ok ingrid corrections

diff --git a/PeCO-EO/articleeo.tex b/PeCO-EO/articleeo.tex
index d4ae9d964e548d9abc49a9d0a6aba66047c52d48..9676c99e0504d0ae6ee3a225c2fa56ad1da56aed 100644 (file)
--- a/PeCO-EO/articleeo.tex
+++ b/PeCO-EO/articleeo.tex
@@ -36,7 +36,7 @@ distributed among sensor  nodes in each subregion.  The novelty  of our approach
 lies essentially  in the  formulation of a  new mathematical  optimization model
 based  on  the  perimeter  coverage   level  to  schedule  sensors'  activities.
 Extensive simulation experiments demonstrate that PeCO can offer longer lifetime
 lies essentially  in the  formulation of a  new mathematical  optimization model
 based  on  the  perimeter  coverage   level  to  schedule  sensors'  activities.
 Extensive simulation experiments demonstrate that PeCO can offer longer lifetime

-coverage for WSNs in comparison with some other protocols.
+coverage for WSNs compared to other protocols.

 
 \begin{keywords}
   Wireless Sensor Networks, Area Coverage, Energy efficiency, Optimization, Scheduling.
 
 \begin{keywords}
   Wireless Sensor Networks, Area Coverage, Energy efficiency, Optimization, Scheduling.


@@ -48,34 +48,34 @@ coverage for WSNs in comparison with some other protocols.
 \label{sec:introduction}
 
 The continuous progress in Micro  Electro-Mechanical Systems (MEMS) and wireless
 \label{sec:introduction}
 
 The continuous progress in Micro  Electro-Mechanical Systems (MEMS) and wireless

-communication hardware has  given rise to the opportunity to  use large networks
+communication hardware has  given rise to the opportunity of using large networks

 of      tiny       sensors,      called      Wireless       Sensor      Networks
 (WSN)~\citep{akyildiz2002wireless,puccinelli2005wireless}, to fulfill monitoring
 tasks.   A  WSN  consists  of  small low-powered  sensors  working  together  by
 communicating with one another through multi-hop radio communications. Each node
 can send the data  it collects in its environment, thanks to  its sensor, to the
 of      tiny       sensors,      called      Wireless       Sensor      Networks
 (WSN)~\citep{akyildiz2002wireless,puccinelli2005wireless}, to fulfill monitoring
 tasks.   A  WSN  consists  of  small low-powered  sensors  working  together  by
 communicating with one another through multi-hop radio communications. Each node
 can send the data  it collects in its environment, thanks to  its sensor, to the

-user by means of  sink nodes. The features of a WSN made  it suitable for a wide
-range of application  in areas such as business,  environment, health, industry,
+user by means of  sink nodes. The features of a WSN makes  it suitable for a wide
+range of applications  in areas such as business,  environment, health, industry,

 military, and so on~\citep{yick2008wireless}.  Typically, a sensor node contains
 three main components~\citep{anastasi2009energy}: a sensing unit able to measure
 physical,  chemical, or  biological  phenomena observed  in  the environment;  a
 processing unit which will process and store the collected measurements; a radio
 military, and so on~\citep{yick2008wireless}.  Typically, a sensor node contains
 three main components~\citep{anastasi2009energy}: a sensing unit able to measure
 physical,  chemical, or  biological  phenomena observed  in  the environment;  a
 processing unit which will process and store the collected measurements; a radio

-communication unit for data transmission and receiving.
+communication unit for data transmission and reception.

 
 The energy needed  by an active sensor node to  perform sensing, processing, and
 
 The energy needed  by an active sensor node to  perform sensing, processing, and

-communication is supplied by a power supply which is a battery. This battery has
+communication is provided by a power supply which is a battery. This battery has

 a limited energy provision and it may  be unsuitable or impossible to replace or
 a limited energy provision and it may  be unsuitable or impossible to replace or

-recharge it in  most applications. Therefore it is necessary  to deploy WSN with
+recharge  in  most applications. Therefore it is necessary  to deploy WSN with

 high density  in order to  increase reliability  and to exploit  node redundancy
 thanks to energy-efficient activity  scheduling approaches.  Indeed, the overlap
 of sensing  areas can be exploited  to schedule alternatively some  sensors in a
 low power sleep mode and thus save  energy. Overall, the main question that must
 high density  in order to  increase reliability  and to exploit  node redundancy
 thanks to energy-efficient activity  scheduling approaches.  Indeed, the overlap
 of sensing  areas can be exploited  to schedule alternatively some  sensors in a
 low power sleep mode and thus save  energy. Overall, the main question that must

-be answered is: how to extend the lifetime coverage of a WSN as long as possible
+be answered is: how is it possible to extend the lifetime coverage of a WSN as long as possible

 while  ensuring  a   high  level  of  coverage?   These  past   few  years  many
 energy-efficient mechanisms have been suggested  to retain energy and extend the
 lifetime of the WSNs~\citep{rault2014energy}.
 
 while  ensuring  a   high  level  of  coverage?   These  past   few  years  many
 energy-efficient mechanisms have been suggested  to retain energy and extend the
 lifetime of the WSNs~\citep{rault2014energy}.
 

-This paper makes the following contributions.
+This paper makes the following contributions :

 \begin{enumerate}
 \item A  framework is devised  to schedule  nodes to be  activated alternatively
   such that  the network  lifetime is  prolonged while  ensuring that  a certain
 \begin{enumerate}
 \item A  framework is devised  to schedule  nodes to be  activated alternatively
   such that  the network  lifetime is  prolonged while  ensuring that  a certain


@@ -88,7 +88,7 @@ This paper makes the following contributions.
   architecture.
 \item A new  mathematical optimization model is proposed.  Instead  of trying to
   cover a set of specified points/targets as  in most of the methods proposed in
   architecture.
 \item A new  mathematical optimization model is proposed.  Instead  of trying to
   cover a set of specified points/targets as  in most of the methods proposed in

-  the literature, we formulate an integer program based on perimeter coverage of
+  the literature, we formulate a mixed-integer program based on the perimeter coverage of

   each sensor.  The  model involves integer variables to  capture the deviations
   between  the actual  level  of coverage  and the  required  level.  Hence,  an
   optimal  schedule will  be  obtained by  minimizing a  weighted  sum of  these
   each sensor.  The  model involves integer variables to  capture the deviations
   between  the actual  level  of coverage  and the  required  level.  Hence,  an
   optimal  schedule will  be  obtained by  minimizing a  weighted  sum of  these


@@ -125,9 +125,9 @@ to  the objective  of coverage  for a  finite number  of discrete  points called
 targets,   and   barrier  coverage~\citep{HeShibo,kim2013maximum}   focuses   on
 preventing  intruders   from  entering   into  the   region  of   interest.   In
 \citep{Deng2012} authors  transform the  area coverage  problem into  the target
 targets,   and   barrier  coverage~\citep{HeShibo,kim2013maximum}   focuses   on
 preventing  intruders   from  entering   into  the   region  of   interest.   In
 \citep{Deng2012} authors  transform the  area coverage  problem into  the target

-coverage one taking into account the  intersection points among disks of sensors
-nodes    or   between    disk   of    sensor   nodes    and   boundaries.     In
-\citep{Huang:2003:CPW:941350.941367}  authors prove  that if  the perimeters  of
+coverage one, taking into account the  intersection points among disks of sensors
+nodes    or   between    disks   of    sensor   nodes    and   boundaries.     In
+\citep{Huang:2003:CPW:941350.941367}  authors prove  that if  the perimeters  of the

 sensors are sufficiently  covered it will be  the case for the  whole area. They
 provide an algorithm in $O(nd~log~d)$  time to compute the perimeter-coverage of
 each sensor. $d$ denotes  the maximum number of sensors that  are neighbors to a
 sensors are sufficiently  covered it will be  the case for the  whole area. They
 provide an algorithm in $O(nd~log~d)$  time to compute the perimeter-coverage of
 each sensor. $d$ denotes  the maximum number of sensors that  are neighbors to a


@@ -139,7 +139,7 @@ sensor, and  $n$ is the  total number  of sensors in  the network. {\it  In PeCO
 The major  approach to extend network  lifetime while preserving coverage  is to
 divide/organize the  sensors into a suitable  number of set covers  (disjoint or
 non-disjoint)  \citep{wang2011coverage},  where  each set  completely  covers  a
 The major  approach to extend network  lifetime while preserving coverage  is to
 divide/organize the  sensors into a suitable  number of set covers  (disjoint or
 non-disjoint)  \citep{wang2011coverage},  where  each set  completely  covers  a

-region of interest,  and to activate these set covers  successively. The network
+region of interest,  and to successively activate these set covers. The network

 activity can be planned in advance and scheduled for the entire network lifetime
 or organized  in periods,  and the  set of  active sensor  nodes decided  at the
 beginning of each  period \citep{ling2009energy}. In fact,  many authors propose
 activity can be planned in advance and scheduled for the entire network lifetime
 or organized  in periods,  and the  set of  active sensor  nodes decided  at the
 beginning of each  period \citep{ling2009energy}. In fact,  many authors propose


@@ -162,20 +162,20 @@ algorithms~\citep{ChinhVu,qu2013distributed,yangnovel}  each  sensor decides  of
 its own  activity scheduling after  an information exchange with  its neighbors.
 The main interest of such an approach  is to avoid long range communications and
 thus to reduce the energy dedicated to the communications.  Unfortunately, since
 its own  activity scheduling after  an information exchange with  its neighbors.
 The main interest of such an approach  is to avoid long range communications and
 thus to reduce the energy dedicated to the communications.  Unfortunately, since

-each node has  only information on its immediate neighbors  (usually the one-hop
-ones)  it may  make a  bad  decision leading  to a  global suboptimal  solution.
+each node has information on its immediate neighbors only  (usually the one-hop
+ones),  it may  make a  bad  decision leading  to a  global suboptimal  solution.

 Conversely,                                                          centralized
 algorithms~\citep{cardei2005improving,zorbas2010solving,pujari2011high}   always
 Conversely,                                                          centralized
 algorithms~\citep{cardei2005improving,zorbas2010solving,pujari2011high}   always

-provide nearly  or close to  optimal solution since  the algorithm has  a global
+provide nearly optimal solutions since  the algorithm has  a global

 view of the whole network. The disadvantage of a centralized method is obviously
 its high cost  in communications needed to  transmit to a single  node, the base
 station which will globally schedule nodes'  activities, data from all the other
 sensor nodes in  the area.  The price  in communications can be  huge since long
 range communications will be needed. In fact  the larger the WSN, the higher the
 communication  energy  cost.  {\it  In  order  to  be suitable  for  large-scale
 view of the whole network. The disadvantage of a centralized method is obviously
 its high cost  in communications needed to  transmit to a single  node, the base
 station which will globally schedule nodes'  activities, data from all the other
 sensor nodes in  the area.  The price  in communications can be  huge since long
 range communications will be needed. In fact  the larger the WSN, the higher the
 communication  energy  cost.  {\it  In  order  to  be suitable  for  large-scale

-  networks,  in PeCO  protocol  the area  of interest  is  divided into  several
+  networks,  in the PeCO  protocol  the area  of interest  is  divided into  several

   smaller subregions, and in each one, a  node called the leader is in charge of
   smaller subregions, and in each one, a  node called the leader is in charge of

-  selecting the  active sensors for the  current period.  Thus PeCO  protocol is
+  selecting the  active sensors for the  current period.  Thus the PeCO  protocol is

   scalable and a globally distributed method,  whereas it is centralized in each
   subregion.}
 
   scalable and a globally distributed method,  whereas it is centralized in each
   subregion.}
 


@@ -195,14 +195,14 @@ practiced techniques for  solving linear programs with too  many variables, have
 also                                                                        been
 used~\citep{castano2013column,doi:10.1080/0305215X.2012.687732,deschinkel2012column}.
 {\it In  the PeCO  protocol, each leader,  in charge of  a subregion,  solves an
 also                                                                        been
 used~\citep{castano2013column,doi:10.1080/0305215X.2012.687732,deschinkel2012column}.
 {\it In  the PeCO  protocol, each leader,  in charge of  a subregion,  solves an

-  integer program which  has a twofold objective: minimize  the overcoverage and
+  integer program which  has a twofold objective: minimizing  the overcoverage and

   the undercoverage of the perimeter of each sensor.}
 
 The  authors   in  \citep{Idrees2}  propose  a   Distributed  Lifetime  Coverage
 Optimization (DiLCO)  protocol, which  maintains the  coverage and  improves the
 lifetime  in WSNs.   It is  an  improved version  of a  research work  presented
 in~\citep{idrees2014coverage}.  First, the area  of interest is partitioned into
   the undercoverage of the perimeter of each sensor.}
 
 The  authors   in  \citep{Idrees2}  propose  a   Distributed  Lifetime  Coverage
 Optimization (DiLCO)  protocol, which  maintains the  coverage and  improves the
 lifetime  in WSNs.   It is  an  improved version  of a  research work  presented
 in~\citep{idrees2014coverage}.  First, the area  of interest is partitioned into

-subregions using a divide-and-conquer method. DiLCO protocol is then distributed
+subregions using a divide-and-conquer method. The DiLCO protocol is then distributed

 on the  sensor nodes  in each  subregion in  a second  step. Hence this protocol
 combines two  techniques: a leader  election in  each subregion, followed  by an
 optimization-based   node  activity   scheduling  performed   by  each   elected
 on the  sensor nodes  in each  subregion in  a second  step. Hence this protocol
 combines two  techniques: a leader  election in  each subregion, followed  by an
 optimization-based   node  activity   scheduling  performed   by  each   elected


@@ -211,8 +211,8 @@ decomposed into 4  phases: information exchange, leader  election, decision, and
 sensing. The  simulations show that DiLCO  is able to increase  the WSN lifetime
 and provides  improved coverage performance.  {\it  In the PeCO protocol,  a new
   mathematical optimization model is proposed. Instead  of trying to cover a set
 sensing. The  simulations show that DiLCO  is able to increase  the WSN lifetime
 and provides  improved coverage performance.  {\it  In the PeCO protocol,  a new
   mathematical optimization model is proposed. Instead  of trying to cover a set

-  of  specified points/targets  as in  DiLCO protocol,  we formulate  an integer
-  program based on perimeter coverage of each sensor. The model involves integer
+  of  specified points/targets  as in  the DiLCO protocol,  we formulate  an integer
+  program based on the perimeter coverage of each sensor. The model involves integer

   variables to capture  the deviations between the actual level  of coverage and
   the required level. The idea is that an optimal scheduling will be obtained by
   minimizing a weighted sum of these deviations.}
   variables to capture  the deviations between the actual level  of coverage and
   the required level. The idea is that an optimal scheduling will be obtained by
   minimizing a weighted sum of these deviations.}


@@ -280,7 +280,7 @@ west  side of  sensor~$u$,  with  the following  respective  coordinates in  the
 sensing area~:  $(v_x,v_y)$ and $(u_x,u_y)$.  From the previous  coordinates the
 euclidean distance between nodes~$u$ and $v$ is computed as follows:
 $$
 sensing area~:  $(v_x,v_y)$ and $(u_x,u_y)$.  From the previous  coordinates the
 euclidean distance between nodes~$u$ and $v$ is computed as follows:
 $$

-  Dist(u,v)=\sqrt{\vert u_x - v_x \vert^2 + \vert u_y-v_y \vert^2},
+  Dist(u,v)=\sqrt{(u_x - v_x)^2 + (u_y-v_y)^2},

 $$
 while the angle~$\alpha$ is obtained through the formula:
  \[
 $$
 while the angle~$\alpha$ is obtained through the formula:
  \[


@@ -342,7 +342,7 @@ above is thus given by the sixth line of the table.
 \end{table}
 
 In  the  PeCO protocol,  the  scheduling  of  the  sensor nodes'  activities  is
 \end{table}
 
 In  the  PeCO protocol,  the  scheduling  of  the  sensor nodes'  activities  is

-formulated    with    an    mixed-integer     program    based    on    coverage
+formulated    with    a    mixed-integer     program    based    on    coverage

 intervals~\citep{doi:10.1155/2010/926075}.  The  formulation   of  the  coverage
 optimization problem is  detailed in~Section~\ref{cp}.  Note that  when a sensor
 node  has a  part of  its sensing  range outside  the WSN  sensing field,  as in
 intervals~\citep{doi:10.1155/2010/926075}.  The  formulation   of  the  coverage
 optimization problem is  detailed in~Section~\ref{cp}.  Note that  when a sensor
 node  has a  part of  its sensing  range outside  the WSN  sensing field,  as in


@@ -396,13 +396,13 @@ of the application.
 \label{figure4}
 \end{figure} 
 
 \label{figure4}
 \end{figure} 
 

-We define two types of packets to be used by PeCO protocol:
+We define two types of packets to be used by the PeCO protocol:

 \begin{itemize} 
 \item INFO  packet: sent  by each  sensor node to  all the  nodes inside  a same
   subregion for information exchange.
 \item ActiveSleep packet: sent  by the leader to all the  nodes in its subregion
   to transmit to  them their respective status (stay Active  or go Sleep) during
 \begin{itemize} 
 \item INFO  packet: sent  by each  sensor node to  all the  nodes inside  a same
   subregion for information exchange.
 \item ActiveSleep packet: sent  by the leader to all the  nodes in its subregion
   to transmit to  them their respective status (stay Active  or go Sleep) during

-  sensing phase.
+  the sensing phase.

 \end{itemize}
 
 Five statuses are possible for a sensor node in the network:
 \end{itemize}
 
 Five statuses are possible for a sensor node in the network:


@@ -511,10 +511,10 @@ criteria for the leader are (in order  of priority):
 \begin{enumerate}
 \item larger number of neighbors;
 \item larger  remaining energy;
 \begin{enumerate}
 \item larger number of neighbors;
 \item larger  remaining energy;

-\item and then  in case  of equality,  larger index.
+\item and then,  in case  of equality,  larger indexes.

 \end{enumerate}
 Once chosen, the leader collects information  to formulate and solve the integer
 \end{enumerate}
 Once chosen, the leader collects information  to formulate and solve the integer

-program  which allows  to construct  the set  of active  sensors in  the sensing
+program  which allows  to build  the set  of active  sensors in  the sensing

 stage.
 
 \section{Perimeter-based Coverage Problem Formulation}
 stage.
 
 \section{Perimeter-based Coverage Problem Formulation}


@@ -536,7 +536,7 @@ First, the following sets:
 \item  $I_j$  designates  the  set  of  coverage  intervals  (CI)  obtained  for
   sensor~$j$.
 \end{itemize}
 \item  $I_j$  designates  the  set  of  coverage  intervals  (CI)  obtained  for
   sensor~$j$.
 \end{itemize}

-$I_j$ refers to the set of  coverage intervals which have been defined according
+$I_j$ refers to the set of  coverage intervals which has been defined according

 to the  method introduced in  Subsection~\ref{CI}. For a coverage  interval $i$,
 let $a^j_{ik}$ denote  the indicator function of whether  sensor~$k$ is involved
 in coverage interval~$i$ of sensor~$j$, that is:
 to the  method introduced in  Subsection~\ref{CI}. For a coverage  interval $i$,
 let $a^j_{ik}$ denote  the indicator function of whether  sensor~$k$ is involved
 in coverage interval~$i$ of sensor~$j$, that is:


@@ -610,10 +610,10 @@ $V_{i}^{j}=l^{i}-l$.
 
 $\alpha^j_i$ and $\beta^j_i$  are nonnegative weights selected  according to the
 relative importance of satisfying the associated level of coverage. For example,
 
 $\alpha^j_i$ and $\beta^j_i$  are nonnegative weights selected  according to the
 relative importance of satisfying the associated level of coverage. For example,

-weights associated with  coverage intervals of a specified part  of a region may
+weights associated with  coverage intervals of the specified part  of a region may

 be given by  a relatively larger magnitude than weights  associated with another
 region. This kind of mixed-integer program  is inspired from the model developed
 be given by  a relatively larger magnitude than weights  associated with another
 region. This kind of mixed-integer program  is inspired from the model developed

-for   brachytherapy  treatment   planning  for   optimizing  dose   distribution
+for   brachytherapy  treatment   planning  to optimize  dose   distribution

 \citep{0031-9155-44-1-012}.  The choice of the values for variables $\alpha$ and
 $\beta$  should be  made according  to the  needs of  the application.  $\alpha$
 should be  large enough  to prevent  undercoverage and so  to reach  the highest
 \citep{0031-9155-44-1-012}.  The choice of the values for variables $\alpha$ and
 $\beta$  should be  made according  to the  needs of  the application.  $\alpha$
 should be  large enough  to prevent  undercoverage and so  to reach  the highest


@@ -667,10 +667,10 @@ coverage task. This value corresponds to the energy needed by the sensing phase,
 obtained by multiplying  the energy consumed in the active  state (9.72 mW) with
 the time in seconds for one period (3600 seconds), and adding the energy for the
 pre-sensing phases.  According  to the interval of initial energy,  a sensor may
 obtained by multiplying  the energy consumed in the active  state (9.72 mW) with
 the time in seconds for one period (3600 seconds), and adding the energy for the
 pre-sensing phases.  According  to the interval of initial energy,  a sensor may

-be active during at most 20 periods. Information exchange to update the coverage
+be active during at most 20 periods. the information exchange to update the coverage

 is executed every  hour, but the length  of the sensing period  could be reduced
 is executed every  hour, but the length  of the sensing period  could be reduced

-and adapted dynamically. On  the one hand a small sensing  period would allow to
-be more  reliable but would  have result in  higher communication costs.  On the
+and adapted dynamically. On  the one hand a small sensing  period would allow the network to
+be more  reliable but would  have resulted in  higher communication costs.  On the

 other hand  the choice of a  long duration may  cause problems in case  of nodes
 failure during the sensing period.
 
 other hand  the choice of a  long duration may  cause problems in case  of nodes
 failure during the sensing period.
 


@@ -681,7 +681,7 @@ so as  to prevent the non-coverage  for the interval~$i$ of  the sensor~$j$.  On
 the other hand, $\beta^j_i$ is assigned to a value which is slightly lower so as
 to minimize the  number of active sensor nodes which  contribute in covering the
 interval. Subsection~\ref{sec:Impact} investigates more deeply how the values of
 the other hand, $\beta^j_i$ is assigned to a value which is slightly lower so as
 to minimize the  number of active sensor nodes which  contribute in covering the
 interval. Subsection~\ref{sec:Impact} investigates more deeply how the values of

-both parameters affect the performance of PeCO protocol.
+both parameters affect the performance of the PeCO protocol.

 
 The following performance metrics are used to evaluate the efficiency of the
 approach.
 
 The following performance metrics are used to evaluate the efficiency of the
 approach.


@@ -741,7 +741,7 @@ approach.
 \subsection{Simulation Results}
 
 In  order  to  assess and  analyze  the  performance  of  our protocol  we  have
 \subsection{Simulation Results}
 
 In  order  to  assess and  analyze  the  performance  of  our protocol  we  have

-implemented PeCO  protocol in OMNeT++~\citep{varga} simulator.   The simulations
+implemented the PeCO  protocol in OMNeT++~\citep{varga} simulator.   The simulations

 were run  on a DELL laptop  with an Intel Core~i3~2370~M  (1.8~GHz) processor (2
 cores) whose MIPS  (Million Instructions Per Second) rate is  equal to 35330. To
 be consistent  with the  use of  a sensor  node based  on Atmels  AVR ATmega103L
 were run  on a DELL laptop  with an Intel Core~i3~2370~M  (1.8~GHz) processor (2
 cores) whose MIPS  (Million Instructions Per Second) rate is  equal to 35330. To
 be consistent  with the  use of  a sensor  node based  on Atmels  AVR ATmega103L


@@ -789,15 +789,15 @@ GAF~\citep{xu2001geography}, consists in dividing the monitoring area into fixed
 squares. Then, during  the decision phase, in each square,  one sensor is chosen
 to  remain  active   during  the  sensing  phase.   The  last   one,  the  DiLCO
 protocol~\citep{Idrees2}, is an improved version of a research work we presented
 squares. Then, during  the decision phase, in each square,  one sensor is chosen
 to  remain  active   during  the  sensing  phase.   The  last   one,  the  DiLCO
 protocol~\citep{Idrees2}, is an improved version of a research work we presented

-in~\citep{idrees2014coverage}. Let us  notice that PeCO and  DiLCO protocols are
+in~\citep{idrees2014coverage}. Let us  notice that the PeCO and  DiLCO protocols are

 based on the same framework. In particular,  the choice for the simulations of a
 partitioning  in   16~subregions  was  made   because  it  corresponds   to  the
 configuration producing  the best results for  DiLCO. Of course, this  number of
 subregions should be adapted according to the  size of the area  of interest and
 the number of sensors.  The protocols  are distinguished from one another by the
 formulation of the integer program providing the set of sensors which have to be
 based on the same framework. In particular,  the choice for the simulations of a
 partitioning  in   16~subregions  was  made   because  it  corresponds   to  the
 configuration producing  the best results for  DiLCO. Of course, this  number of
 subregions should be adapted according to the  size of the area  of interest and
 the number of sensors.  The protocols  are distinguished from one another by the
 formulation of the integer program providing the set of sensors which have to be

-activated in each sensing phase. DiLCO protocol tries to satisfy the coverage of
-a set of primary  points, whereas PeCO protocol objective is  to reach a desired
+activated in each sensing phase. The DiLCO protocol tries to satisfy the coverage of
+a set of primary  points, whereas the objective of the PeCO protocol is  to reach a desired

 level of coverage for each sensor perimeter. In our experimentations, we chose a
 level of coverage equal to one ($l=1$).
 
 level of coverage for each sensor perimeter. In our experimentations, we chose a
 level of coverage equal to one ($l=1$).
 


@@ -807,8 +807,8 @@ Figure~\ref{figure5} shows  the average  coverage ratio  for 200  deployed nodes
 obtained with the four protocols. DESK, GAF, and DiLCO provide a slightly better
 coverage ratio with respectively 99.99\%,  99.91\%, and 99.02\%, compared to the
 98.76\% produced by PeCO for the first periods.  This is due to the fact that at
 obtained with the four protocols. DESK, GAF, and DiLCO provide a slightly better
 coverage ratio with respectively 99.99\%,  99.91\%, and 99.02\%, compared to the
 98.76\% produced by PeCO for the first periods.  This is due to the fact that at

-the  beginning DiLCO  and  PeCO protocols  put to  sleep  status more  redundant
-sensors  (which slightly  decreases the  coverage  ratio), while  the two  other
+the  beginning the DiLCO  and  PeCO protocols  put more  redundant
+sensors to  sleep  status  (which slightly  decreases the  coverage  ratio), while  the two  other

 protocols  activate more  sensor nodes.  Later, when  the number  of periods  is
 beyond~70, it  clearly appears that  PeCO provides  a better coverage  ratio and
 keeps a coverage ratio greater than 50\% for longer periods (15 more compared to
 protocols  activate more  sensor nodes.  Later, when  the number  of periods  is
 beyond~70, it  clearly appears that  PeCO provides  a better coverage  ratio and
 keeps a coverage ratio greater than 50\% for longer periods (15 more compared to


@@ -825,13 +825,13 @@ allows later a substantial increase of the coverage performance.
 
 \subsubsection{Active Sensors Ratio}
 
 
 \subsubsection{Active Sensors Ratio}
 

-Having the less active sensor nodes in  each period is essential to minimize the
+Minimizing the number of active sensor nodes in  each period is essential to minimize the

 energy   consumption    and   thus    to   maximize   the    network   lifetime.
 Figure~\ref{figure6}  shows the  average  active nodes  ratio  for 200  deployed
 nodes.  We observe that DESK and GAF have 30.36~\% and 34.96~\% active nodes for
 energy   consumption    and   thus    to   maximize   the    network   lifetime.
 Figure~\ref{figure6}  shows the  average  active nodes  ratio  for 200  deployed
 nodes.  We observe that DESK and GAF have 30.36~\% and 34.96~\% active nodes for

-the first fourteen  rounds, and DiLCO and PeCO protocols  compete perfectly with
+the first fourteen  rounds, and the DiLCO and PeCO protocols  compete perfectly with

 only 17.92~\%  and 20.16~\% active nodes  during the same time  interval. As the
 only 17.92~\%  and 20.16~\% active nodes  during the same time  interval. As the

-number of periods increases, PeCO protocol has a lower number of active nodes in
+number of periods increases, the PeCO protocol has a lower number of active nodes in

 comparison with the  three other approaches and exhibits a  slow decrease, while
 keeping a greater coverage ratio as shown in Figure \ref{figure5}.
 
 comparison with the  three other approaches and exhibits a  slow decrease, while
 keeping a greater coverage ratio as shown in Figure \ref{figure5}.
 


@@ -848,13 +848,13 @@ The  effect  of  the  energy  consumed by  the  WSN  during  the  communication,
 computation,  listening,  active, and  sleep  status  is studied  for  different
 network densities  and the  four approaches  compared.  Figures~\ref{figure7}(a)
 and (b)  illustrate the energy consumption  for different network sizes  and for
 computation,  listening,  active, and  sleep  status  is studied  for  different
 network densities  and the  four approaches  compared.  Figures~\ref{figure7}(a)
 and (b)  illustrate the energy consumption  for different network sizes  and for

-$Lifetime95$ and $Lifetime50$.  The results show  that PeCO protocol is the most
+$Lifetime95$ and $Lifetime50$.  The results show  that the PeCO protocol is the most

 competitive from the energy consumption point of view. As shown by both figures,
 PeCO consumes much less energy than the  other methods. One might think that the
 resolution of the integer program is too  costly in energy, but the results show
 that it is very beneficial to lose a  bit of time in the selection of sensors to
 activate.  Indeed  the optimization program  allows to reduce  significantly the
 competitive from the energy consumption point of view. As shown by both figures,
 PeCO consumes much less energy than the  other methods. One might think that the
 resolution of the integer program is too  costly in energy, but the results show
 that it is very beneficial to lose a  bit of time in the selection of sensors to
 activate.  Indeed  the optimization program  allows to reduce  significantly the

-number of  active sensors  and so  the energy consumption  while keeping  a good
+number of  active sensors  and also  the energy consumption  while keeping  a good

 coverage level. Let  us notice that the energy overhead  when increasing network
 size is the lowest with PeCO.
 
 coverage level. Let  us notice that the energy overhead  when increasing network
 size is the lowest with PeCO.
 


@@ -870,14 +870,14 @@ size is the lowest with PeCO.
 
 \subsubsection{Network Lifetime}
 
 
 \subsubsection{Network Lifetime}
 

-We observe the  superiority of both PeCO and DiLCO  protocols in comparison with
+We observe the  superiority of both the PeCO and DiLCO  protocols in comparison with

 the   two   other  approaches   in   prolonging   the  network   lifetime.    In
 Figures~\ref{figure8}(a) and  (b), $Lifetime95$  and $Lifetime50$ are  shown for
 different  network  sizes.  As  can  be  seen  in  these figures,  the  lifetime
 the   two   other  approaches   in   prolonging   the  network   lifetime.    In
 Figures~\ref{figure8}(a) and  (b), $Lifetime95$  and $Lifetime50$ are  shown for
 different  network  sizes.  As  can  be  seen  in  these figures,  the  lifetime

-increases with the size of the network,  and it is clearly largest for DiLCO and
+increases with the size of the network,  and it is clearly larger for the DiLCO and

 PeCO protocols.  For  instance, for a network of 300~sensors  and coverage ratio
 greater than  50\%, we can see  on Figure~\ref{figure8}(b) that the  lifetime is
 PeCO protocols.  For  instance, for a network of 300~sensors  and coverage ratio
 greater than  50\%, we can see  on Figure~\ref{figure8}(b) that the  lifetime is

-about  twice  longer with  PeCO  compared  to  DESK protocol.   The  performance
+about  twice  longer with  PeCO  compared  to  the DESK protocol.   The  performance

 difference    is   more    obvious    in    Figure~\ref{figure8}(b)   than    in
 Figure~\ref{figure8}(a) because the gain induced by our protocols increases with
 time, and the lifetime with a coverage over 50\% is far longer than with 95\%.
 difference    is   more    obvious    in    Figure~\ref{figure8}(b)   than    in
 Figure~\ref{figure8}(a) because the gain induced by our protocols increases with
 time, and the lifetime with a coverage over 50\% is far longer than with 95\%.


@@ -892,7 +892,7 @@ time, and the lifetime with a coverage over 50\% is far longer than with 95\%.
   \label{figure8}
 \end{figure} 
 
   \label{figure8}
 \end{figure} 
 

-Figure~\ref{figure9} compares the lifetime coverage  of DiLCO and PeCO protocols
+Figure~\ref{figure9} compares the lifetime coverage  of the DiLCO and PeCO protocols

 for  different   coverage  ratios.   We  denote  by   Protocol/50,  Protocol/80,
 Protocol/85, Protocol/90,  and Protocol/95 the  amount of time during  which the
 network  can satisfy  an  area  coverage greater  than  $50\%$, $80\%$,  $85\%$,
 for  different   coverage  ratios.   We  denote  by   Protocol/50,  Protocol/80,
 Protocol/85, Protocol/90,  and Protocol/95 the  amount of time during  which the
 network  can satisfy  an  area  coverage greater  than  $50\%$, $80\%$,  $85\%$,


@@ -916,13 +916,13 @@ sizes.
 
 Table~\ref{my-labelx}  shows network  lifetime results  for different  values of
 $\alpha$ and $\beta$, and  a network size equal to 200 sensor  nodes. On the one
 
 Table~\ref{my-labelx}  shows network  lifetime results  for different  values of
 $\alpha$ and $\beta$, and  a network size equal to 200 sensor  nodes. On the one

-hand, the choice  of $\beta \gg \alpha$ prevents the  overcoverage, and so limit
+hand, the choice  of $\beta \gg \alpha$ prevents the  overcoverage, and also limits

 the activation of a large number of  sensors, but as $\alpha$ is low, some areas
 may be poorly covered.  This explains  the results obtained for {\it Lifetime50}
 with $\beta \gg \alpha$: a large number  of periods with low coverage ratio.  On
 the other hand, when we choose $\alpha \gg \beta$, we favor the coverage even if
 the activation of a large number of  sensors, but as $\alpha$ is low, some areas
 may be poorly covered.  This explains  the results obtained for {\it Lifetime50}
 with $\beta \gg \alpha$: a large number  of periods with low coverage ratio.  On
 the other hand, when we choose $\alpha \gg \beta$, we favor the coverage even if

-some areas may  be overcovered, so high  coverage ratio is reached,  but a large
-number  of  sensors are  activated  to  achieve  this goal.   Therefore  network
+some areas may  be overcovered, so ahigh  coverage ratio is reached,  but a large
+number  of  sensors are  activated  to  achieve  this goal.   Therefore the  network

 lifetime is reduced.   The choice $\alpha=0.6$ and $\beta=0.4$  seems to achieve
 the best compromise  between lifetime and coverage ratio.  That  explains why we
 have  chosen  this  setting  for  the  experiments  presented  in  the  previous
 lifetime is reduced.   The choice $\alpha=0.6$ and $\beta=0.4$  seems to achieve
 the best compromise  between lifetime and coverage ratio.  That  explains why we
 have  chosen  this  setting  for  the  experiments  presented  in  the  previous


@@ -973,7 +973,7 @@ lifetime, coverage ratio, active sensors ratio, and energy consumption.
 We plan to extend  our framework so that the schedules  are planned for multiple
 sensing  periods. We  also want  to  improve the  integer program  to take  into
 account heterogeneous sensors from both energy and node characteristics point of
 We plan to extend  our framework so that the schedules  are planned for multiple
 sensing  periods. We  also want  to  improve the  integer program  to take  into
 account heterogeneous sensors from both energy and node characteristics point of

-views.  Finally,  it would  be interesting  to implement  PeCO protocol  using a
+views.  Finally,  it would  be interesting  to implement the  PeCO protocol  using a

 sensor-testbed to evaluate it in real world applications.
 
 
 sensor-testbed to evaluate it in real world applications.
 
 

diff --git a/PeCO-EO/reponse.tex b/PeCO-EO/reponse.tex
index 9d11094d40f0f98772cd66ab0dfa49906a254d03..1fb3f07b35466d04a4ccaa0da35d8dfd11fdb48f 100644 (file)
--- a/PeCO-EO/reponse.tex
+++ b/PeCO-EO/reponse.tex
@@ -73,7 +73,7 @@ methodology uses existing methods and the original contribution lies only in the
 application of these methods for the coverage scheduling problem.\\
 
 \textcolor{blue}{\textbf{\textsc{Answer:}  To  the  best of  our  knowledge,  no
 application of these methods for the coverage scheduling problem.\\
 
 \textcolor{blue}{\textbf{\textsc{Answer:}  To  the  best of  our  knowledge,  no

-    integer  linear programming  based on  perimeter coverage  has been  already
+    integer  linear programming  based on  perimeter coverage  has ever been  

     proposed in the literature.  As specified in the paper, in  Section 4, it is
     inspired from a model developed for brachytherapy  treatment planning for
     optimizing dose distribution. In this  model the deviation between an actual
     proposed in the literature.  As specified in the paper, in  Section 4, it is
     inspired from a model developed for brachytherapy  treatment planning for
     optimizing dose distribution. In this  model the deviation between an actual


@@ -86,9 +86,9 @@ application of these methods for the coverage scheduling problem.\\
 assumption made on the selection criteria for the leader seems too vague.  \\
 
 \textcolor{blue}{\textbf{\textsc{Answer:} The selection  criteria for the leader
 assumption made on the selection criteria for the leader seems too vague.  \\
 
 \textcolor{blue}{\textbf{\textsc{Answer:} The selection  criteria for the leader

-    inside each subregion  is explained in page~9, at  the end of Section~3.3
-    After information  exchange among  the sensor nodes  in the  subregion, each
-    node will have all the information needed to decide if it will the leader or
+    inside each subregion  is explained page~9, at  the end of Section~3.3
+    After the information  exchange among  the sensor nodes  in the  subregion, each
+    node will have all the information needed to decide if it will be the leader or

     not. The decision is based on selecting  the sensor node that has the larger
     number of one-hop neighbors. If this value is the same for many sensors, the
     node that has the largest remaining energy will be selected as a leader.  If
     not. The decision is based on selecting  the sensor node that has the larger
     number of one-hop neighbors. If this value is the same for many sensors, the
     node that has the largest remaining energy will be selected as a leader.  If


@@ -139,9 +139,9 @@ results showing how the algorithm performs with different alphas and betas.\\
     for alpha  and beta.   Table 4 presents  the results obtained  for a  WSN of
     200~sensor nodes.  It explains the  value chosen for the simulation settings
     in Table~2. \\ \indent The choice of alpha and beta should be made according
     for alpha  and beta.   Table 4 presents  the results obtained  for a  WSN of
     200~sensor nodes.  It explains the  value chosen for the simulation settings
     in Table~2. \\ \indent The choice of alpha and beta should be made according

-    to the  needs of the  application. Alpha should  be enough large  to prevent
-    undercoverage and  so to  reach the highest  possible coverage  ratio.  Beta
-    should be enough large to prevent  overcoverage and so to activate a minimum
+    to the  needs of the  application. Alpha should  be large enough  to prevent
+    undercoverage and  thus to  reach the highest  possible coverage  ratio.  Beta
+    should be enough large to prevent  overcoverage and thus to activate a minimum

     number of sensors.  The values of  $\alpha_{i}^{j}$ can be identical for all
     coverage  intervals $i$  of one  sensor  $j$ in  order to  express that  the
     perimeter of each  sensor should be uniformly  covered, but $\alpha_{i}^{j}$
     number of sensors.  The values of  $\alpha_{i}^{j}$ can be identical for all
     coverage  intervals $i$  of one  sensor  $j$ in  order to  express that  the
     perimeter of each  sensor should be uniformly  covered, but $\alpha_{i}^{j}$


@@ -151,9 +151,9 @@ results showing how the algorithm performs with different alphas and betas.\\
     as $\alpha$  is low,  some areas  may be poorly  covered. This  explains the
     results obtained for $Lifetime_{50}$ with $\beta \gg \alpha$: a large number
     of periods with  low coverage ratio.  With $\alpha \gg  \beta$, we favor the
     as $\alpha$  is low,  some areas  may be poorly  covered. This  explains the
     results obtained for $Lifetime_{50}$ with $\beta \gg \alpha$: a large number
     of periods with  low coverage ratio.  With $\alpha \gg  \beta$, we favor the

-    coverage even  if some areas may  be overcovered, so high  coverage ratio is
+    coverage even  if some areas may  be overcovered, so a high  coverage ratio is

     reached, but a  large number of sensors are activated  to achieve this goal.
     reached, but a  large number of sensors are activated  to achieve this goal.

-    Therefore  network  lifetime  is   reduced.   The  choice  $\alpha=0.6$  and
+    Therefore  the network  lifetime  is   reduced.   The  choice  $\alpha=0.6$  and

     $\beta=0.4$  seems  to achieve  the  best  compromise between  lifetime  and
     coverage ratio.}}\\
 
     $\beta=0.4$  seems  to achieve  the  best  compromise between  lifetime  and
     coverage ratio.}}\\
 


@@ -192,10 +192,10 @@ may be an  issue if this approach  is used in an application  that requires high
 coverage ratio. \\
 
 \textcolor{blue}{\textbf{\textsc{Answer:} Your  remark is very interesting.  Indeed,
 coverage ratio. \\
 
 \textcolor{blue}{\textbf{\textsc{Answer:} Your  remark is very interesting.  Indeed,

-    Figures 8(a) and (b) highlight this  result. PeCO protocol allows to achieve
+    Figures 8(a) and (b) highlight this  result. The PeCO protocol allows to achieve

     a coverage  ratio greater than $50\%$  for far more periods  than the others
     three  methods, but  for applications  requiring  a high  level of  coverage
     a coverage  ratio greater than $50\%$  for far more periods  than the others
     three  methods, but  for applications  requiring  a high  level of  coverage

-    (greater than  $95\%$), DiLCO method is  more efficient. It is  explained at
+    (greater than  $95\%$), the DiLCO method is  more efficient. It is  explained at

     the end of Section 5.2.4.}}\\
 
 %%%%%%%%%%%%%%%%%%%%%%  ENGLISH and GRAMMAR %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
     the end of Section 5.2.4.}}\\
 
 %%%%%%%%%%%%%%%%%%%%%%  ENGLISH and GRAMMAR %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


@@ -283,7 +283,7 @@ how should this common duration should be chosen?\\
     do  not  have  the  same  Quality of  Service  requirements.   In  our  case,
     information exchange is  executed every hour, but the length  of the sensing
     period could  be reduced and  adapted dynamically. On  the one hand,  a small
     do  not  have  the  same  Quality of  Service  requirements.   In  our  case,
     information exchange is  executed every hour, but the length  of the sensing
     period could  be reduced and  adapted dynamically. On  the one hand,  a small

-    sensing  period would  allow  to  be more  reliable  but  would have  higher
+    sensing  period would  allow  the network to  be more  reliable  but  would have  higher

     communication costs.   On the other hand,  the choice of a  long duration may
     cause problems in case of nodes failure during the sensing period.
     Several  explanations on  these points  are given  throughout the  paper. In
     communication costs.   On the other hand,  the choice of a  long duration may
     cause problems in case of nodes failure during the sensing period.
     Several  explanations on  these points  are given  throughout the  paper. In


@@ -320,8 +320,7 @@ and explain how the protocol is built to optimize these objectives.  \\
 
 \textcolor{blue}{\textbf{\textsc{Answer:}  Right.   The   mixed  Integer  Linear
     Program adresses  a multiobjective  problem, where the  goal is  to minimize
 
 \textcolor{blue}{\textbf{\textsc{Answer:}  Right.   The   mixed  Integer  Linear
     Program adresses  a multiobjective  problem, where the  goal is  to minimize

-    overcoverage and  undercoverage for each  coverage interval of a  sensor. As
-    far as  we know, representing  the objective function  as a weighted  sum of
+    overcoverage and  undercoverage for each  coverage interval of a  sensor. To the best of our knowledge, representing  the objective function  as a weighted  sum of

     criteria  to  be  minimized  in  case of  multicriteria  optimization  is  a
     classical method.   In Section 5, the  comparison of protocols with  a large
     variety of performance metrics allows  to select the most appropriate method
     criteria  to  be  minimized  in  case of  multicriteria  optimization  is  a
     classical method.   In Section 5, the  comparison of protocols with  a large
     variety of performance metrics allows  to select the most appropriate method


@@ -387,7 +386,7 @@ of nodes &&&&relaxation &B\&B tree &\\
 \medskip  \\
 It  is noteworthy  that the  difference  of memory  used with  GLPK between  the
 resolution of  the IP  and its  LP-relaxation is  very weak  (not more  than 0.1
 \medskip  \\
 It  is noteworthy  that the  difference  of memory  used with  GLPK between  the
 resolution of  the IP  and its  LP-relaxation is  very weak  (not more  than 0.1

-MB). The size of  the branch and bound tree dos not exceed  3 nodes. This result
+MB). The size of  the branch and bound tree does not exceed  3 nodes. This result

 leads one to  believe that the memory use with  CPLEX\textregistered for solving
 the IP would be very close to that  for the LP-relaxation, that is to say around
 100 Kb for a subregion containing $S=10$ sensors.  Moreover the IP seems to have
 leads one to  believe that the memory use with  CPLEX\textregistered for solving
 the IP would be very close to that  for the LP-relaxation, that is to say around
 100 Kb for a subregion containing $S=10$ sensors.  Moreover the IP seems to have


@@ -399,7 +398,7 @@ Optimization, issn 1572-5286).
 \item  the subdivision  of the  region of  interest. To  make the  resolution of
   integer programming tractable by a leader  sensor, we need to limit the number
   of nodes  in each subregion  (the number of  variables and constraints  of the
 \item  the subdivision  of the  region of  interest. To  make the  resolution of
   integer programming tractable by a leader  sensor, we need to limit the number
   of nodes  in each subregion  (the number of  variables and constraints  of the

-  integer  programming  is  directly  depending  on  the  number  of  nodes  and
+  integer  programming  directly  depends  on  the  number  of  nodes  and

   neigbors). It is therefore necessary to  adapt the subdvision according to the
   number of sensors deployed in the area  and their sensing range (impact on the
   number of coverage intervals).
   neigbors). It is therefore necessary to  adapt the subdvision according to the
   number of sensors deployed in the area  and their sensing range (impact on the
   number of coverage intervals).


@@ -487,8 +486,8 @@ A discussion about memory consumption has been added in Section 5.2}}
 
 \textcolor{blue}{\textbf{\textsc{Answer:} For minimizing the objective function,
     $M_{i}^{j}$ and  $V_{i}^{j}$ should  be set to  the smallest  possible value
 
 \textcolor{blue}{\textbf{\textsc{Answer:} For minimizing the objective function,
     $M_{i}^{j}$ and  $V_{i}^{j}$ should  be set to  the smallest  possible value

-    such that  the inequalities are satisfied.  It is explained in  the answer 4
-    for  the reviewer  1.  But,  at optimality,  constraints  are not  necessary
+    such that  the inequalities are satisfied.  It is explained in  answer 4
+    for reviewer  1.  But,  at optimality,  constraints  are not  necessary

     satisfied with equality. For instance, if a sensor $j$ is overcovered, there
     exists at least one of its coverage  interval (say $i$) for which the number
     of active sensors  (denoted by $l^{i}$) covering this part  of the perimeter
     satisfied with equality. For instance, if a sensor $j$ is overcovered, there
     exists at least one of its coverage  interval (say $i$) for which the number
     of active sensors  (denoted by $l^{i}$) covering this part  of the perimeter