Last modifications

[LiCO.git] / PeCO-EO / articleeo.tex~

diff --git a/PeCO-EO/articleeo.tex~ b/PeCO-EO/articleeo.tex~
index d4ae9d964e548d9abc49a9d0a6aba66047c52d48..5ba7f55932dd982a40e034a21050950216875f02 100644 (file)
--- a/PeCO-EO/articleeo.tex~
+++ b/PeCO-EO/articleeo.tex~
@@ -5,6 +5,7 @@
 %\usepackage[linesnumbered,ruled,vlined,commentsnumbered]{algorithm2e}
 %\renewcommand{\algorithmcfname}{ALGORITHM}
 \usepackage{indentfirst}
 %\usepackage[linesnumbered,ruled,vlined,commentsnumbered]{algorithm2e}
 %\renewcommand{\algorithmcfname}{ALGORITHM}
 \usepackage{indentfirst}

+\usepackage{color}

 \usepackage[algo2e,ruled,vlined]{algorithm2e}
 \begin{document}
 
 \usepackage[algo2e,ruled,vlined]{algorithm2e}
 \begin{document}
 


@@ -15,7 +16,7 @@
 \title{{\itshape Perimeter-based Coverage Optimization \\
   to Improve Lifetime in Wireless Sensor Networks}}
 
 \title{{\itshape Perimeter-based Coverage Optimization \\
   to Improve Lifetime in Wireless Sensor Networks}}
 

-\author{Ali Kadhum Idrees$^{a,b}$, Karine Deschinkel$^{a}$$^{\ast}$\thanks{$^\ast$Corresponding author. Email: karine.deschinkel@univ-fcomte.fr}, Michel Salomon$^{a}$ and Rapha\"el Couturier $^{a}$
+\author{Ali Kadhum Idrees$^{a,b}$, Karine Deschinkel$^{a}$$^{\ast}$\thanks{$^\ast$Corresponding author. Email: karine.deschinkel@univ-fcomte.fr}, Michel Salomon$^{a}$, and Rapha\"el Couturier $^{a}$

   $^{a}${\em{FEMTO-ST Institute, UMR 6174 CNRS, \\
   University Bourgogne Franche-Comt\'e, Belfort, France}} \\ 
   $^{b}${\em{Department of Computer Science, University of Babylon, Babylon, Iraq}}
   $^{a}${\em{FEMTO-ST Institute, UMR 6174 CNRS, \\
   University Bourgogne Franche-Comt\'e, Belfort, France}} \\ 
   $^{b}${\em{Department of Computer Science, University of Babylon, Babylon, Iraq}}


@@ -36,7 +37,7 @@ distributed among sensor  nodes in each subregion.  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 demonstrate that PeCO can offer longer lifetime
 lies essentially  in the  formulation of a  new mathematical  optimization model
 based  on  the  perimeter  coverage   level  to  schedule  sensors'  activities.
 Extensive simulation experiments demonstrate that PeCO can offer longer lifetime

-coverage for WSNs in comparison with some other protocols.
+coverage for WSNs compared to other protocols.

 
 \begin{keywords}
   Wireless Sensor Networks, Area Coverage, Energy efficiency, Optimization, Scheduling.
 
 \begin{keywords}
   Wireless Sensor Networks, Area Coverage, Energy efficiency, Optimization, Scheduling.


@@ -48,34 +49,34 @@ coverage for WSNs in comparison with some other protocols.
 \label{sec:introduction}
 
 The continuous progress in Micro  Electro-Mechanical Systems (MEMS) and wireless
 \label{sec:introduction}
 
 The continuous progress in Micro  Electro-Mechanical Systems (MEMS) and wireless

-communication hardware has  given rise to the opportunity to  use large networks
+communication hardware has given rise to the opportunity of using large networks

 of      tiny       sensors,      called      Wireless       Sensor      Networks
 (WSN)~\citep{akyildiz2002wireless,puccinelli2005wireless}, to fulfill monitoring
 tasks.   A  WSN  consists  of  small low-powered  sensors  working  together  by
 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
 of      tiny       sensors,      called      Wireless       Sensor      Networks
 (WSN)~\citep{akyildiz2002wireless,puccinelli2005wireless}, to fulfill monitoring
 tasks.   A  WSN  consists  of  small low-powered  sensors  working  together  by
 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,
+user by means of sink nodes. The features  of a WSN makes it suitable for a wide
+range of applications in areas  such as business, environment, health, industry,

 military, and so on~\citep{yick2008wireless}.  Typically, a sensor node contains
 three main components~\citep{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
 military, and so on~\citep{yick2008wireless}.  Typically, a sensor node contains
 three main components~\citep{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

-communication unit for data transmission and receiving.
+communication unit for data transmission and reception.

 
 The energy needed  by an active sensor node to  perform sensing, processing, and
 
 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
+communication is provided 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
 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 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
-while  ensuring  a   high  level  of  coverage?   These  past   few  years  many
+recharge in most applications. Therefore it is necessary to deploy WSN with 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 is it possible to extend the lifetime coverage of a WSN as long
+as possible 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~\citep{rault2014energy}.
 
 energy-efficient mechanisms have been suggested  to retain energy and extend the
 lifetime of the WSNs~\citep{rault2014energy}.
 

-This paper makes the following contributions.
+This paper makes the following contributions :

 \begin{enumerate}
 \item A  framework is devised  to schedule  nodes to be  activated alternatively
   such that  the network  lifetime is  prolonged while  ensuring that  a certain
 \begin{enumerate}
 \item A  framework is devised  to schedule  nodes to be  activated alternatively
   such that  the network  lifetime is  prolonged while  ensuring that  a certain


@@ -88,13 +89,13 @@ This paper makes the following contributions.
   architecture.
 \item A new  mathematical optimization model is proposed.  Instead  of trying to
   cover a set of specified points/targets as  in most of the methods proposed in
   architecture.
 \item A new  mathematical optimization model is proposed.  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.  Hence,  an
-  optimal  schedule will  be  obtained by  minimizing a  weighted  sum of  these
-  deviations.
+  the literature,  we formulate a  mixed-integer program based on  the perimeter
+  coverage of each sensor.  The model  involves integer variables to capture the
+  deviations  between the  actual  level  of coverage  and  the required  level.
+  Hence, an  optimal schedule will be  obtained by minimizing a  weighted sum of
+  these deviations.

 \item Extensive  simulation experiments are  conducted using the  discrete event
 \item Extensive  simulation experiments are  conducted using the  discrete event

-  simulator  OMNeT++, to  demonstrate the  efficiency of  our protocol.  We have
+  simulator OMNeT++,  to demonstrate  the efficiency of  our protocol.   We have

   compared  the  PeCO  protocol  to  two approaches  found  in  the  literature:
   DESK~\citep{ChinhVu} and GAF~\citep{xu2001geography}, and also to our previous
   protocol DiLCO published in~\citep{Idrees2}. DiLCO  uses the same framework as
   compared  the  PeCO  protocol  to  two approaches  found  in  the  literature:
   DESK~\citep{ChinhVu} and GAF~\citep{xu2001geography}, and also to our previous
   protocol DiLCO published in~\citep{Idrees2}. DiLCO  uses the same framework as


@@ -125,12 +126,12 @@ to  the objective  of coverage  for a  finite number  of discrete  points called
 targets,   and   barrier  coverage~\citep{HeShibo,kim2013maximum}   focuses   on
 preventing  intruders   from  entering   into  the   region  of   interest.   In
 \citep{Deng2012} authors  transform the  area coverage  problem into  the target
 targets,   and   barrier  coverage~\citep{HeShibo,kim2013maximum}   focuses   on
 preventing  intruders   from  entering   into  the   region  of   interest.   In
 \citep{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
-\citep{Huang:2003:CPW:941350.941367}  authors prove  that if  the perimeters  of
-sensors are sufficiently  covered it will be  the case for the  whole area. They
-provide an algorithm in $O(nd~log~d)$  time to compute the perimeter-coverage of
-each sensor. $d$ denotes  the maximum number of sensors that  are neighbors to a
+coverage one, taking into account the intersection points among disks of sensors
+nodes   or    between   disks    of   sensor    nodes   and    boundaries.    In
+\citep{huang2005coverage} authors  prove that if  the perimeters of  the sensors
+are sufficiently covered it will be the case for the whole area. They provide an
+algorithm  in  $O(nd~log~d)$ time  to  compute  the perimeter-coverage  of  each
+sensor.  $d$ denotes  the maximum  number  of sensors  that are  neighbors to  a

 sensor, and  $n$ is the  total number  of sensors in  the network. {\it  In PeCO
   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
 sensor, and  $n$ is the  total number  of sensors in  the network. {\it  In PeCO
   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


@@ -139,7 +140,7 @@ sensor, and  $n$ is the  total number  of sensors in  the network. {\it  In PeCO
 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
 non-disjoint)  \citep{wang2011coverage},  where  each set  completely  covers  a
 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
 non-disjoint)  \citep{wang2011coverage},  where  each set  completely  covers  a

-region of interest,  and to activate these set covers  successively. The network
+region of interest,  and to successively activate these set covers. The network

 activity can be planned in advance and scheduled for the entire network lifetime
 or organized  in periods,  and the  set of  active sensor  nodes decided  at the
 beginning of each  period \citep{ling2009energy}. In fact,  many authors propose
 activity can be planned in advance and scheduled for the entire network lifetime
 or organized  in periods,  and the  set of  active sensor  nodes decided  at the
 beginning of each  period \citep{ling2009energy}. In fact,  many authors propose


@@ -162,22 +163,22 @@ algorithms~\citep{ChinhVu,qu2013distributed,yangnovel}  each  sensor decides  of
 its 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
 its 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)  it may  make a  bad  decision leading  to a  global suboptimal  solution.
+each node has  information on its immediate neighbors only  (usually the one-hop
+ones),  it may  make a  bad decision  leading to  a global  suboptimal solution.

 Conversely,                                                          centralized
 algorithms~\citep{cardei2005improving,zorbas2010solving,pujari2011high}   always
 Conversely,                                                          centralized
 algorithms~\citep{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  huge since long
-range communications will be needed. In fact  the larger the WSN, the higher the
+provide nearly  optimal solutions 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 huge since  long range
+communications  will be  needed. In  fact  the larger  the WSN,  the higher  the

 communication  energy  cost.  {\it  In  order  to  be suitable  for  large-scale
 communication  energy  cost.  {\it  In  order  to  be suitable  for  large-scale

-  networks,  in PeCO  protocol  the area  of interest  is  divided into  several
+  networks, in  the PeCO protocol the  area of interest is  divided into several

   smaller subregions, and in each one, a  node called the leader is in charge of
   smaller subregions, and in each one, a  node called the leader is in charge of

-  selecting the  active sensors for the  current period.  Thus PeCO  protocol is
-  scalable and a globally distributed method,  whereas it is centralized in each
-  subregion.}
+  selecting the active  sensors for the current period.  Thus  the PeCO protocol
+  is scalable  and a globally distributed  method, whereas it is  centralized in
+  each subregion.}

 
 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
 
 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


@@ -195,27 +196,27 @@ practiced techniques for  solving linear programs with too  many variables, have
 also                                                                        been
 used~\citep{castano2013column,doi:10.1080/0305215X.2012.687732,deschinkel2012column}.
 {\it In  the PeCO  protocol, each leader,  in charge of  a subregion,  solves an
 also                                                                        been
 used~\citep{castano2013column,doi:10.1080/0305215X.2012.687732,deschinkel2012column}.
 {\it In  the PeCO  protocol, each leader,  in charge of  a subregion,  solves an

-  integer program which  has a twofold objective: minimize  the overcoverage and
+  integer program which  has a twofold objective: minimizing  the overcoverage and

   the undercoverage of the perimeter of each sensor.}
 
 The  authors   in  \citep{Idrees2}  propose  a   Distributed  Lifetime  Coverage
 Optimization (DiLCO)  protocol, which  maintains the  coverage and  improves the
 lifetime  in WSNs.   It is  an  improved version  of a  research work  presented
 in~\citep{idrees2014coverage}.  First, the area  of interest is partitioned into
   the undercoverage of the perimeter of each sensor.}
 
 The  authors   in  \citep{Idrees2}  propose  a   Distributed  Lifetime  Coverage
 Optimization (DiLCO)  protocol, which  maintains the  coverage and  improves the
 lifetime  in WSNs.   It is  an  improved version  of a  research work  presented
 in~\citep{idrees2014coverage}.  First, the area  of interest is partitioned into

-subregions using a divide-and-conquer method. DiLCO protocol is then distributed
-on the  sensor nodes  in each  subregion in  a second  step. Hence this protocol
-combines two  techniques: a leader  election in  each subregion, followed  by an
-optimization-based   node  activity   scheduling  performed   by  each   elected
+subregions  using  a  divide-and-conquer  method. The  DiLCO  protocol  is  then
+distributed on the sensor  nodes in each subregion in a  second step. Hence this
+protocol combines two techniques: a  leader election in each subregion, followed
+by  an optimization-based  node activity  scheduling performed  by each  elected

 leader. The proposed DiLCO protocol is  a periodic protocol where each period is
 decomposed into 4  phases: information exchange, leader  election, decision, and
 sensing. The  simulations show that DiLCO  is able to increase  the WSN lifetime
 and provides  improved coverage performance.  {\it  In the PeCO protocol,  a new
   mathematical optimization model is proposed. Instead  of trying to cover a set
 leader. The proposed DiLCO protocol is  a periodic protocol where each period is
 decomposed into 4  phases: information exchange, leader  election, decision, and
 sensing. The  simulations show that DiLCO  is able to increase  the WSN lifetime
 and provides  improved coverage performance.  {\it  In the PeCO protocol,  a new
   mathematical optimization model is proposed. Instead  of trying to cover a set

-  of  specified points/targets  as in  DiLCO protocol,  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. The idea is that an optimal scheduling will be obtained by
-  minimizing a weighted sum of these deviations.}
+  of specified points/targets as in the  DiLCO protocol, we formulate an integer
+  program based  on the perimeter  coverage of  each sensor. The  model involves
+  integer  variables to  capture  the  deviations between  the  actual level  of
+  coverage and the  required level. The idea is that  an optimal scheduling will
+  be obtained by minimizing a weighted sum of these deviations.}

   
 \section{ The P{\scshape e}CO Protocol Description}
 \label{sec:The PeCO Protocol Description}
   
 \section{ The P{\scshape e}CO Protocol Description}
 \label{sec:The PeCO Protocol Description}


@@ -280,7 +281,7 @@ 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 the
 euclidean distance between nodes~$u$ and $v$ is computed as follows:
 $$
 sensing area~:  $(v_x,v_y)$ and $(u_x,u_y)$.  From the previous  coordinates the
 euclidean distance between nodes~$u$ and $v$ is computed as follows:
 $$

-  Dist(u,v)=\sqrt{\vert u_x - v_x \vert^2 + \vert u_y-v_y \vert^2},
+  Dist(u,v)=\sqrt{(u_x - v_x)^2 + (u_y-v_y)^2},

 $$
 while the angle~$\alpha$ is obtained through the formula:
  \[
 $$
 while the angle~$\alpha$ is obtained through the formula:
  \[


@@ -342,7 +343,7 @@ above is thus given by the sixth line of the table.
 \end{table}
 
 In  the  PeCO protocol,  the  scheduling  of  the  sensor nodes'  activities  is
 \end{table}
 
 In  the  PeCO protocol,  the  scheduling  of  the  sensor nodes'  activities  is

-formulated    with    an    mixed-integer     program    based    on    coverage
+formulated    with    a    mixed-integer     program    based    on    coverage

 intervals~\citep{doi:10.1155/2010/926075}.  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
 intervals~\citep{doi:10.1155/2010/926075}.  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


@@ -396,13 +397,13 @@ of the application.
 \label{figure4}
 \end{figure} 
 
 \label{figure4}
 \end{figure} 
 

-We define two types of packets to be used by PeCO protocol:
+We define two types of packets to be used by the PeCO protocol:

 \begin{itemize} 
 \item INFO  packet: sent  by each  sensor node to  all the  nodes inside  a same
   subregion for information exchange.
 \item ActiveSleep packet: sent  by the leader to all the  nodes in its subregion
   to transmit to  them their respective status (stay Active  or go Sleep) during
 \begin{itemize} 
 \item INFO  packet: sent  by each  sensor node to  all the  nodes inside  a same
   subregion for information exchange.
 \item ActiveSleep packet: sent  by the leader to all the  nodes in its subregion
   to transmit to  them their respective status (stay Active  or go Sleep) during

-  sensing phase.
+  the sensing phase.

 \end{itemize}
 
 Five statuses are possible for a sensor node in the network:
 \end{itemize}
 
 Five statuses are possible for a sensor node in the network:


@@ -506,15 +507,16 @@ 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, remaining energy, sensor node ID,
 and the number of their one-hop  live neighbors during the information exchange.
 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 their one-hop  live neighbors during the information exchange.

+\textcolor{blue}{Both INFO packet and ActiveSleep packet contain two parts: header and data payload. The sensor ID is included in the header, where the header size is 8 bits. The data part includes position coordinates (64 bits), remaining energy (32 bits), and the number of one-hop live neighbors (8 bits). Therefore the size of the INFO packet is 112 bits. The ActiveSleep packet is 16 bits size, 8 bits for the header and 8 bits for data part that includes only sensor status (0 or 1).}

 The sensors  inside a same  region cooperate to  elect a leader.   The selection
 criteria for the leader are (in order  of priority):
 \begin{enumerate}
 \item larger number of neighbors;
 \item larger  remaining energy;
 The sensors  inside a same  region cooperate to  elect a leader.   The selection
 criteria for the leader are (in order  of priority):
 \begin{enumerate}
 \item larger number of neighbors;
 \item larger  remaining energy;

-\item and then  in case  of equality,  larger index.
+\item and then,  in case  of equality,  larger indexes.

 \end{enumerate}
 Once chosen, the leader collects information  to formulate and solve the integer
 \end{enumerate}
 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
+program  which allows  to build  the set  of active  sensors in  the sensing

 stage.
 
 \section{Perimeter-based Coverage Problem Formulation}
 stage.
 
 \section{Perimeter-based Coverage Problem Formulation}


@@ -536,7 +538,7 @@ First, the following sets:
 \item  $I_j$  designates  the  set  of  coverage  intervals  (CI)  obtained  for
   sensor~$j$.
 \end{itemize}
 \item  $I_j$  designates  the  set  of  coverage  intervals  (CI)  obtained  for
   sensor~$j$.
 \end{itemize}

-$I_j$ refers to the set of  coverage intervals which have been defined according
+$I_j$ refers to the set of  coverage intervals which has been defined according

 to the  method introduced in  Subsection~\ref{CI}. For a coverage  interval $i$,
 let $a^j_{ik}$ denote  the indicator function of whether  sensor~$k$ is involved
 in coverage interval~$i$ of sensor~$j$, that is:
 to the  method introduced in  Subsection~\ref{CI}. For a coverage  interval $i$,
 let $a^j_{ik}$ denote  the indicator function of whether  sensor~$k$ is involved
 in coverage interval~$i$ of sensor~$j$, that is:


@@ -610,10 +612,10 @@ $V_{i}^{j}=l^{i}-l$.
 
 $\alpha^j_i$ and $\beta^j_i$  are nonnegative weights selected  according to the
 relative importance of satisfying the associated level of coverage. For example,
 
 $\alpha^j_i$ and $\beta^j_i$  are nonnegative weights selected  according to the
 relative importance of satisfying the associated level of coverage. For example,

-weights associated with  coverage intervals of a specified part  of a region may
+weights associated with  coverage intervals of the specified part  of a region may

 be given by  a relatively larger magnitude than weights  associated with another
 region. This kind of mixed-integer program  is inspired from the model developed
 be given by  a relatively larger magnitude than weights  associated with another
 region. This kind of mixed-integer program  is inspired from the model developed

-for   brachytherapy  treatment   planning  for   optimizing  dose   distribution
+for   brachytherapy  treatment   planning  to optimize  dose   distribution

 \citep{0031-9155-44-1-012}.  The choice of the values for variables $\alpha$ and
 $\beta$  should be  made according  to the  needs of  the application.  $\alpha$
 should be  large enough  to prevent  undercoverage and so  to reach  the highest
 \citep{0031-9155-44-1-012}.  The choice of the values for variables $\alpha$ and
 $\beta$  should be  made according  to the  needs of  the application.  $\alpha$
 should be  large enough  to prevent  undercoverage and so  to reach  the highest


@@ -667,10 +669,10 @@ coverage task. This value corresponds to the energy needed by the sensing phase,
 obtained by multiplying  the energy consumed in the active  state (9.72 mW) with
 the time in seconds for one period (3600 seconds), and adding the energy for the
 pre-sensing phases.  According  to the interval of initial energy,  a sensor may
 obtained by multiplying  the energy consumed in the active  state (9.72 mW) with
 the time in seconds for one period (3600 seconds), and adding the energy for the
 pre-sensing phases.  According  to the interval of initial energy,  a sensor may

-be active during at most 20 periods. Information exchange to update the coverage
+be active during at most 20 periods. the information exchange to update the coverage

 is executed every  hour, but the length  of the sensing period  could be reduced
 is executed every  hour, but the length  of the sensing period  could be reduced

-and adapted dynamically. On  the one hand a small sensing  period would allow to
-be more  reliable but would  have result in  higher communication costs.  On the
+and adapted dynamically. On  the one hand a small sensing  period would allow the network to
+be more  reliable but would  have resulted in  higher communication costs.  On the

 other hand  the choice of a  long duration may  cause problems in case  of nodes
 failure during the sensing period.
 
 other hand  the choice of a  long duration may  cause problems in case  of nodes
 failure during the sensing period.
 


@@ -681,7 +683,7 @@ so as  to prevent the non-coverage  for the interval~$i$ of  the sensor~$j$.  On
 the other hand, $\beta^j_i$ is assigned to a value which is slightly lower so as
 to minimize the  number of active sensor nodes which  contribute in covering the
 interval. Subsection~\ref{sec:Impact} investigates more deeply how the values of
 the other hand, $\beta^j_i$ is assigned to a value which is slightly lower so as
 to minimize the  number of active sensor nodes which  contribute in covering the
 interval. Subsection~\ref{sec:Impact} investigates more deeply how the values of

-both parameters affect the performance of PeCO protocol.
+both parameters affect the performance of the PeCO protocol.

 
 The following performance metrics are used to evaluate the efficiency of the
 approach.
 
 The following performance metrics are used to evaluate the efficiency of the
 approach.


@@ -716,6 +718,15 @@ approach.
   where $|A_r^p|$ is  the number of active  sensors in the subregion  $r$ in the
   sensing period~$p$, $R$  is the number of subregions, and  $|J|$ is the number
   of sensors in the network.
   where $|A_r^p|$ is  the number of active  sensors in the subregion  $r$ in the
   sensing period~$p$, $R$  is the number of subregions, and  $|J|$ is the number
   of sensors in the network.

+  
+\item {\bf \textcolor{blue}{Energy Saving Ratio (ESR)}}:  
+\textcolor{blue}{this metric, which shows the ability of a protocol to save energy, is defined by:
+\begin{equation*}
+\scriptsize
+\mbox{ESR}(\%) = \frac{\mbox{Number of alive sensors during this round}}
+{\mbox{Total number of sensors in the network}} \times 100.
+\end{equation*}  
+  }

 \item {\bf Energy Consumption (EC)}: energy consumption can be seen as the total
   energy  consumed by  the  sensors during  $Lifetime_{95}$ or  $Lifetime_{50}$,
   divided by  the number of  periods. The value of  EC is computed  according to
 \item {\bf Energy Consumption (EC)}: energy consumption can be seen as the total
   energy  consumed by  the  sensors during  $Lifetime_{95}$ or  $Lifetime_{50}$,
   divided by  the number of  periods. The value of  EC is computed  according to


@@ -741,14 +752,14 @@ approach.
 \subsection{Simulation Results}
 
 In  order  to  assess and  analyze  the  performance  of  our protocol  we  have
 \subsection{Simulation Results}
 
 In  order  to  assess and  analyze  the  performance  of  our protocol  we  have

-implemented PeCO  protocol in OMNeT++~\citep{varga} simulator.   The simulations
-were run  on a DELL laptop  with an Intel Core~i3~2370~M  (1.8~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  equal to 6, the  original execution
-time  on  the  laptop  is multiplied  by  2944.2  $\left(\frac{35330}{2}  \times
-\frac{1}{6} \right)$.  Energy  consumption is calculated according  to the power
-consumption  values,  in  milliWatt  per  second,  given  in  Table~\ref{tab:EC}.
+implemented  the   PeCO  protocol   in  OMNeT++~\citep{varga}   simulator.   The
+simulations were  run on a  DELL laptop  with an Intel  Core~i3~2370~M (1.8~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 equal to  6, the original
+execution  time on  the laptop  is multiplied  by 2944.2  $\left(\frac{35330}{2}
+\times \frac{1}{6} \right)$.  Energy consumption  is calculated according to the
+power consumption values, in milliWatt  per second, given in Table~\ref{tab:EC},

 based on the energy model proposed in \citep{ChinhVu}.
 
 \begin{table}[h]
 based on the energy model proposed in \citep{ChinhVu}.
 
 \begin{table}[h]


@@ -780,7 +791,7 @@ consuming and more efficient, or implement a lightweight heuristic. For example,
 for  a WSN  of 200  sensor nodes,  a leader  node has  to deal  with constraints
 induced  by about  12 sensor  nodes.  In  that case,  to solve  the optimization
 problem  a memory  consumption of  more  than 1~MB  can be  observed with  GLPK,
 for  a WSN  of 200  sensor nodes,  a leader  node has  to deal  with constraints
 induced  by about  12 sensor  nodes.  In  that case,  to solve  the optimization
 problem  a memory  consumption of  more  than 1~MB  can be  observed with  GLPK,

-whereas less than 300~kB would be needed with CPLEX.
+whereas less than 300~KB would be needed with CPLEX.

 
 Besides  PeCO,   three  other  protocols   will  be  evaluated   for  comparison
 purposes. The first one, called DESK,  is a fully distributed coverage algorithm
 
 Besides  PeCO,   three  other  protocols   will  be  evaluated   for  comparison
 purposes. The first one, called DESK,  is a fully distributed coverage algorithm


@@ -789,17 +800,17 @@ GAF~\citep{xu2001geography}, consists in dividing the monitoring area into fixed
 squares. Then, during  the decision phase, in each square,  one sensor is chosen
 to  remain  active   during  the  sensing  phase.   The  last   one,  the  DiLCO
 protocol~\citep{Idrees2}, is an improved version of a research work we presented
 squares. Then, during  the decision phase, in each square,  one sensor is chosen
 to  remain  active   during  the  sensing  phase.   The  last   one,  the  DiLCO
 protocol~\citep{Idrees2}, is an improved version of a research work we presented

-in~\citep{idrees2014coverage}. Let us  notice that PeCO and  DiLCO protocols are
-based on the same framework. In particular,  the choice for the simulations of a
-partitioning  in   16~subregions  was  made   because  it  corresponds   to  the
+in~\citep{idrees2014coverage}. Let us  notice that the PeCO  and DiLCO protocols
+are based on  the same framework. In particular, the  choice for the simulations
+of  a partitioning  in  16~subregions was  made because  it  corresponds to  the

 configuration producing  the best results for  DiLCO. Of course, this  number of
 configuration producing  the best results for  DiLCO. Of course, this  number of

-subregions should be adapted according to the  size of the area  of interest and
+subregions should be adapted  according to the size of the  area of interest and

 the number of sensors.  The protocols  are distinguished from one another by the
 formulation of the integer program providing the set of sensors which have to be
 the number of sensors.  The protocols  are distinguished from one another by the
 formulation of the integer program providing the set of sensors which have to be

-activated in each sensing phase. DiLCO protocol tries to satisfy the coverage of
-a set of primary  points, whereas 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 ($l=1$).
+activated  in each  sensing  phase.  The DiLCO  protocol  tries  to satisfy  the
+coverage of a set of primary points,  whereas the objective of the PeCO protocol
+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{Coverage Ratio}
 
 
 \subsubsection{Coverage Ratio}
 


@@ -807,9 +818,9 @@ Figure~\ref{figure5} shows  the average  coverage ratio  for 200  deployed nodes
 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
 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  beginning DiLCO  and  PeCO protocols  put to  sleep  status more  redundant
-sensors  (which slightly  decreases the  coverage  ratio), while  the two  other
-protocols  activate more  sensor nodes.  Later, when  the number  of periods  is
+the beginning the  DiLCO and PeCO protocols put more  redundant sensors to sleep
+status  (which slightly  decreases  the  coverage ratio),  while  the two  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 greater than 50\% for longer periods (15 more compared to
 DiLCO, 40 more compared to DESK). The  energy saved by PeCO in the early periods
 beyond~70, it  clearly appears that  PeCO 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). The  energy saved by PeCO in the early periods


@@ -825,13 +836,13 @@ allows later a substantial increase of the coverage performance.
 
 \subsubsection{Active Sensors Ratio}
 
 
 \subsubsection{Active Sensors Ratio}
 

-Having the less active sensor nodes in  each period is essential to minimize the
+Minimizing the number of active sensor nodes in  each period is essential to minimize the

 energy   consumption    and   thus    to   maximize   the    network   lifetime.
 Figure~\ref{figure6}  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
 energy   consumption    and   thus    to   maximize   the    network   lifetime.
 Figure~\ref{figure6}  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
+the first fourteen  rounds, and the DiLCO and PeCO protocols  compete perfectly with

 only 17.92~\%  and 20.16~\% active nodes  during the same time  interval. As the
 only 17.92~\%  and 20.16~\% active nodes  during the same time  interval. As the

-number of periods increases, PeCO protocol has a lower number of active nodes in
+number of periods increases, the PeCO protocol has a lower number of active nodes in

 comparison with the  three other approaches and exhibits a  slow decrease, while
 keeping a greater coverage ratio as shown in Figure \ref{figure5}.
 
 comparison with the  three other approaches and exhibits a  slow decrease, while
 keeping a greater coverage ratio as shown in Figure \ref{figure5}.
 


@@ -842,19 +853,51 @@ keeping a greater coverage ratio as shown in Figure \ref{figure5}.
 \label{figure6}
 \end{figure} 
 
 \label{figure6}
 \end{figure} 
 

+\subsubsection{\textcolor{blue}{Energy Saving Ratio (ESR)}} 
+
+%\textcolor{blue}{In this experiment, we study the energy saving ratio, see Figure~\ref{fig5}, for 200 deployed nodes. 
+%The larger the ratio  is,  the more  redundant sensor  nodes are switched off, and consequently  the longer the  network may  liv%e. }
+
+\textcolor{blue}{The simulation  results show that  our protocol PeCO  allows to
+  efficiently save energy by turning off  some sensors during the sensing phase.
+  As shown in Figure~\ref{fig5}, GAF provides better energy saving than PeCO for
+  the  first fifty  rounds, because  GAF  balances the  energy consumption  among
+  sensor nodes inside each  small fixed grid and thus permits to  extend the life of
+  sensors in  each grid  fairly but  in the same  time turn  on large  number of
+  sensors during sensing  that lead later to quickly  deplete sensor's batteries
+  together. After that  GAF  provide  less energy  saving  compared with  other
+  approaches because of the large number of dead nodes. DESK algorithm shows less
+  energy saving compared with other approaches  due to activate a large number of
+  sensors during the  sensing. DiLCO protocol provides less  energy saving ratio
+  compared with  PeCO because it generally  activate a larger number  of sensor
+  nodes during sensing.  Note that again as the number  of rounds increases PeCO
+  becomes the most  performing one, since it consumes less  energy compared with
+  other approaches.}
+
+\begin{figure}[h!]
+%\centering
+% \begin{multicols}{6}
+\centering
+\includegraphics[scale=0.5]{ESR.eps} %\\~ ~ ~(a)
+\caption{Energy Saving Ratio for 200 deployed nodes}
+\label{fig5}
+\end{figure} 
+
+
+

 \subsubsection{Energy Consumption}
 
 The  effect  of  the  energy  consumed by  the  WSN  during  the  communication,
 computation,  listening,  active, and  sleep  status  is studied  for  different
 network densities  and the  four approaches  compared.  Figures~\ref{figure7}(a)
 and (b)  illustrate the energy consumption  for different network sizes  and for
 \subsubsection{Energy Consumption}
 
 The  effect  of  the  energy  consumed by  the  WSN  during  the  communication,
 computation,  listening,  active, and  sleep  status  is studied  for  different
 network densities  and the  four approaches  compared.  Figures~\ref{figure7}(a)
 and (b)  illustrate the energy consumption  for different network sizes  and for

-$Lifetime95$ and $Lifetime50$.  The results show  that PeCO protocol is the most
+$Lifetime_{95}$ and $Lifetime_{50}$.  The results show  that the PeCO protocol is the most

 competitive from the energy consumption point of view. As shown by both figures,
 PeCO consumes much less energy than the  other methods. One might think that the
 resolution of the integer program is too  costly in energy, but the results show
 that it is very beneficial to lose a  bit of time in the selection of sensors to
 activate.  Indeed  the optimization program  allows to reduce  significantly the
 competitive from the energy consumption point of view. As shown by both figures,
 PeCO consumes much less energy than the  other methods. One might think that the
 resolution of the integer program is too  costly in energy, but the results show
 that it is very beneficial to lose a  bit of time in the selection of sensors to
 activate.  Indeed  the optimization program  allows to reduce  significantly the

-number of  active sensors  and so  the energy consumption  while keeping  a good
+number of  active sensors  and also  the energy consumption  while keeping  a good

 coverage level. Let  us notice that the energy overhead  when increasing network
 size is the lowest with PeCO.
 
 coverage level. Let  us notice that the energy overhead  when increasing network
 size is the lowest with PeCO.
 


@@ -870,14 +913,14 @@ size is the lowest with PeCO.
 
 \subsubsection{Network Lifetime}
 
 
 \subsubsection{Network Lifetime}
 

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

 the   two   other  approaches   in   prolonging   the  network   lifetime.    In
 the   two   other  approaches   in   prolonging   the  network   lifetime.    In

-Figures~\ref{figure8}(a) and  (b), $Lifetime95$  and $Lifetime50$ are  shown for
+Figures~\ref{figure8}(a) and  (b), $Lifetime_{95}$  and $Lifetime_{50}$ are  shown for

 different  network  sizes.  As  can  be  seen  in  these figures,  the  lifetime
 different  network  sizes.  As  can  be  seen  in  these figures,  the  lifetime

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

 PeCO protocols.  For  instance, for a network of 300~sensors  and coverage ratio
 greater than  50\%, we can see  on Figure~\ref{figure8}(b) that the  lifetime is
 PeCO protocols.  For  instance, for a network of 300~sensors  and coverage ratio
 greater than  50\%, we can see  on Figure~\ref{figure8}(b) that the  lifetime is

-about  twice  longer with  PeCO  compared  to  DESK protocol.   The  performance
+about  twice  longer with  PeCO  compared  to  the DESK protocol.   The  performance

 difference    is   more    obvious    in    Figure~\ref{figure8}(b)   than    in
 Figure~\ref{figure8}(a) because the gain induced by our protocols increases with
 time, and the lifetime with a coverage over 50\% is far longer than with 95\%.
 difference    is   more    obvious    in    Figure~\ref{figure8}(b)   than    in
 Figure~\ref{figure8}(a) because the gain induced by our protocols increases with
 time, and the lifetime with a coverage over 50\% is far longer than with 95\%.


@@ -892,18 +935,19 @@ time, and the lifetime with a coverage over 50\% is far longer than with 95\%.
   \label{figure8}
 \end{figure} 
 
   \label{figure8}
 \end{figure} 
 

-Figure~\ref{figure9} compares the lifetime coverage  of DiLCO and PeCO protocols
-for  different   coverage  ratios.   We  denote  by   Protocol/50,  Protocol/80,
+Figure~\ref{figure9} compares the lifetime coverage  of the DiLCO and PeCO protocols
+for  different   coverage  ratios.   We  denote  by   Protocol/70,  Protocol/80,

 Protocol/85, Protocol/90,  and Protocol/95 the  amount of time during  which the
 Protocol/85, Protocol/90,  and Protocol/95 the  amount of time during  which the

-network  can satisfy  an  area  coverage greater  than  $50\%$, $80\%$,  $85\%$,
+network  can satisfy  an  area  coverage greater  than  $70\%$, $80\%$,  $85\%$,

 $90\%$, and  $95\%$ respectively,  where the  term Protocol  refers to  DiLCO or
 $90\%$, and  $95\%$ 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 not ineffective for  the smallest network
-sizes.
+PeCO.  \textcolor{blue}{Indeed there are applications that do not require a 100\% coverage of the
+area to be  monitored. For example, forest
+fire application might require complete coverage
+in summer seasons while only require 80$\%$ of the area to be covered in rainy seasons~\citep{li2011transforming}. As another example, birds habit study requires only 70$\%$-coverage at nighttime when the birds are sleeping while requires 100$\%$-coverage at daytime when the birds are active~\citep{1279193}. 
+%Mudflows monitoring applications may require part of the area to be covered in sunny days. Thus, to extend network lifetime, the coverage quality can be decreased if it is acceptable~\citep{wang2014keeping}}. 
+ PeCO always  outperforms DiLCO  for the  three  lower coverage  ratios, moreover  the
+improvements grow  with the network  size. DiLCO outperforms PeCO when the coverage ratio is required to be $>90\%$, but PeCo extends the network lifetime significantly when coverage ratio can be relaxed.}
+%DiLCO  is better for  coverage ratios near 100\%, but  in that case PeCO  is not ineffective for  the smallest network sizes.

 
 \begin{figure}[h!]
 \centering \includegraphics[scale=0.55]{figure9.eps}
 
 \begin{figure}[h!]
 \centering \includegraphics[scale=0.55]{figure9.eps}


@@ -916,17 +960,17 @@ sizes.
 
 Table~\ref{my-labelx}  shows network  lifetime results  for different  values of
 $\alpha$ and $\beta$, and  a network size equal to 200 sensor  nodes. On the one
 
 Table~\ref{my-labelx}  shows network  lifetime results  for different  values of
 $\alpha$ and $\beta$, and  a network size equal to 200 sensor  nodes. On the one

-hand, the choice  of $\beta \gg \alpha$ prevents the  overcoverage, and so limit
-the activation of a large number of  sensors, but as $\alpha$ is low, some areas
-may be poorly covered.  This explains  the results obtained for {\it Lifetime50}
-with $\beta \gg \alpha$: a large number  of periods with low coverage ratio.  On
-the other hand, when we choose $\alpha \gg \beta$, we favor the coverage even if
-some areas may  be overcovered, so high  coverage ratio is reached,  but a large
-number  of  sensors are  activated  to  achieve  this goal.   Therefore  network
-lifetime is reduced.   The choice $\alpha=0.6$ and $\beta=0.4$  seems to achieve
-the best compromise  between lifetime and coverage ratio.  That  explains why we
-have  chosen  this  setting  for  the  experiments  presented  in  the  previous
-subsections.
+hand,  the choice  of $\beta  \gg \alpha$  prevents the  overcoverage, and  also
+limits the activation of a large number of sensors, but as $\alpha$ is low, some
+areas  may  be   poorly  covered.   This  explains  the   results  obtained  for
+$Lifetime_{50}$ with  $\beta \gg  \alpha$: a  large number  of periods  with low
+coverage ratio.  On the other hand, when  we choose $\alpha \gg \beta$, we favor
+the coverage even if some areas may  be overcovered, so a high coverage ratio is
+reached,  but a  large number  of sensors  are activated  to achieve  this goal.
+Therefore  the  network  lifetime  is  reduced.   The  choice  $\alpha=0.6$  and
+$\beta=0.4$ seems to  achieve the best compromise between  lifetime and coverage
+ratio.   That explains  why  we have  chosen this  setting  for the  experiments
+presented in the previous subsections.

 
 %As can be seen in Table~\ref{my-labelx},  it is obvious and clear that when $\alpha$ decreased and $\beta$ increased by any step, the network lifetime for $Lifetime_{50}$ increased and the $Lifetime_{95}$ decreased. Therefore, selecting the values of $\alpha$ and $\beta$ depend on the application type used in the sensor nework. In PeCO protocol, $\alpha$ and $\beta$ are chosen based on the largest value of network lifetime for $Lifetime_{95}$.
 
 
 %As can be seen in Table~\ref{my-labelx},  it is obvious and clear that when $\alpha$ decreased and $\beta$ increased by any step, the network lifetime for $Lifetime_{50}$ increased and the $Lifetime_{95}$ decreased. Therefore, selecting the values of $\alpha$ and $\beta$ depend on the application type used in the sensor nework. In PeCO protocol, $\alpha$ and $\beta$ are chosen based on the largest value of network lifetime for $Lifetime_{95}$.
 


@@ -973,18 +1017,17 @@ lifetime, coverage ratio, active sensors ratio, and energy consumption.
 We plan to extend  our framework so that the schedules  are planned for multiple
 sensing  periods. We  also want  to  improve the  integer program  to take  into
 account heterogeneous sensors from both energy and node characteristics point of
 We plan to extend  our framework so that the schedules  are planned for multiple
 sensing  periods. We  also want  to  improve the  integer program  to take  into
 account heterogeneous sensors from both energy and node characteristics point of

-views.  Finally,  it would  be interesting  to implement  PeCO protocol  using a
+views.  Finally, it would be interesting  to implement the PeCO protocol using a

 sensor-testbed to evaluate it in real world applications.
 
 sensor-testbed to evaluate it in real world applications.
 

-
-\subsection*{Acknowledgements}
+\subsection*{Acknowledgments}

 The  authors  are   deeply  grateful  to  the  anonymous   reviewers  for  their
 constructive advice,  which improved the  technical quality  of the paper.  As a
 The  authors  are   deeply  grateful  to  the  anonymous   reviewers  for  their
 constructive advice,  which improved the  technical quality  of the paper.  As a

-Ph.D.   student, Ali  Kadhum IDREES  would  like to  gratefully acknowledge  the
+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
 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).
-
+(contract ANR-11-LABX-01-01).  
+ 

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