corrections

diff --git a/Example.tex b/Example.tex
index ac05f6c8b3c28e7f090ca1386e6392f3defd0aeb..a7e85c3e5c6fd1702a2996389d24c1eea347d9fe 100644 (file)
--- a/Example.tex
+++ b/Example.tex
@@ -412,7 +412,7 @@ $X_{13}=( p_x + R_s * (0), p_y + R_s * (\frac{-\sqrt{2}}{2})) $.
 
 \fi
 
 
 \fi
 

-\subsection{The main idea}
+\subsection{Main idea}

 \label{main_idea}
 
 \noindent We start  by applying a divide-and-conquer algorithm  to partition the
 \label{main_idea}
 
 \noindent We start  by applying a divide-and-conquer algorithm  to partition the


@@ -428,7 +428,7 @@ executed   simultaneously  in   each   subregion.
 
 As  shown  in Figure~\ref{fig2},  the  proposed  DiLCO  protocol is  a  periodic
 protocol where  each period is  decomposed into 4~phases:  Information Exchange,
 
 As  shown  in Figure~\ref{fig2},  the  proposed  DiLCO  protocol is  a  periodic
 protocol where  each period is  decomposed into 4~phases:  Information Exchange,

-Leader Election ,  Decision, and Sensing. For each period  there will be exactly
+Leader Election,  Decision, and Sensing. For each period  there will be exactly

 one  cover  set  in charge  of  the  sensing  task.   A periodic  scheduling  is
 interesting  because it  enhances the  robustness  of the  network against  node
 failures. First,  a node  that has not  enough energy  to complete a  period, or
 one  cover  set  in charge  of  the  sensing  task.   A periodic  scheduling  is
 interesting  because it  enhances the  robustness  of the  network against  node
 failures. First,  a node  that has not  enough energy  to complete a  period, or


@@ -567,7 +567,7 @@ sensor in the subregion and then describe it in more detail.  \fi
 \end{algorithm}
 
 \iffalse
 \end{algorithm}
 
 \iffalse

-The DiLCO protocol work in rounds and executed at each sensor node in the network , each sensor node can still sense data while being in
+The DiLCO protocol work in rounds and executed at each sensor node in the network, each sensor node can still sense data while being in

 LISTENING mode. Thus, by entering the LISTENING mode at the beginning of each round,
 sensor nodes still executing sensing task while participating in the leader election and decision phases. More specifically, The DiLCO protocol algorithm works as follow: 
 Initially, the sensor node check it's remaining energy in order to participate in the current round. Each sensor node determines it's position and it's subregion based Embedded GPS  or Location Discovery Algorithm. After that, All the sensors collect position coordinates, current remaining energy, sensor node id, and the number of its one-hop live neighbors during the information exchange. It stores this information into a list L.
 LISTENING mode. Thus, by entering the LISTENING mode at the beginning of each round,
 sensor nodes still executing sensing task while participating in the leader election and decision phases. More specifically, The DiLCO protocol algorithm works as follow: 
 Initially, the sensor node check it's remaining energy in order to participate in the current round. Each sensor node determines it's position and it's subregion based Embedded GPS  or Location Discovery Algorithm. After that, All the sensors collect position coordinates, current remaining energy, sensor node id, and the number of its one-hop live neighbors during the information exchange. It stores this information into a list L.


@@ -583,7 +583,7 @@ objective is  to find a  maximum number of  disjoint cover sets.   To accomplish
 this goal,  the authors proposed  an 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
 this goal,  the authors proposed  an 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

-model, we  consider binary  variable $X_{j}$ which  determine the  activation of
+model, we consider that the binary variable $X_{j}$ determines the activation of

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


@@ -640,7 +640,7 @@ U_{p} = \left \{
 %\label{c1} 
 %\sum_{t \in T} X_{j,t} \leq \frac{RE_j}{e_t} &\forall j \in J \\
 %\label{c2}
 %\label{c1} 
 %\sum_{t \in T} X_{j,t} \leq \frac{RE_j}{e_t} &\forall j \in J \\
 %\label{c2}

-\Theta_{p}\in \mathbb{N} , &\forall p \in P\\
+\Theta_{p}\in \mathbb{N}, &\forall p \in P\\

 U_{p} \in \{0,1\}, &\forall p \in P \\
 X_{j} \in \{0,1\}, &\forall j \in J
 \end{array}
 U_{p} \in \{0,1\}, &\forall p \in P \\
 X_{j} \in \{0,1\}, &\forall j \in J
 \end{array}


@@ -775,7 +775,7 @@ symmetric  communication costs), and  we set  their respective  size to  112 and
 is equal to 0.2575 mW.
 
 Each node has an initial energy level, in Joules, which is randomly drawn in the
 is equal to 0.2575 mW.
 
 Each node has an initial energy level, in Joules, which is randomly drawn in the

-interval  $[500-700]$.  If  it's  energy  provision reaches  a  value below  the
+interval  $[500-700]$.  If  its  energy  provision reaches  a  value below  the

 threshold  $E_{th}=36$~Joules, the  minimum energy  needed  for a  node to  stay
 active during one period, it will no more participate in the coverage task. This
 value  corresponds  to the  energy  needed by  the  sensing  phase, obtained  by
 threshold  $E_{th}=36$~Joules, the  minimum energy  needed  for a  node to  stay
 active during one period, it will no more participate in the coverage task. This
 value  corresponds  to the  energy  needed by  the  sensing  phase, obtained  by


@@ -842,7 +842,7 @@ Where: $A_r^t$ is the number of active sensors in the subregion $r$ during round
 
 where $M$  corresponds to the number  of periods.  The total  energy consumed by
 the  sensors (EC)  comes  through  taking into  consideration  four main  energy
 
 where $M$  corresponds to the number  of periods.  The total  energy consumed by
 the  sensors (EC)  comes  through  taking into  consideration  four main  energy

-factors. The  first one , denoted $E^{\scriptsize  \mbox{com}}_m$, represent the
+factors. The  first one, denoted $E^{\scriptsize  \mbox{com}}_m$, represent the

 energy consumption  spent by  all the nodes  for wireless  communications during
 period $m$.   $E^{\scriptsize \mbox{list}}_m$,  the next factor,  corresponds to
 the  energy consumed by  the sensors  in LISTENING  status before  receiving the
 energy consumption  spent by  all the nodes  for wireless  communications during
 period $m$.   $E^{\scriptsize \mbox{list}}_m$,  the next factor,  corresponds to
 the  energy consumed by  the sensors  in LISTENING  status before  receiving the


@@ -1075,9 +1075,10 @@ difficult, but will reduce the communication overhead. \fi
 
 \section*{\uppercase{Acknowledgements}}
 
 
 \section*{\uppercase{Acknowledgements}}
 

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

 acknowledge  the University  of Babylon  - IRAQ  for the  financial  support and
 acknowledge  the University  of Babylon  - IRAQ  for the  financial  support and

-Campus France for the received support.
+Campus France for  the received support. This paper is  also partially funded by
+the Labex ACTION program (contract ANR-11-LABX-01-01).

 
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