Michel - Minor corrections

[Sensornets15.git] / Example.tex

diff --git a/Example.tex b/Example.tex
index 41f84a1d01dd242e19a9697a7687aa193628ab0e..3f5d44c1a1ddbd29501925b03787d46747f295e7 100644 (file)
--- a/Example.tex
+++ b/Example.tex
@@ -41,27 +41,27 @@ Optimization, Scheduling.}
   region) of interest  to be monitored, while simultaneously  preventing as much
   as possible a network failure due to battery-depleted nodes.  In this paper we
   propose a protocol, called Distributed Lifetime Coverage Optimization protocol
   region) of interest  to be monitored, while simultaneously  preventing as much
   as possible a network failure due to battery-depleted nodes.  In this paper we
   propose a protocol, called Distributed Lifetime Coverage Optimization protocol

-  (DiLCO), which maintains the coverage  and improves the lifetime of a wireless
+  (DiLCO), which maintains the coverage and  improves the lifetime of a wireless

   sensor network. First, we partition the area of interest into subregions using
   a classical divide-and-conquer method.  Our DiLCO protocol is then distributed
   sensor network. First, we partition the area of interest into subregions using
   a classical divide-and-conquer method.  Our DiLCO protocol is then distributed

-  on  the sensor  nodes  in each  subregion in  a  second step.  To fulfill  our
-  objective, the  proposed protocol combines two effective  techniques: a leader
+  on  the sensor  nodes in  each subregion  in a  second step.   To fulfill  our
+  objective, the proposed  protocol combines two effective  techniques: a leader

   election in  each subregion, followed  by an optimization-based  node activity
   election in  each subregion, followed  by an optimization-based  node activity

-  scheduling  performed by  each elected  leader.  This  two-step  process takes
+  scheduling  performed by  each elected  leader.  This  two-step process  takes

   place periodically, in  order to choose a small set  of nodes remaining active
   for sensing during a time slot.  Each set is built to ensure coverage at a low
   place periodically, in  order to choose a small set  of nodes remaining active
   for sensing during a time slot.  Each set is built to ensure coverage at a low

-  energy  cost, allowing  to optimize  the network  lifetime. 
-       %More  precisely, a
-  %period  consists   of  four  phases:   (i)~Information  Exchange,  (ii)~Leader
-  %Election,  (iii)~Decision,  and  (iv)~Sensing.  
-       The decision  process,  which
+  energy cost,  allowing to optimize  the network lifetime.  %More  precisely, a
+  %period  consists  of  four   phases:  (i)~Information  Exchange,  (ii)~Leader
+  %Election,  (iii)~Decision, and  (iv)~Sensing.   The  decision process,  which

   results in  an activity  scheduling vector,  is carried out  by a  leader node
   results in  an activity  scheduling vector,  is carried out  by a  leader node

-  through  the solving  of an  integer program. 
-       {\color{red} Simulations are conducted using the discret event simulator OMNET++.
-       We refer to the characterictics of a Medusa II sensor for the energy consumption and the time computation.
-       In comparison  with  two other  existing methods, our  approach is  able to  increase the  WSN lifetime  and provides
-  improved coverage performance. }}
-       
+  through the solving of an integer program.
+% MODIF - BEGIN
+  Simulations are conducted using the discret event simulator
+  OMNET++.  We  refer to the characterictics  of a Medusa II  sensor for
+  the energy consumption  and the computation time.   In comparison with
+  two other existing  methods, our approach is able to  increase the WSN
+  lifetime and provides improved coverage performance. }
+% MODIF - END

 
 \onecolumn \maketitle \normalsize \vfill
 
 
 \onecolumn \maketitle \normalsize \vfill
 


@@ -101,11 +101,17 @@ the sensors for  the sensing phase of the current period  is obtained by solving
 an integer program.  The resulting activation vector is  broadcast by a leader
 to every node of its subregion. 
 
 an integer program.  The resulting activation vector is  broadcast by a leader
 to every node of its subregion. 
 

-{\color{red} Our previous paper ~\cite{idrees2014coverage} relies almost exclusively on the framework of the DiLCO approach and the coverage problem formulation.
-In this paper we strengthen our simulations by taking into account the characteristics of a Medusa II sensor ~\cite{raghunathan2002energy} to measure the energy consumption and the computation time.
-We have implemented two other existing approaches (a distributed one DESK ~\cite{ChinhVu} and a centralized one GAF ~\cite{xu2001geography}) in order to compare their performances with our approach.
-We also focus on performance analysis based on the number of subregions. }
-
+% MODIF - BEGIN
+Our previous  paper ~\cite{idrees2014coverage} relies almost  exclusively on the
+framework of the  DiLCO approach and the coverage problem  formulation.  In this
+paper  we   made  more  realistic   simulations  by  taking  into   account  the
+characteristics of  a Medusa II sensor  ~\cite{raghunathan2002energy} to measure
+the energy consumption and the computation  time.  We have implemented two other
+existing approaches (a distributed one,  DESK ~\cite{ChinhVu}, and a centralized
+one called GAF  ~\cite{xu2001geography}) in order to  compare their performances
+with our approach.  We also focus on performance analysis based on the number of
+subregions. }
+% MODIF - END

 
 The remainder  of the  paper continues with  Section~\ref{sec:Literature Review}
 where a  review of some related  works is presented. The  next section describes
 
 The remainder  of the  paper continues with  Section~\ref{sec:Literature Review}
 where a  review of some related  works is presented. The  next section describes


@@ -333,10 +339,10 @@ Active-Sleep packet to know its state for the coming sensing phase.
 \section{\uppercase{Coverage problem formulation}}
 \label{cp}
 
 \section{\uppercase{Coverage problem formulation}}
 \label{cp}
 

-{\color{red}
+% MODIF - BEGIN

 We formulate the coverage optimization problem with an integer program.
 The objective function consists in minimizing the undercoverage and the overcoverage of the area as suggested in \cite{pedraza2006}. 
 We formulate the coverage optimization problem with an integer program.
 The objective function consists in minimizing the undercoverage and the overcoverage of the area as suggested in \cite{pedraza2006}. 

-The area coverage problem is transformed to the coverage of a fraction of points called primary points. 
+The area coverage problem is expressed as the coverage of a fraction of points called primary points. 

 Details on the choice and the number of primary points can be found in \cite{idrees2014coverage}. The set of primary points is denoted by $P$
 and the set of sensors by $J$. As we consider a boolean disk coverage model, we use the boolean indicator $\alpha_{jp}$ which is equal to 1 if the primary point $p$ is in the sensing range of the sensor $j$. The binary variable $X_j$ represents the activation or not of the sensor $j$. So we can express the number of  active sensors  that cover  the primary  point $p$ by $\sum_{j \in J} \alpha_{jp} * X_{j}$. We deduce the overcoverage denoted by $\Theta_p$ of the primary point $p$ :
 \begin{equation}
 Details on the choice and the number of primary points can be found in \cite{idrees2014coverage}. The set of primary points is denoted by $P$
 and the set of sensors by $J$. As we consider a boolean disk coverage model, we use the boolean indicator $\alpha_{jp}$ which is equal to 1 if the primary point $p$ is in the sensing range of the sensor $j$. The binary variable $X_j$ represents the activation or not of the sensor $j$. So we can express the number of  active sensors  that cover  the primary  point $p$ by $\sum_{j \in J} \alpha_{jp} * X_{j}$. We deduce the overcoverage denoted by $\Theta_p$ of the primary point $p$ :
 \begin{equation}


@@ -360,11 +366,11 @@ U_{p} = \left \{
 \end{array} \right.
 \label{eq14} 
 \end{equation}
 \end{array} \right.
 \label{eq14} 
 \end{equation}

-There is, of course, a relationship between the three variables $X_j$, $\Theta_p$ and $U_p$ which can be formulated as follows :
+There is, of course, a relationship between the three variables $X_j$, $\Theta_p$, and $U_p$ which can be formulated as follows :

 \begin{equation}
 \sum_{j \in J}  \alpha_{jp} X_{j} - \Theta_{p}+ U_{p} =1, \forall p \in P
 \end{equation}
 \begin{equation}
 \sum_{j \in J}  \alpha_{jp} X_{j} - \Theta_{p}+ U_{p} =1, \forall p \in P
 \end{equation}

-If the point $p$ is not covered, $U_p=1$,  $\sum_{j \in J}  \alpha_{jp} X_{j}=0$ and $\Theta_{p}=0$ by defintion, so the equality is satisfied.
+If the point $p$ is not covered, $U_p=1$,  $\sum_{j \in J}  \alpha_{jp} X_{j}=0$ and $\Theta_{p}=0$ by definition, so the equality is satisfied.

 On the contrary, if the point $p$ is covered, $U_p=0$, and $\Theta_{p}=\left( \sum_{j \in J} \alpha_{jp}  X_{j} \right)- 1$. 
 \noindent Our coverage optimization problem can then be formulated as follows:
 \begin{equation} \label{eq:ip2r}
 On the contrary, if the point $p$ is covered, $U_p=0$, and $\Theta_{p}=\left( \sum_{j \in J} \alpha_{jp}  X_{j} \right)- 1$. 
 \noindent Our coverage optimization problem can then be formulated as follows:
 \begin{equation} \label{eq:ip2r}


@@ -385,7 +391,7 @@ X_{j} \in \{0,1\}, &\forall j \in J
 The objective function is a weighted sum of overcoverage and undercoverage. The goal is to limit the overcoverage in order to activate a minimal number of sensors while simultaneously preventing undercoverage. Both  weights $w_\theta$  and $w_U$ must  be carefully  chosen in
 order to  guarantee that the  maximum number of  points are covered  during each
 period.
 The objective function is a weighted sum of overcoverage and undercoverage. The goal is to limit the overcoverage in order to activate a minimal number of sensors while simultaneously preventing undercoverage. Both  weights $w_\theta$  and $w_U$ must  be carefully  chosen in
 order to  guarantee that the  maximum number of  points are covered  during each
 period.

-}
+% MODIF - END