ok

[Sensornets15.git] / Example.tex

diff --git a/Example.tex b/Example.tex
index 38cc14f5cca00795a4c2108785bb15b62fa44b31..3b522661430b3a17e87f6845d1e45241ea42fa74 100644 (file)
--- a/Example.tex
+++ b/Example.tex
@@ -300,12 +300,14 @@ and  the number  of  one-hop neighbors  still  alive. \textcolor{blue}{INFO pack
 completed, the nodes  of a subregion choose a leader to  take the decision based
 on  the  following  criteria   with  decreasing  importance:  larger  number  of
 neighbors, larger remaining energy, and  then in case of equality, larger index.
 completed, the nodes  of a subregion choose a leader to  take the decision based
 on  the  following  criteria   with  decreasing  importance:  larger  number  of
 neighbors, larger remaining energy, and  then in case of equality, larger index.

-After that,  if the sensor node is  leader, it will execute  the integer program
-algorithm (see Section~\ref{cp})  which provides a set of  sensors planned to be
-active in the next sensing phase. As leader, it will send an Active-Sleep packet
+After that,  if the sensor node is  leader, it will solve  an integer program 
+(see Section~\ref{cp}). \textcolor{blue}{This integer program contains boolean variables $X_j$  where ($X_j=1$) means that sensor $j$ will be active in the next sensing phase. Only sensors with enough remaining energy are involved in the integer program ($J$ is the set of all sensors involved). As the leader consumes energy (computation energy, denoted by $E^{comp}$) to solve the optimization problem, it will be included in the integer program only if it has enough energy to achieve the computation and to stay alive during the next sensing phase, that is to say if $RE_j > E^{comp}+E_{th}$. Once the optimization problem is solved, each leader will send an Active-Sleep packet

 to each sensor  in the same subregion to  indicate it if it has to  be active or
 to each sensor  in the same subregion to  indicate it if it has to  be active or

-not.  Alternately, if  the  sensor  is not  the  leader, it  will  wait for  the
-Active-Sleep packet to know its state for the coming sensing phase.
+not. Otherwise, if  the  sensor  is not  the  leader, it  will  wait for  the
+Active-Sleep packet to know its state for the coming sensing phase.}
+%which provides a set of  sensors planned to be
+%active in the next sensing phase.
+

 
 
 \begin{algorithm}[h!]                
 
 
 \begin{algorithm}[h!]                


@@ -354,7 +356,7 @@ 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 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 $P$
 The objective function consists in minimizing the undercoverage and the overcoverage of the area as suggested in \cite{pedraza2006}. 
 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 $p$ :
+and the set of alive 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}
  \Theta_{p} = \left \{ 
 \begin{array}{l l}
 \begin{equation}
  \Theta_{p} = \left \{ 
 \begin{array}{l l}


@@ -398,9 +400,14 @@ X_{j} \in \{0,1\}, &\forall j \in J
 \end{array}
 \right.
 \end{equation}
 \end{array}
 \right.
 \end{equation}

-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.  \textcolor{blue}{ By
+    choosing  $w_{U}$ much  larger than $w_{\theta}$,  the coverage  of a
+    maximum of  primary points  is ensured.  Then for the  same number  of covered
+    primary points,  the solution  with a  minimal number  of active  sensors is
+    preferred. }
+%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
 
 
 % MODIF - END