Last Version after correction

[UIC2013.git] / bare_conf.tex

diff --git a/bare_conf.tex b/bare_conf.tex
old mode 100755 (executable)
new mode 100644 (file)
index 832076e..80629a9
--- a/bare_conf.tex
+++ b/bare_conf.tex
@@ -29,7 +29,7 @@
 \usepackage{epsfig}
 \usepackage{caption}
 \usepackage{multicol}
 \usepackage{epsfig}
 \usepackage{caption}
 \usepackage{multicol}

-
+\usepackage{times}

 \usepackage{graphicx,epstopdf}
 \epstopdfsetup{suffix=}
 \DeclareGraphicsExtensions{.ps}
 \usepackage{graphicx,epstopdf}
 \epstopdfsetup{suffix=}
 \DeclareGraphicsExtensions{.ps}


@@ -37,13 +37,17 @@
 
 \begin{document}
 
 
 \begin{document}
 

-\title{Energy-Efficient Activity Scheduling in Heterogeneous Energy Wireless Sensor Networks}
+%\title{ Coverage and Lifetime Optimization in Heterogeneous Energy Wireless Sensor Networks} 
+\title{Coverage and Lifetime Optimization in Heterogeneous Energy Wireless Sensor Networks}
+%Activity Scheduling for Coverage and Lifetime Optimization in  Wireless Sensor Networks}

 
 % author names and affiliations
 % use a multiple column layout for up to three different
 % affiliations
 
 % author names and affiliations
 % use a multiple column layout for up to three different
 % affiliations

-\author{\IEEEauthorblockN{Ali Kadhum Idrees, Karine Deschinkel, Michel Salomon, and Rapha\"el Couturier }
-\IEEEauthorblockA{FEMTO-ST Institute, UMR 6174 CNRS, University of Franche-Comte, Belfort, France \\
+\author{\IEEEauthorblockN{Ali Kadhum Idrees, Karine Deschinkel, Michel Salomon, and Rapha\"el Couturier}
+\IEEEauthorblockA{FEMTO-ST Institute, UMR 6174 CNRS \\ 
+University of Franche-Comt\'e \\
+Belfort, France \\

 Email: ali.idness@edu.univ-fcomte.fr, $\lbrace$karine.deschinkel, michel.salomon, raphael.couturier$\rbrace$@univ-fcomte.fr}
 %\email{\{ali.idness, karine.deschinkel, michel.salomon, raphael.couturier\}@univ-fcomte.fr}
 %\and
 Email: ali.idness@edu.univ-fcomte.fr, $\lbrace$karine.deschinkel, michel.salomon, raphael.couturier$\rbrace$@univ-fcomte.fr}
 %\email{\{ali.idness, karine.deschinkel, michel.salomon, raphael.couturier\}@univ-fcomte.fr}
 %\and


@@ -60,7 +64,7 @@ Email: ali.idness@edu.univ-fcomte.fr, $\lbrace$karine.deschinkel, michel.salomon
 One of  the fundamental challenges in Wireless  Sensor Networks (WSNs)
 is  the coverage  preservation  and  the extension  of  the  network  lifetime
 continuously  and  effectively  when  monitoring a  certain  area  (or
 One of  the fundamental challenges in Wireless  Sensor Networks (WSNs)
 is  the coverage  preservation  and  the extension  of  the  network  lifetime
 continuously  and  effectively  when  monitoring a  certain  area  (or

-region) of interest. In this paper a coverage optimization protocol to
+region) of interest. In this paper, a coverage optimization protocol to

 improve the lifetime in  heterogeneous energy wireless sensor networks
 is proposed.   The area of  interest is first divided  into subregions
 using a  divide-and-conquer method and then the scheduling  of sensor node
 improve the lifetime in  heterogeneous energy wireless sensor networks
 is proposed.   The area of  interest is first divided  into subregions
 using a  divide-and-conquer method and then the scheduling  of sensor node


@@ -69,46 +73,27 @@ considers  rounds during  which  a small  number  of nodes,  remaining
 active  for  sensing, is  selected  to  ensure  coverage.  Each  round
 consists  of   four  phases:  (i)~Information   Exchange,  (ii)~Leader
 Election, (iii)~Decision,  and (iv)~Sensing.  The  decision process is
 active  for  sensing, is  selected  to  ensure  coverage.  Each  round
 consists  of   four  phases:  (i)~Information   Exchange,  (ii)~Leader
 Election, (iii)~Decision,  and (iv)~Sensing.  The  decision process is

-carried  out  by  a  leader  node which  solves  an  integer  program.
+carried  out  by  a  leader  node, which  solves  an  integer  program.

 Simulation  results show that  the proposed  approach can  prolong the
 network lifetime and improve the coverage performance.
 \end{abstract}
 
 Simulation  results show that  the proposed  approach can  prolong the
 network lifetime and improve the coverage performance.
 \end{abstract}
 

-%\keywords{Area Coverage, Wireless Sensor Networks, lifetime Optimization, Distributed Protocol.}
+\begin{IEEEkeywords}
+Area Coverage, Network lifetime, Optimization, Scheduling, Distributed Protocol.
+\end{IEEEkeywords}
+%\keywords{Area Coverage, Network lifetime, Optimization, Distributed Protocol}

  
 \IEEEpeerreviewmaketitle
 
 \section{Introduction}
 
  
 \IEEEpeerreviewmaketitle
 
 \section{Introduction}
 

-\noindent Recent years have witnessed significant advances in wireless
-communications and embedded micro-sensing MEMS technologies which have
-led to the  emergence of wireless  sensor networks  as one  of the  most promising
-technologies~\cite{asc02}.   In fact, they  present huge  potential in
-several  domains ranging  from  health care  applications to  military
-applications.  A sensor network is  composed of a large number of tiny
-sensing  devices deployed  in a  region of  interest. Each  device has
-processing  and wireless communication  capabilities, which  enable it to
-sense its environment, to compute, to store information, and to deliver
-report messages to a base station.
-%These sensor nodes run on batteries with limited capacities. To achieve a long life of the network, it is important to conserve battery power. Therefore, lifetime optimisation is one of the most critical issues in wireless sensor networks.
-One of the main design issues in Wireless Sensor Networks (WSNs) is to
-prolong the  network lifetime,  while achieving acceptable  quality of
-service for applications.  Indeed, sensor nodes have limited resources
-in terms of memory, energy, and computational power.
-
-Since sensor nodes have limited battery life and without being able to
-replace batteries,  especially in remote and  hostile environments, it
-is desirable that  a WSN should be deployed  with high density because
-spatial redundancy can  then be exploited to increase  the lifetime of
-the network. In such a high  density network, if all sensor nodes were
-to be  activated at the same  time, the lifetime would  be reduced. To
-extend the lifetime  of the network, the main idea  is to take advantage
-of  the overlapping  sensing regions  of some  sensor nodes  to save
-energy  by  turning  off  some  of  them  during  the  sensing  phase.
-Obviously, the deactivation of nodes  is only relevant if the coverage
-of the monitored area  is not affected.  Consequently, future softwares
-may  need to  adapt  appropriately to  achieve  acceptable quality  of
-service  for  applications.  In  this  paper  we  concentrate on  the area
+\noindent The fast developments in the low-cost sensor devices and wireless communications have allowed the emergence the WSNs. WSN includes a large number of small , limited-power sensors  that can sense, process and transmit
+ data over a wireless communication . They communicate with each other by using multi-hop wireless communications , cooperate together to monitor the area of interest, and the measured data can be reported
+ to a monitoring center
+called, sink, for analysis it~\cite{Ammari01, Sudip03}. There are several applications used the WSN including health, home, environmental, military,and industrial applications~\cite{Akyildiz02}.
+The coverage  problem is one of the fundamental challenges in WSNs~\cite{Nayak04} that consists in monitoring efficiently and  continuously the area of interest. The limited energy of sensors represents the main challenge in the WSNs design~\cite{Ammari01}, where it is difficult to replace and/or
+ recharge their batteries because the the area of interest nature (such as hostile environments) and the cost. So, it is necessary that a WSN deployed with high density  because spatial redundancy can then be exploited to increase the lifetime of the network . However, turn on all the sensor nodes, which monitor the same region at the same time leads to decrease the lifetime of the network. To extend the lifetime of the network, the main idea is to take advantage of the overlapping sensing regions of some sensor nodes to save energy by turning off some of them during the sensing phase~\cite{Misra05}. WSNs require energy-efficient solutions to improve the network lifetime that is constrained by the limited power of each sensor node ~\cite{Akyildiz02}. 
+In  this  paper,  we  concentrate on  the area

 coverage  problem,  with  the  objective  of  maximizing  the  network
 lifetime  by using  an adaptive  scheduling. The  area of  interest is
 divided into subregions and an activity scheduling for sensor nodes is
 coverage  problem,  with  the  objective  of  maximizing  the  network
 lifetime  by using  an adaptive  scheduling. The  area of  interest is
 divided into subregions and an activity scheduling for sensor nodes is


@@ -121,14 +106,14 @@ Our scheduling  scheme considers rounds,  where a round starts  with a
 discovery  phase  to  exchange  information  between  sensors  of  the
 subregion,  in order to  choose in  a suitable manner  a sensor  node to
 carry  out a coverage  strategy. This  coverage strategy  involves the
 discovery  phase  to  exchange  information  between  sensors  of  the
 subregion,  in order to  choose in  a suitable manner  a sensor  node to
 carry  out a coverage  strategy. This  coverage strategy  involves the

-solving of  an integer  program which provides  the activation  of the
+solving of  an integer  program, which provides  the activation  of the

 sensors for the sensing phase of the current round.
 
 The remainder of the paper is organized as follows.  The next section
 % Section~\ref{rw}
 reviews the related work in the field.  Section~\ref{pd} is devoted to
 the    scheduling     strategy    for    energy-efficient    coverage.
 sensors for the sensing phase of the current round.
 
 The remainder of the paper is organized as follows.  The next section
 % Section~\ref{rw}
 reviews the related work in the field.  Section~\ref{pd} is devoted to
 the    scheduling     strategy    for    energy-efficient    coverage.

-Section~\ref{cp} gives the coverage model formulation which is used to
+Section~\ref{cp} gives the coverage model formulation, which is used to

 schedule  the  activation  of  sensors.  Section~\ref{exp}  shows  the
 simulation  results obtained  using  the discrete  event simulator OMNeT++  \cite{varga}. They  fully demonstrate  the usefulness  of the
 proposed  approach.   Finally, we  give  concluding  remarks and  some
 schedule  the  activation  of  sensors.  Section~\ref{exp}  shows  the
 simulation  results obtained  using  the discrete  event simulator OMNeT++  \cite{varga}. They  fully demonstrate  the usefulness  of the
 proposed  approach.   Finally, we  give  concluding  remarks and  some


@@ -153,7 +138,8 @@ to recall the main definitions and assumptions related to our work.
 
 %\item Barrier Coverage An objective to determine the maximal support/breach paths that traverse a sensor field. Barrier coverage is expressed as finding one or more routes with starting position and ending position when the targets pass through the area deployed with sensor nodes~\cite{Santosh04,Ai05}.
 %\end{itemize}
 
 %\item Barrier Coverage An objective to determine the maximal support/breach paths that traverse a sensor field. Barrier coverage is expressed as finding one or more routes with starting position and ending position when the targets pass through the area deployed with sensor nodes~\cite{Santosh04,Ai05}.
 %\end{itemize}

-{\bf Coverage}
+\subsection{Coverage} 
+%{\bf Coverage}

 
 The most  discussed coverage problems in literature  can be classified
 into two types \cite{ma10}: area coverage (also called full or blanket
 
 The most  discussed coverage problems in literature  can be classified
 into two types \cite{ma10}: area coverage (also called full or blanket


@@ -163,10 +149,10 @@ area is within the sensing range  of at least one working sensor node.
 Target coverage problem  is to cover only a  finite number of discrete
 points  called targets.   This type  of coverage  has  mainly military
 applications. Our work will concentrate on the area coverage by design
 Target coverage problem  is to cover only a  finite number of discrete
 points  called targets.   This type  of coverage  has  mainly military
 applications. Our work will concentrate on the area coverage by design

-and implementation of a  strategy which efficiently selects the active
+and implementation of a  strategy, which efficiently selects the active

 nodes   that  must   maintain  both   sensing  coverage   and  network
 connectivity and at the same time improve the lifetime of the wireless
 nodes   that  must   maintain  both   sensing  coverage   and  network
 connectivity and at the same time improve the lifetime of the wireless

-sensor  network.   But  requiring  that  all physical  points  of  the
+sensor  network.   But,  requiring  that  all physical  points  of  the

 considered region are covered may  be too strict, especially where the
 sensor network is not dense.   Our approach represents an area covered
 by a sensor as a set of primary points and tries to maximize the total
 considered region are covered may  be too strict, especially where the
 sensor network is not dense.   Our approach represents an area covered
 by a sensor as a set of primary points and tries to maximize the total


@@ -174,7 +160,8 @@ number  of  primary points  that  are  covered  in each  round,  while
 minimizing  overcoverage (points  covered by  multiple  active sensors
 simultaneously).
 
 minimizing  overcoverage (points  covered by  multiple  active sensors
 simultaneously).
 

-{\bf Lifetime}
+\subsection{Lifetime} 
+%{\bf Lifetime}

 
 Various   definitions   exist   for   the   lifetime   of   a   sensor
 network~\cite{die09}.  The main definitions proposed in the literature are
 
 Various   definitions   exist   for   the   lifetime   of   a   sensor
 network~\cite{die09}.  The main definitions proposed in the literature are


@@ -189,7 +176,8 @@ during the WSN lifetime.  Network connectivity is important because an
 active sensor node without  connectivity towards a base station cannot
 transmit information on an event in the area that it monitors.
 
 active sensor node without  connectivity towards a base station cannot
 transmit information on an event in the area that it monitors.
 

-{\bf Activity scheduling}
+\subsection{Activity scheduling} 
+%{\bf Activity scheduling}

 
 Activity scheduling is to  schedule the activation and deactivation of
 sensor nodes.  The  basic objective is to decide  which sensors are in
 
 Activity scheduling is to  schedule the activation and deactivation of
 sensor nodes.  The  basic objective is to decide  which sensors are in


@@ -203,7 +191,8 @@ only using  local neighbor information. In  centralized algorithms, a
 central controller  (a node or  base station) informs every  sensors of
 the time intervals to be activated.
 
 central controller  (a node or  base station) informs every  sensors of
 the time intervals to be activated.
 

-{\bf Distributed approaches}
+\subsection{Distributed approaches}
+%{\bf Distributed approaches}

 
 Some      distributed     algorithms      have      been     developed
 in~\cite{Gallais06,Tian02,Ye03,Zhang05,HeinzelmanCB02}  to perform the
 
 Some      distributed     algorithms      have      been     developed
 in~\cite{Gallais06,Tian02,Ye03,Zhang05,HeinzelmanCB02}  to perform the


@@ -217,7 +206,7 @@ area   \cite{Berman05efficientenergy},   maximum   uncovered   targets
 into rounds, where each round  has a self-scheduling phase followed by
 a sensing phase.  Each sensor  broadcasts a message containing the node ID
 and the node location  to its neighbors at the beginning  of each round. A
 into rounds, where each round  has a self-scheduling phase followed by
 a sensing phase.  Each sensor  broadcasts a message containing the node ID
 and the node location  to its neighbors at the beginning  of each round. A

-sensor determines  its status by  a rule named off-duty  eligible rule
+sensor determines  its status by  a rule named off-duty  eligible rule,

 which tells  him to  turn off if  its sensing  area is covered  by its
 neighbors. A  back-off scheme is  introduced to let each  sensor delay
 the decision process  with a random period of time,  in order to avoid
 which tells  him to  turn off if  its sensing  area is covered  by its
 neighbors. A  back-off scheme is  introduced to let each  sensor delay
 the decision process  with a random period of time,  in order to avoid


@@ -252,7 +241,8 @@ sensor  maintains its  own timer  and its  wake-up time is randomized
 
 %In this paper we focus on centralized algorithms because distributed algorithms are outside the scope of our work. Note that centralized coverage algorithms have the advantage of requiring very low processing power from the sensor nodes which have usually limited processing capabilities. Moreover, a recent study conducted in \cite{pc10} concludes that there is a threshold in terms of network size to switch from a localized to a centralized algorithm. Indeed the exchange of messages in large networks may consume  a considerable amount of energy in a localized approach compared to a centralized one. 
 
 
 %In this paper we focus on centralized algorithms because distributed algorithms are outside the scope of our work. Note that centralized coverage algorithms have the advantage of requiring very low processing power from the sensor nodes which have usually limited processing capabilities. Moreover, a recent study conducted in \cite{pc10} concludes that there is a threshold in terms of network size to switch from a localized to a centralized algorithm. Indeed the exchange of messages in large networks may consume  a considerable amount of energy in a localized approach compared to a centralized one. 
 

-{\bf Centralized approaches}
+\subsection{Centralized approaches}
+%{\bf Centralized approaches}

 
 Power  efficient  centralized  schemes  differ  according  to  several
 criteria \cite{Cardei:2006:ECP:1646656.1646898},  such as the coverage
 
 Power  efficient  centralized  schemes  differ  according  to  several
 criteria \cite{Cardei:2006:ECP:1646656.1646898},  such as the coverage


@@ -266,15 +256,15 @@ these set covers successively.
 The first algorithms  proposed in the  literature consider that  the cover
 sets  are  disjoint: a  sensor  node appears  in  exactly  one of  the
 generated  cover  sets.    For  instance,  Slijepcevic  and  Potkonjak
 The first algorithms  proposed in the  literature consider that  the cover
 sets  are  disjoint: a  sensor  node appears  in  exactly  one of  the
 generated  cover  sets.    For  instance,  Slijepcevic  and  Potkonjak

-\cite{Slijepcevic01powerefficient}   propose    an   algorithm   which
+\cite{Slijepcevic01powerefficient}   propose    an   algorithm, which

 allocates sensor nodes in mutually independent sets to monitor an area
 divided into  several fields.  Their algorithm builds  a cover  set by
 allocates sensor nodes in mutually independent sets to monitor an area
 divided into  several fields.  Their algorithm builds  a cover  set by

-including in  priority the sensor  nodes which cover  critical fields,
+including in  priority the sensor  nodes, which cover  critical fields,

 that  is to  say fields  that are  covered by  the smallest  number of
 sensors. The time complexity of  their heuristic is $O(n^2)$ where $n$
 that  is to  say fields  that are  covered by  the smallest  number of
 sensors. The time complexity of  their heuristic is $O(n^2)$ where $n$

-is the number of  sensors.  \cite{cardei02}~describes a graph coloring
-technique  to achieve energy  savings by  organizing the  sensor nodes
-into a maximum number of  disjoint dominating sets which are activated
+is the number of  sensors. In~\cite{cardei02}, a graph coloring
+technique is described to achieve energy  savings by  organizing the  sensor nodes
+into a maximum number of  disjoint dominating sets, which are activated

 successively. The dominating sets do not guarantee the coverage of the
 whole        region        of        interest.        Abrams        et
 al.~\cite{Abrams:2004:SKA:984622.984684}  design  three  approximation
 successively. The dominating sets do not guarantee the coverage of the
 whole        region        of        interest.        Abrams        et
 al.~\cite{Abrams:2004:SKA:984622.984684}  design  three  approximation


@@ -300,7 +290,7 @@ integer      programming     solving.       %Cardei      and     Du
 \cite{Cardei:2005:IWS:1160086.1160098} propose a method to efficiently
 compute the maximum  number of disjoint set covers  such that each set
 can  monitor all  targets. They  first  transform the  problem into  a
 \cite{Cardei:2005:IWS:1160086.1160098} propose a method to efficiently
 compute the maximum  number of disjoint set covers  such that each set
 can  monitor all  targets. They  first  transform the  problem into  a

-maximum  flow   problem  which  is  formulated  as   a  mixed  integer
+maximum  flow   problem, which  is  formulated  as   a  mixed  integer

 programming (MIP). Then their heuristic  uses the output of the MIP to
 compute  disjoint  set  covers.  Results  show  that  this  heuristic
 provides  a   number  of  set  covers  slightly   larger  compared  to
 programming (MIP). Then their heuristic  uses the output of the MIP to
 compute  disjoint  set  covers.  Results  show  that  this  heuristic
 provides  a   number  of  set  covers  slightly   larger  compared  to


@@ -318,7 +308,7 @@ cover sets with a slight growth rate in execution time.
 %More recently Manju and Pujari\cite{Manju2011}
 
 In the  case of non-disjoint algorithms  \cite{Manju2011}, sensors may
 %More recently Manju and Pujari\cite{Manju2011}
 
 In the  case of non-disjoint algorithms  \cite{Manju2011}, sensors may

-participate  in more  than  one cover  set.   In some  cases this  may
+participate  in more  than  one cover  set.   In some  cases, this  may

 prolong  the lifetime  of the  network in  comparison to  the disjoint
 cover set algorithms, but  designing algorithms for non-disjoint cover
 sets  generally induces a  higher order  of complexity.   Moreover, in
 prolong  the lifetime  of the  network in  comparison to  the disjoint
 cover set algorithms, but  designing algorithms for non-disjoint cover
 sets  generally induces a  higher order  of complexity.   Moreover, in


@@ -336,9 +326,10 @@ authors  have formulated  the lifetime  problem and  suggested another
 algorithm~\cite{garg98}, provably near
 the optimal solution,    is also proposed.
 
 algorithm~\cite{garg98}, provably near
 the optimal solution,    is also proposed.
 

-{\bf Our contribution}
+\subsection{Our contribution}
+%{\bf Our contribution}

 
 

-There are  three main questions which  should be addressed  to build a
+There are  three main questions, which should be addressed  to build a

 scheduling strategy. We  give a brief answer to  these three questions
 to describe our  approach before going into details  in the subsequent
 sections.
 scheduling strategy. We  give a brief answer to  these three questions
 to describe our  approach before going into details  in the subsequent
 sections.


@@ -359,11 +350,11 @@ sections.
   \cite{pc10}, both centralized  and distributed algorithms have their
   own  advantages and  disadvantages. Centralized  coverage algorithms
   have the advantage  of requiring very low processing  power from the
   \cite{pc10}, both centralized  and distributed algorithms have their
   own  advantages and  disadvantages. Centralized  coverage algorithms
   have the advantage  of requiring very low processing  power from the

-  sensor  nodes which  have usually  limited  processing capabilities.
+  sensor  nodes, which  have usually  limited  processing capabilities.

   Distributed  algorithms  are  very  adaptable  to  the  dynamic  and
   scalable nature of sensors network.  Authors in \cite{pc10} conclude
   that there is a threshold in  terms of network size to switch from a
   Distributed  algorithms  are  very  adaptable  to  the  dynamic  and
   scalable nature of sensors network.  Authors in \cite{pc10} conclude
   that there is a threshold in  terms of network size to switch from a

-  localized  to  a  centralized  algorithm.  Indeed  the  exchange  of
+  localized  to  a  centralized  algorithm.  Indeed, the  exchange  of

   messages  in large  networks may  consume a  considerable  amount of
   energy in a centralized approach  compared to a distributed one. Our
   work does not  consider only one leader to  compute and to broadcast
   messages  in large  networks may  consume a  considerable  amount of
   energy in a centralized approach  compared to a distributed one. Our
   work does not  consider only one leader to  compute and to broadcast


@@ -430,7 +421,7 @@ active mode.
 %The working phase works in rounding fashion. Each round include 3 steps described as follow :
 
 \subsection{Leader election phase}
 %The working phase works in rounding fashion. Each round include 3 steps described as follow :
 
 \subsection{Leader election phase}

-This  step includes choosing  the Wireless  Sensor Node  Leader (WSNL)
+This  step includes choosing  the Wireless  Sensor Node  Leader (WSNL),

 which  will  be  responsible  for executing  the coverage  algorithm.  Each
 subregion  in  the   area  of  interest  will  select   its  own  WSNL
 independently  for each  round.  All the  sensor  nodes cooperate  to
 which  will  be  responsible  for executing  the coverage  algorithm.  Each
 subregion  in  the   area  of  interest  will  select   its  own  WSNL
 independently  for each  round.  All the  sensor  nodes cooperate  to


@@ -462,7 +453,7 @@ starting a new round.
 
 %\noindent We try to produce an adaptive scheduling which allows sensors to operate alternatively so as to prolong the network lifetime. For convenience, the notations and assumptions are described first.
 %The wireless sensor node use the  binary disk sensing model by which each sensor node will has a certain sensing range is reserved within a circular disk called radius $R_s$.
 
 %\noindent We try to produce an adaptive scheduling which allows sensors to operate alternatively so as to prolong the network lifetime. For convenience, the notations and assumptions are described first.
 %The wireless sensor node use the  binary disk sensing model by which each sensor node will has a certain sensing range is reserved within a circular disk called radius $R_s$.

-\noindent We consider a boolean  disk coverage model which is the most
+\indent We consider a boolean  disk coverage model which is the most

 widely used sensor coverage model in the literature. Each sensor has a
 constant sensing range $R_s$. All  space points within a disk centered
 at  the sensor with  the radius  of the  sensing range  is said  to be
 widely used sensor coverage model in the literature. Each sensor has a
 constant sensing range $R_s$. All  space points within a disk centered
 at  the sensor with  the radius  of the  sensing range  is said  to be


@@ -487,7 +478,7 @@ connectivity among the working nodes in the active mode.
 %We choose to representEach wireless sensor node will be represented into a selected number of primary points by which we can know if the sensor node is covered or not.
 % Figure ~\ref{fig:cluster2} shows the selected primary points that represents the area of the sensor node and according to the sensing range of the wireless sensor node.
 
 %We choose to representEach wireless sensor node will be represented into a selected number of primary points by which we can know if the sensor node is covered or not.
 % Figure ~\ref{fig:cluster2} shows the selected primary points that represents the area of the sensor node and according to the sensing range of the wireless sensor node.
 

-\noindent Instead of working with the coverage area, we consider for each
+\indent Instead of working with the coverage area, we consider for each

 sensor a set of points called  primary points. We also assume that the
 sensing disk defined  by a sensor is covered if  all the primary points of
 this sensor are covered.
 sensor a set of points called  primary points. We also assume that the
 sensing disk defined  by a sensor is covered if  all the primary points of
 this sensor are covered.


@@ -507,7 +498,7 @@ increased or decreased if necessary)  as references to ensure that the
 monitored  region  of interest  is  covered  by  the selected  set  of
 sensors, instead of using all the points in the area.
 
 monitored  region  of interest  is  covered  by  the selected  set  of
 sensors, instead of using all the points in the area.
 

-\noindent  We can  calculate  the positions  of  the selected  primary
+\indent  We can  calculate  the positions  of  the selected  primary

 points in  the circle disk of  the sensing range of  a wireless sensor
 node (see figure~\ref{fig2}) as follows:\\
 $(p_x,p_y)$ = point center of wireless sensor node\\  
 points in  the circle disk of  the sensing range of  a wireless sensor
 node (see figure~\ref{fig2}) as follows:\\
 $(p_x,p_y)$ = point center of wireless sensor node\\  


@@ -547,13 +538,13 @@ $X_{13}=( p_x + R_s * (0), p_y + R_s * (\frac{-\sqrt{2}}{2})) $.
 
 %To satisfy the coverage requirement, the set of the principal points that will represent all the sensor nodes in the monitored region as $PSET= \lbrace P_1,\ldots ,P_p, \ldots , P_{N_P^k} \rbrace $, where $N_P^k = N_{sp} * N^k $ and according to the proposed model in figure ~\ref{fig:cluster2}. These points can be used by the wireless sensor node leader which will be chosen in each region in A to build a new parameter $\alpha_{jp}$  that represents the coverage possibility for each principal point $P_p$ of each wireless sensor node $s_j$ in $A^k$ as in \eqref{eq12}:\\
 
 
 %To satisfy the coverage requirement, the set of the principal points that will represent all the sensor nodes in the monitored region as $PSET= \lbrace P_1,\ldots ,P_p, \ldots , P_{N_P^k} \rbrace $, where $N_P^k = N_{sp} * N^k $ and according to the proposed model in figure ~\ref{fig:cluster2}. These points can be used by the wireless sensor node leader which will be chosen in each region in A to build a new parameter $\alpha_{jp}$  that represents the coverage possibility for each principal point $P_p$ of each wireless sensor node $s_j$ in $A^k$ as in \eqref{eq12}:\\
 

-\noindent   Our   model   is   based   on  the   model   proposed   by
+\indent   Our   model   is   based   on  the   model   proposed   by

 \cite{pedraza2006} where the objective is  to find a maximum number of
 disjoint  cover sets.   To accomplish  this goal,  authors  proposed an
 \cite{pedraza2006} where the objective is  to find a maximum number of
 disjoint  cover sets.   To accomplish  this goal,  authors  proposed an

-integer program which forces undercoverage and overcoverage of targets
+integer program, which forces undercoverage and overcoverage of targets

 to  become  minimal at  the  same  time.   They use  binary  variables
 $x_{jl}$ to indicate  if sensor $j$ belongs to cover  set $l$.  In our
 to  become  minimal at  the  same  time.   They use  binary  variables
 $x_{jl}$ to indicate  if sensor $j$ belongs to cover  set $l$.  In our

-model,  we  consider  binary  variables $X_{j}$  which  determine  the
+model,  we  consider  binary  variables $X_{j}$,  which  determine  the

 activation of  sensor $j$ in the  sensing phase of the  round. We also
 consider  primary points  as targets.   The set  of primary  points is
 denoted by $P$ and the set of sensors by $J$.
 activation of  sensor $j$ in the  sensing phase of the  round. We also
 consider  primary points  as targets.   The set  of primary  points is
 denoted by $P$ and the set of sensors by $J$.


@@ -631,7 +622,7 @@ The first group  of constraints indicates that some  primary point $p$
 should be covered by at least one  sensor and, if it is not always the
 case,  overcoverage  and  undercoverage  variables  help  balancing  the
 restriction  equations by taking  positive values.  There are  two main         
 should be covered by at least one  sensor and, if it is not always the
 case,  overcoverage  and  undercoverage  variables  help  balancing  the
 restriction  equations by taking  positive values.  There are  two main         

-objectives.  First we limit the overcoverage of primary points in order to
+objectives.  First, we limit the overcoverage of primary points in order to

 activate a minimum number of sensors.  Second we prevent the absence of monitoring on
  some parts of the subregion by  minimizing the undercoverage.   The
 weights  $w_\theta$  and  $w_U$  must  be properly  chosen  so  as  to
 activate a minimum number of sensors.  Second we prevent the absence of monitoring on
  some parts of the subregion by  minimizing the undercoverage.   The
 weights  $w_\theta$  and  $w_U$  must  be properly  chosen  so  as  to


@@ -687,11 +678,11 @@ defined by~\cite{HeinzelmanCB02} as  energy consumption model for each
 wireless  sensor node  when  transmitting or  receiving packets.   The
 energy of  each node in a  network is initialized  randomly within the
 range 24-60~joules, and each sensor node will consume 0.2 watts during
 wireless  sensor node  when  transmitting or  receiving packets.   The
 energy of  each node in a  network is initialized  randomly within the
 range 24-60~joules, and each sensor node will consume 0.2 watts during

-the sensing period which will last 60 seconds. Thus, an
+the sensing period, which will last 60 seconds. Thus, an

 active  node will  consume  12~joules during the sensing  phase, while  a
 sleeping  node will  use  0.002  joules.  Each  sensor  node will  not
 participate in the next round if its remaining energy is less than 12
 active  node will  consume  12~joules during the sensing  phase, while  a
 sleeping  node will  use  0.002  joules.  Each  sensor  node will  not
 participate in the next round if its remaining energy is less than 12

-joules.  In  all  experiments  the  parameters  are  set  as  follows:
+joules.  In  all  experiments,  the  parameters  are  set  as  follows:

 $R_s=5~m$, $w_{\Theta}=1$, and $w_{U}=|P^2|$.
 
 We  evaluate the  efficiency of  our approach by using  some performance
 $R_s=5~m$, $w_{\Theta}=1$, and $w_{U}=|P^2|$.
 
 We  evaluate the  efficiency of  our approach by using  some performance


@@ -804,11 +795,11 @@ simultaneously disconnected.
 
 \subsection{The percentage of stopped simulation runs}
 
 
 \subsection{The percentage of stopped simulation runs}
 

-We  will now  study  the percentage  of  simulations which  stopped due  to
+We  will now  study  the percentage  of  simulations, which  stopped due  to

 network  disconnections per round  for each  of the  three approaches.
 Figure~\ref{fig6} illustrates the percentage of stopped simulation
 runs per  round for 150 deployed  nodes.  It can be  observed that the
 network  disconnections per round  for each  of the  three approaches.
 Figure~\ref{fig6} illustrates the percentage of stopped simulation
 runs per  round for 150 deployed  nodes.  It can be  observed that the

-simple heuristic is  the approach which  stops first because  the nodes
+simple heuristic is  the approach, which  stops first because  the nodes

 are   randomly chosen.   Among  the  two   proposed  strategies,  the
 centralized  one  first  exhibits  network  disconnections.   Thus,  as
 explained previously, in case  of the strategy with several subregions
 are   randomly chosen.   Among  the  two   proposed  strategies,  the
 centralized  one  first  exhibits  network  disconnections.   Thus,  as
 explained previously, in case  of the strategy with several subregions


@@ -866,7 +857,7 @@ on a laptop of the decision phase (solving of the optimization problem)
 during one  round.  They  are given for  the different  approaches and
 various numbers of sensors.  The lack of any optimization explains why
 the heuristic has very  low execution times.  Conversely, the strategy
 during one  round.  They  are given for  the different  approaches and
 various numbers of sensors.  The lack of any optimization explains why
 the heuristic has very  low execution times.  Conversely, the strategy

-with  one  leader which  requires  to  solve  an optimization  problem
+with  one  leader, which  requires  to  solve  an optimization  problem

 considering  all  the  nodes  presents  redhibitory  execution  times.
 Moreover, increasing the network size by 50~nodes   multiplies the time
 by  almost a  factor of  10. The  strategy with  two leaders  has more
 considering  all  the  nodes  presents  redhibitory  execution  times.
 Moreover, increasing the network size by 50~nodes   multiplies the time
 by  almost a  factor of  10. The  strategy with  two leaders  has more


@@ -876,7 +867,7 @@ nodes.   Overall,  to  be  able to  deal  with  very  large  networks,  a
 distributed method is clearly required.
 
 \begin{table}[ht]
 distributed method is clearly required.
 
 \begin{table}[ht]

-\caption{The execution time(s) vs the number of sensors}
+\caption{THE EXECUTION TIME(S) VS THE NUMBER OF SENSORS}

 % title of Table
 \centering
 
 % title of Table
 \centering
 


@@ -972,12 +963,12 @@ approach like the one we propose  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.
 
 single global optimization problem  by partitioning it in many smaller
 problems, one per subregion, that can be solved more easily.
 

-In  future work, we plan  to study  and propose  a coverage  protocol which
+In  future work, we plan  to study  and propose  a coverage  protocol, which

 computes  all  active  sensor  schedules  in  one time,  using
 optimization  methods  such  as  swarms optimization  or  evolutionary
 algorithms.  The round  will still  consist of 4  phases, but  the
 computes  all  active  sensor  schedules  in  one time,  using
 optimization  methods  such  as  swarms optimization  or  evolutionary
 algorithms.  The round  will still  consist of 4  phases, but  the

-  decision phase will compute the schedules for several sensing phases
-  which, aggregated together, define a kind of meta-sensing phase.
+  decision phase will compute the schedules for several sensing phases,
+  which aggregated together, define a kind of meta-sensing phase.

 The computation of all cover sets in one time is far more
 difficult, but will reduce the communication overhead.
 % use section* for acknowledgement
 The computation of all cover sets in one time is far more
 difficult, but will reduce the communication overhead.
 % use section* for acknowledgement