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[JournalMultiPeriods.git] / article.tex

diff --git a/article.tex b/article.tex
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+++ b/article.tex
@@ -644,16 +644,16 @@ $W_{U}$ & $|P|^2$ \\
   solver returns  the best solution  found, which  is not necessary  the optimal
   one. In practice, we only set time  limit values for $T=5$ and $T=7$. In fact,
   for $T=5$ we limited the time for  250~nodes, whereas for $T=7$ it was for the
   solver returns  the best solution  found, which  is not necessary  the optimal
   one. In practice, we only set time  limit values for $T=5$ and $T=7$. In fact,
   for $T=5$ we limited the time for  250~nodes, whereas for $T=7$ it was for the

-  three  largest network  sizes.  Therefore  we used  the  following values  (in
+  three  largest network  sizes.  Therefore  we  used the  following values  (in

   second): 0.03 for  250~nodes when $T=5$, while for $T=7$  we chose 0.03, 0.06,
   second): 0.03 for  250~nodes when $T=5$, while for $T=7$  we chose 0.03, 0.06,

-  and 0.08 for respectively 150, 200, and 250~nodes.
-  These time limit thresholds have been  set empirically. The basic idea consists
-  in considering  the average execution  time to  solve the integer  programs to
-  optimality, then in  dividing this average time by three  to set the threshold
-  value.  After that,  this threshold value is increased if  necessary so that
-  the solver is able  to deliver a feasible solution within  the time limit.  In
-  fact, selecting the optimal values for the time limits will be investigated in
-  the future.}
+  and  0.08  for  respectively  150,  200,  and  250~nodes.   These  time  limit
+  thresholds  have been  set  empirically. The  basic idea  is  to consider  the
+  average execution  time to solve  the integer  programs to optimality  for 100
+  nodes and then to adjust the time linearly according to the increasing network
+  size. After that,  this threshold value is increased if  necessary so that the
+  solver is able to deliver a feasible  solution within the time limit. In fact,
+  selecting the optimal  values for the time limits will  be investigated in the
+  future.}

 
  In the  following, we will make  comparisons with two other  methods. The first
  method,  called DESK  and proposed  by  \cite{ChinhVu}, is  a full  distributed
 
  In the  following, we will make  comparisons with two other  methods. The first
  method,  called DESK  and proposed  by  \cite{ChinhVu}, is  a full  distributed


@@ -663,13 +663,13 @@ $W_{U}$ & $|P|^2$ \\
  phase time.
 
 Some preliminary experiments were performed to study the choice of the number of
  phase time.
 
 Some preliminary experiments were performed to study the choice of the number of

-subregions  which subdivides  the  sensing field,  considering different  network
+subregions  which subdivides  the sensing  field, considering  different network

 sizes. They show that as the number of subregions increases, so does the network
 lifetime. Moreover,  it makes  the MuDiLCO protocol  more robust  against random
 sizes. They show that as the number of subregions increases, so does the network
 lifetime. Moreover,  it makes  the MuDiLCO protocol  more robust  against random

-network  disconnection due  to node  failures.  However,  too  many subdivisions
-reduce the advantage  of the optimization. In fact, there  is a balance between
-the  benefit  from the  optimization  and the  execution  time  needed to  solve
-it. In the following we have set the number of subregions to 16.
+network  disconnection due  to node  failures.  However,  too many  subdivisions
+reduce the  advantage of the optimization.  In fact, there is  a balance between
+the benefit from the optimization and the  execution time needed to solve it. In
+the following we have set the number of subregions to 16.

 
 \subsection{Energy model}
 
 
 \subsection{Energy model}
 


@@ -982,12 +982,12 @@ for different network sizes.
 As expected,  the execution time increases  with the number of  rounds $T$ taken
 into  account to  schedule  the sensing  phase. \textcolor{blue}{Obviously,  the
   number of variables and constraints of the integer program increases with $T$,
 As expected,  the execution time increases  with the number of  rounds $T$ taken
 into  account to  schedule  the sensing  phase. \textcolor{blue}{Obviously,  the
   number of variables and constraints of the integer program increases with $T$,

-  as was explained  in section~\ref{decision} The times obtained  for $T=1,3$ or
+  as  explained  in section~\ref{decision}, the times obtained  for $T=1,3$ or

   $5$ seem  bearable. But for  $T=7$, without any  limitation of the  time, they
   become  quickly unsuitable  for  a  sensor node,  especially  when the  sensor
   network size  increases as  demonstrated by Unlimited-MuDiLCO-7.   Notice that
   for 250  nodes, we also  limited the execution  time for $T=5$,  otherwise the
   $5$ seem  bearable. But for  $T=7$, without any  limitation of the  time, they
   become  quickly unsuitable  for  a  sensor node,  especially  when the  sensor
   network size  increases as  demonstrated by Unlimited-MuDiLCO-7.   Notice that
   for 250  nodes, we also  limited the execution  time for $T=5$,  otherwise the

-  execution time  would have  been above  MuDiLCO-7.  On the  one hand,  a large
+  execution time, denoted by Unlimited-MuDiLCO-5, is also above  MuDiLCO-7.  On the  one hand,  a large

   value  for  $T$  permits  to  reduce the  energy-overhead  due  to  the  three
   pre-sensing phases, on  the other hand a leader node  may waste a considerable
   amount of  energy to solve the  optimization problem. Thus, limiting  the time
   value  for  $T$  permits  to  reduce the  energy-overhead  due  to  the  three
   pre-sensing phases, on  the other hand a leader node  may waste a considerable
   amount of  energy to solve the  optimization problem. Thus, limiting  the time


@@ -1004,14 +1004,14 @@ node  density  which results  in  more  and more  redundant  nodes  that can  be
 deactivated and thus save energy.  Compared to the other approaches, our MuDiLCO
 protocol  maximizes the  lifetime of  the network.   In particular  the gain  in
 lifetime for a coverage  over 95\%, and a network of  250~nodes, is greater than
 deactivated and thus save energy.  Compared to the other approaches, our MuDiLCO
 protocol  maximizes the  lifetime of  the network.   In particular  the gain  in
 lifetime for a coverage  over 95\%, and a network of  250~nodes, is greater than

-38\% when switching from GAF to MuDiLCO-5.
+43\% when switching from GAF to MuDiLCO-5.

 %The lower performance that can be observed  for MuDiLCO-7 in case
 %of  $Lifetime_{95}$  with  large  wireless  sensor  networks  results  from  the
 %difficulty  of the optimization  problem to  be solved  by the  integer program.
 %This  point was  already noticed  in subsection  \ref{subsec:EC} devoted  to the
 %energy consumption,  since network lifetime and energy  consumption are directly
 %linked.
 %The lower performance that can be observed  for MuDiLCO-7 in case
 %of  $Lifetime_{95}$  with  large  wireless  sensor  networks  results  from  the
 %difficulty  of the optimization  problem to  be solved  by the  integer program.
 %This  point was  already noticed  in subsection  \ref{subsec:EC} devoted  to the
 %energy consumption,  since network lifetime and energy  consumption are directly
 %linked.

-\textcolor{blue}{Overall,  it appears  clearly that  computing a  scheduling for
+\textcolor{blue}{Overall,  it  clearly appears  that  computing a  scheduling for

   several rounds is possible and relevant,  providing that the execution time to
   solve the  optimization problem for  large instances is limited.   Notice that
   rather than limiting the execution time,  similar results might be obtained by
   several rounds is possible and relevant,  providing that the execution time to
   solve the  optimization problem for  large instances is limited.   Notice that
   rather than limiting the execution time,  similar results might be obtained by