X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/JournalMultiPeriods.git/blobdiff_plain/8affde3b4ffda73c483b714702ea3a2f9e5b9b61..c5fe479b505a28e5762ea016dba2d5e3b7cced85:/article.tex?ds=inline

diff --git a/article.tex b/article.tex
index 4a63d7d..f81734e 100644
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+++ b/article.tex
@@ -249,6 +249,10 @@ suggested another (LP)  technique to solve this problem.  A centralized solution
 based  on  the  Garg-K\"{o}nemann  algorithm~\cite{garg98},  provably  near  the
 optimal solution, is also proposed.
 
+In~\cite{yang2014maximum}, The authors are proposed a linear programming approach for selecting the minimum number of sensor nodes in working station so as to preserve a maximum coverage and extend lifetime of the network. Cheng et al.~\cite{cheng2014energy} are proposed a heuristic algorithm called Cover Sets Balance (CSB) algorithm to choose a set of active nodes using the tuple (data coverage range, residual energy). Then, they are introduced a new Correlated Node Set Computing (CNSC) algorithm to find the correlated node set for a given node.  After that, they are proposed a High Residual Energy First (HREF) node selection algorithm to minimize the number of active nodes so as to prolong the network lifetime. 
+In~\cite{castano2013column,rossi2012exact,deschinkel2012column}, The authors are proposed a centralized methods based on column generation approach to extend lifetime in wireless sensor networks while coverage preservation.
+
+
 \subsection{Distributed approaches}
 %{\bf Distributed approaches}
 In distributed  and localized coverage  algorithms, the required  computation to
@@ -740,10 +744,11 @@ $w_{U}$ & $|P^2|$
 % is used to refer this table in the text
 \end{table}
   
-Our protocol  is declined into  four versions: MuDiLCO-1,  MuDiLCO-3, MuDiLCO-5,
+Our protocol is declined into four versions: MuDiLCO-1,  MuDiLCO-3, MuDiLCO-5,
 and  MuDiLCO-7, corresponding  respectively to  $T=1,3,5,7$ ($T$  the  number of
 rounds  in one  sensing period).  In  the following,  the general  case will  be
-denoted by MuDiLCO-T.   We compare MuDiLCO-T with two  other methods.  The first
+denoted by MuDiLCO-T. We are studied the impact of dividing the sensing feild on the performance of our  MuDiLCO-T protocol with different network sizes using Divide and Conquer method, and we are found that as the number of subregions increase, the network lifetime increase and the MuDiLCO-T protocol become more powerful against the network disconnection.
+This subdivision should be stopped when there is no benefit from the optimization, therefore Our MuDiLCO-T protocol is distributed over 16 rather than 32 subregions because there is a balance between the benefit from the optimization and the execution time is needed to sove it.    We compare MuDiLCO-T with two  other methods.  The first
 method,  called  DESK and  proposed  by  \cite{ChinhVu}  is a  full  distributed
 coverage  algorithm.   The  second  method,  called  GAF~\cite{xu2001geography},
 consists in dividing the region  into fixed squares.  During the decision phase,
@@ -838,7 +843,7 @@ To evaluate our approach we consider the following performance metrics:
 \end{equation*}
 where $n^t$ is  the number of covered  grid points by the active  sensors of all
 subregions during round $t$ in the current sensing phase and $N$ is total number
-of grid points in the sensing field of the network.
+of grid points in the sensing field of the network. In our simulation $N = 51 \times 26 = 1326$ grid points.
 %The accuracy of this method depends on the distance between grids. In our
 %simulations, the sensing field has been divided into 50 by 25 grid points, which means
 %there are $51 \times 26~ = ~ 1326$ points in total.
@@ -1122,7 +1127,9 @@ and thus to an excessive energy consumption.
 %In  future work, we plan  to study and propose adjustable sensing range coverage optimization protocol, which computes  all active sensor schedules in one time, by using
 %optimization  methods. This protocol can prolong the network lifetime by minimizing the number of the active sensor nodes near the borders by optimizing the sensing range of sensor nodes.
 % use section* for acknowledgement
-%\section*{Acknowledgment}
+
+\section*{Acknowledgment}
+As a Ph.D. student, Ali Kadhum IDREES would like to gratefully acknowledge the University of Babylon - IRAQ for the financial support and in the same time would like to acknowledge Campus France (The French national agency for the promotion of higher education, international student services, and international mobility) and University of Franche-Comt\'e - FRANCE for all the support in FRANCE.
 
 %% \linenumbers