is also partially funded by the Labex ACTION program (contract ANR-11-LABX-01-01). 
 
 acknowledge the  University of Babylon -  IRAQ for financial support  and Campus
 France for the  received support. This work is also partially funded by the Labex ACTION program (contract ANR-11-LABX-01-01).