X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/LiCO.git/blobdiff_plain/d2af1567d110987ebd8f80152c8a37de9dbd5d26..f65c2462e1842e661a546d573a5e717d160c5fc7:/LiCO_Journal.tex

diff --git a/LiCO_Journal.tex b/LiCO_Journal.tex
index 1775b94..c8e2eb5 100644
--- a/LiCO_Journal.tex
+++ b/LiCO_Journal.tex
@@ -64,10 +64,10 @@ region of interest is first subdivided  into subregions and our protocol is then
 distributed among sensor nodes in each  subregion. A sensor node which runs LiCO
 protocol  repeats   periodically  four  stages:  information   exchange,  leader
 election, optimization decision, and sensing.  More precisely, the scheduling of
-nodes activities (sleep/wake up  duty cycles) is achieved in each  subregion by a
+nodes' activities (sleep/wake up duty cycles) is achieved in each subregion by a
 leader selected after  cooperation between nodes within the  same subregion. The
 novelty of  approach lies essentially in  the formulation of a  new mathematical
-optimization  model  based  on  perimeter coverage  level  to  schedule  sensors
+optimization  model  based on  perimeter  coverage  level to  schedule  sensors'
 activities.  Extensive simulation experiments have been performed using OMNeT++,
 the  discrete event  simulator, to  demonstrate that  LiCO is  capable to  offer
 longer lifetime coverage for WSNs in comparison with some other protocols.
@@ -88,7 +88,7 @@ wireless communication hardware  has given rise to the opportunity  to use large
 networks    of     tiny    sensors,    called    Wireless     Sensor    Networks
 (WSN)~\cite{akyildiz2002wireless,puccinelli2005wireless}, to  fulfill monitoring
 tasks.   A  WSN  consists  of  small low-powered  sensors  working  together  by
-communicating with one another through  multihop radio communications. Each node
+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,
@@ -107,7 +107,7 @@ 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
-while  ensuring   a  high  level   of  coverage?   So,  this  last   years  many
+while  ensuring   a  high  level  of   coverage?   So,  this  last   years  many
 energy-efficient mechanisms have been suggested  to retain energy and extend the
 lifetime of the WSNs~\cite{rault2014energy}.
 
@@ -125,7 +125,7 @@ This paper makes the following contributions.
   temporal subdivision.   On the one hand  the area of interest  if divided into
   several smaller subregions and on the other hand the time line is divided into
   periods of equal length. In each subregion the sensor nodes will cooperatively
-  choose a  leader which will  schedule nodes  activities, and this  grouping of
+  choose a  leader which will schedule  nodes' activities, and this  grouping of
   sensors is similar to typical cluster architecture.
 \item We  propose a new mathematical  optimization model.  Instead of  trying to
   cover a set of specified points/targets as  in most of the methods proposed in
@@ -206,30 +206,30 @@ concepts, have  been proposed  to extend the  network lifetime.   In distributed
 algorithms~\cite{yangnovel,ChinhVu,qu2013distributed}  each  sensors decides  of
 its own  activity scheduling after  an information exchange with  its neighbors.
 The main interest of  a such approach is to avoid  long range communications and
-thus to reduce the energy  dedicated to the comunications.  Unfortunately, since
+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  take a  bad  decision leading  to a  global suboptimal  solution.
-Converseley,                                                         centralized
+Conversely,                                                          centralized
 algorithms~\cite{cardei2005improving,zorbas2010solving,pujari2011high}    always
 provide nearly  or close to  optimal solution 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 comunications  can be very  huge since
-long range communications will be needed. In faxt the larger the WNS, the higher
+station which will globally schedule nodes'  activities, data from all the other
+sensor nodes in  the area.  The price  in communications can be  very huge since
+long range communications will be needed. In fact the larger the WNS, the higher
 the  communication and  thus energy  cost.   {\it In  order to  be suitable  for
   large-scale networks,  in the LiCO  protocol the  area of interest  is divided
   into several smaller subregions, and in each  one, a node called the leader is
   in charge  for selecting the active  sensors for the current  period. Thus our
   protocol  is  scalable  and  a  globally distributed  method,  whereas  it  is
-  centralized in each subregion.} 
+  centralized in each subregion.}
 
 Various  coverage scheduling  algorithms have  been developed  this last  years.
 Many of  them, dealing with  the maximization of the  number of cover  sets, are
-heuristics.  These  heuristics  involve  the  construction of  a  cover  set  by
+heuristics.   These  heuristics involve  the  construction  of  a cover  set  by
 including in priority the sensor nodes  which cover critical targets, that is to
 say   targets   that  are   covered   by   the   smallest  number   of   sensors
-\cite{berman04,zorbas2010solving}.  Other approaches  are based  on mathematical
+\cite{berman04,zorbas2010solving}.  Other  approaches are based  on mathematical
 programming formulations~\cite{cardei2005energy,5714480,pujari2011high,Yang2014}
 and dedicated techniques (solving with a branch-and-bound algorithm available in
 optimization  solver).  The  problem is  formulated as  an optimization  problem
@@ -285,55 +285,99 @@ used~\cite{castano2013column,rossi2012exact,deschinkel2012column}. {\it  In LiCO
 
 \noindent  In  this  section,  we  describe in  details  our  Lifetime  Coverage
 Optimization protocol.  First we present the  assumptions we made and the models
-we considered (in particular the perimter  coverage one), second we describe the
+we considered (in particular the perimeter coverage one), second we describe the
 background idea of our protocol, and third  we give the outline of the algorithm
 executed by each node.
 
-% MICHEL TO BE CONTINUED FROM HERE
-
 % It is based on two efficient-energy mechanisms: the first, is partitioning the sensing field into smaller subregions, and one leader is elected for each subregion;  the second, a sensor activity scheduling based new optimization model so as to produce the optimal cover set of active sensors for the sensing stage during the period.  Obviously, these two mechanisms can be contribute in extend the network lifetime coverage efficiently. 
 %Before proceeding in the presentation of the main ideas of the protocol, we will briefly describe the perimeter coverage model and give some necessary assumptions and definitions.
 
-\subsection{ Assumptions and Models}
-\noindent A WSN consisting of $J$ stationary sensor nodes randomly and uniformly distributed in a bounded sensor field is considered. The  wireless sensors  are deployed in high density to ensure initially a high coverage ratio of the interested area. We assume that all the sensor nodes are homogeneous in terms of  communication, sensing, and processing capabilities and heterogeneous in term of energy supply. The  location  information is available to the  sensor node  either through hardware such as embedded GPS or through location discovery algorithms. We assume that each sensor node can directly transmit its measurements to a mobile sink node. For example, a sink can be an unmanned aerial vehicle (UAV) flying regularly over the sensor field to collect measurements from sensor nodes. A mobile sink node collects the measurements and transmits them to the base station.  We consider a boolean  disk coverage model which is the most widely used sensor coverage model in the literature. Each sensor has a constant sensing range $R_s$. All space points within a disk centered at the sensor with the radius of the sensing range is said to be covered by this sensor. We also assume that the communication range $R_c \geq 2R_s$. In  fact,   Zhang  and Zhou~\cite{Zhang05} proved that if the transmission range fulfills the previous hypothesis, a complete coverage of a convex area implies connectivity among the working nodes in the active mode.
-
-\indent LiCO protocol uses the perimeter-coverage model which states in ~\cite{huang2005coverage} as following: The sensor is said to be perimeter covered if all the points on its perimeter are covered by at least one sensor other than itself. Huang and Tseng in \cite{huang2005coverage} proves that a network area is $k$-covered if and only if each sensor in the network is $k$-perimeter-covered.
+\subsection{Assumptions and Models}
+
+\noindent A WSN consisting of $J$ stationary sensor nodes randomly and uniformly
+distributed in  a bounded sensor field  is considered. The wireless  sensors are
+deployed in high density  to ensure initially a high coverage  ratio of the area
+of interest.  We  assume that all the  sensor nodes are homogeneous  in terms of
+communication,  sensing,  and  processing capabilities  and  heterogeneous  from
+energy provision  point of  view.  The  location information  is available  to a
+sensor node either  through hardware such as embedded GPS  or location discovery
+algorithms.   We  assume  that  each  sensor  node  can  directly  transmit  its
+measurements to  a mobile  sink node.  For  example, a sink  can be  an unmanned
+aerial  vehicle  (UAV)  flying  regularly  over  the  sensor  field  to  collect
+measurements from sensor nodes. A mobile sink node collects the measurements and
+transmits them to the base station.   We consider a Boolean disk coverage model,
+which is the most  widely used sensor coverage model in  the literature, and all
+sensor nodes  have a constant sensing  range $R_s$.  Thus, all  the space points
+within a disk centered at a sensor with  a radius equal to the sensing range are
+said to be covered  by this sensor. We also assume  that the communication range
+$R_c$ satisfies $R_c  \geq 2 \cdot R_s$. In fact,  Zhang and Zhou~\cite{Zhang05}
+proved  that if  the  transmission  range fulfills  the  previous hypothesis,  a
+complete coverage of a convex area implies connectivity among active nodes.
+
+\indent  LiCO protocol  uses the  same perimeter-coverage  model than  Huang and
+Tseng in~\cite{huang2005coverage}. It  can be expressed as follows:  a sensor is
+said to be perimeter  covered if all the points on its  perimeter are covered by
+at least  one sensor  other than  itself.  They  proved that  a network  area is
+$k$-covered if and only if each sensor in the network is $k$-perimeter-covered.
 %According to this model, we named the intersections among the sensor nodes in the sensing field as intersection points. Instead of working with the coverage area, we consider for each sensor a set of intersection points which are determined by using perimeter-coverage model. 
-Figure~\ref{pcmfig} illuminates the perimeter coverage of the sensor node $0$. On this figure, sensor $0$ has $9$ neighbors. We report for each sensor $i$ having an intersection with sensor $0$, the two intersection points,  $iL$ for left point and $iR$ for right point. These intersections points subdivide the perimeter of the sensor $0$ (the perimeter of the disk covered by the sensor)  into portions called segments.
+Figure~\ref{pcm2sensors}(a)  shows  the coverage  of  sensor  node~$0$. On  this
+figure, we can  see that sensor~$0$ has  nine neighbors and we  have reported on
+its  perimeter (the  perimeter  of the  disk  covered by  the  sensor) for  each
+neighbor  the  two  points  resulting  from  intersection  of  the  two  sensing
+areas. These points are denoted for  neighbor~$i$ by $iL$ and $iR$, respectively
+for  left and  right from  neighbor  point of  view.  The  resulting couples  of
+intersection points subdivide  the perimeter of sensor~$0$  into portions called
+arcs.
 
 \begin{figure}[ht!]
-\centering
-\includegraphics[width=75mm]{pcm.jpg}  
-\caption{Perimeter coverage of sensor node 0}
-\label{pcmfig}
+  \centering
+  \begin{tabular}{@{}cr@{}}
+    \includegraphics[width=75mm]{pcm.jpg}        &        \raisebox{3.25cm}{(a)}
+    \\ \includegraphics[width=75mm]{twosensors.jpg} & \raisebox{2.75cm}{(b)}
+  \end{tabular}
+  \caption{Perimeter coverage of sensor node 0  (a) and finding the arc of $u$'s
+    perimeter covered by $v$.}
+  \label{pcm2sensors}
 \end{figure} 
 
-Figure~\ref{twosensors} demonstrates the way of locating the left and right points of a segment for a sensor node $u$ covered by a sensor node $v$. This figure assumes that the neighbor sensor node $v$ is located on the west of a sensor $u$. It is assumed  that the two sensor nodes $v$ and $u$ are located in the positions $(v_x,v_y)$ and $(u_x,u_y)$, respectively. The distance between $v$ and $u$ is computed by $Dist(u,v) = \sqrt{\vert u_x - v_x \vert^2 + \vert u_y - v_y \vert^2}$. The angle $\alpha$ is computed through the formula $\alpha = arccos \left(\dfrac{Dist(u,v)}{2R_s} \right)$. So, the arch of sensor $u$ falling in the angle $[\pi - \alpha,\pi + \alpha]$, is said to be perimeter-covered by sensor node $v$. 
-
-The left and right points of each segment are placed on the line segment $[0,2\pi]$. Figure~\ref{pcmfig} illustrates the segments for the 9 neighbors of sensor $0$. The points reported on the line segment $[0,2\pi]$ separates it in intervals as shown in figure~\ref{expcm}. For example, for each neighboring sensor of sensor 0, place the points  $\alpha^ 1_L$, $\alpha^ 1_R$, $\alpha^ 2_L$, $\alpha^ 2_R$, $\alpha^ 3_L$, $\alpha^ 3_R$, $\alpha^ 4_L$, $\alpha^ 4_R$, $\alpha^ 5_L$, $\alpha^ 5_R$, $\alpha^ 6_L$, $\alpha^ 6_R$, $\alpha^ 7_L$, $\alpha^ 7_R$, $\alpha^ 8_L$, $\alpha^ 8_R$, $\alpha^ 9_L$, and $\alpha^ 9_R$; on the line segment $[0,2\pi]$, and then sort all these points in an ascending order into a list.  Traverse the line segment $[0,2\pi]$ by visiting each point in the sorted list from left to right and determine the coverage level of each interval of the sensor 0 (see figure \ref{expcm}). For each interval, we sum up the number of parts of segments, and we deduce a level of coverage for each interval. For instance, the interval delimited by the points $5L$ and $6L$ contains three parts of segments. That means that this part of the perimeter of the sensor $0$ may be covered by three sensors, sensor $0$ itself and sensors $2$ and $5$. The level of coverage of this interval may reach $3$ if all previously mentioned sensors are active. Let say that sensors $0$, $2$ and $5$ are involved in the coverage of this interval. Table~\ref{my-label} summarizes the level of coverage for each interval and the sensors involved in for sensor node 0 in figure~\ref{pcmfig}. 
+Figure~\ref{pcm2sensors}(b) describes the geometric information used to find the
+locations of the  left and right points of  an arc on the perimeter  of a sensor
+node~$u$ covered by a sensor node~$v$. Node~$s$ is supposed to be located on the
+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 we can
+compute the euclidean distance between nodes~$u$ and $v$: $Dist(u,v)=\sqrt{\vert
+  u_x  - v_x  \vert^2 +  \vert u_y-v_y  \vert^2}$, while  the angle~$\alpha$  is
+obtained  through the  formula  $\alpha  = arccos  \left(\dfrac{Dist(u,v)}{2R_s}
+\right)$.   So, the  arc on  the perimeter  of node~$u$  defined by  the angular
+interval $[\pi - \alpha,\pi + \alpha]$ is said to be perimeter-covered by sensor
+node $v$.
+
+Every couple of intersection points is placed on the angular interval $[0,2\pi]$
+in  a  counterclockwise manner,  leading  to  a  partitioning of  the  interval.
+Figure~\ref{pcm2sensors}(a)  illustrates  the arcs  for  the  nine neighbors  of
+sensor $0$ and  figure~\ref{expcm} gives the position of  the corresponding arcs
+in  the interval  $[0,2\pi]$. More  precisely, we  can see  that the  points are
+ordered according  to the  measures of  the angles  defined by  their respective
+positions. The intersection points are  then visited one after another, starting
+from  first  intersection point  after  point~zero,  and  the maximum  level  of
+coverage is determined  for each interval defined by two  successive points. The
+maximum  level of  coverage is  equal to  the number  of overlapping  arcs.  For
+example, between~$5L$  and~$6L$ the maximum  level of  coverage is equal  to $3$
+(the value is highlighted in yellow  at the bottom of figure~\ref{expcm}), which
+means that at most 2~neighbors can cover  the perimeter in addition to node $0$.
+Table~\ref{my-label} summarizes for each coverage  interval the maximum level of
+coverage and  the sensor  nodes covering the  perimeter.  The  example discussed
+above is thus given by the sixth line of the table.
+
+%The points reported on the line segment $[0,2\pi]$ separates it in intervals as shown in figure~\ref{expcm}. For example, for each neighboring sensor of sensor 0, place the points  $\alpha^ 1_L$, $\alpha^ 1_R$, $\alpha^ 2_L$, $\alpha^ 2_R$, $\alpha^ 3_L$, $\alpha^ 3_R$, $\alpha^ 4_L$, $\alpha^ 4_R$, $\alpha^ 5_L$, $\alpha^ 5_R$, $\alpha^ 6_L$, $\alpha^ 6_R$, $\alpha^ 7_L$, $\alpha^ 7_R$, $\alpha^ 8_L$, $\alpha^ 8_R$, $\alpha^ 9_L$, and $\alpha^ 9_R$; on the line segment $[0,2\pi]$, and then sort all these points in an ascending order into a list.  Traverse the line segment $[0,2\pi]$ by visiting each point in the sorted list from left to right and determine the coverage level of each interval of the sensor 0 (see figure \ref{expcm}). For each interval, we sum up the number of parts of segments, and we deduce a level of coverage for each interval. For instance, the interval delimited by the points $5L$ and $6L$ contains three parts of segments. That means that this part of the perimeter of the sensor $0$ may be covered by three sensors, sensor $0$ itself and sensors $2$ and $5$. The level of coverage of this interval may reach $3$ if all previously mentioned sensors are active. Let say that sensors $0$, $2$ and $5$ are involved in the coverage of this interval. Table~\ref{my-label} summarizes the level of coverage for each interval and the sensors involved in for sensor node 0 in figure~\ref{pcm2sensors}(a). 
 % to determine the level of the perimeter coverage for each left and right point of a segment.
-\begin{figure}[ht!]
-\centering
-\includegraphics[width=75mm]{twosensors.jpg}  
-\caption{Locating the segment of $u$$\rq$s perimeter covered by $v$.}
-\label{twosensors}
-\end{figure} 
-
 
-\begin{figure}[ht!]
+\begin{figure*}[ht!]
 \centering
-\includegraphics[width=75mm]{expcm.pdf}  
-\caption{ Coverage levels for sensor node $0$.}
+\includegraphics[width=137.5mm]{expcm.pdf}  
+\caption{Maximum coverage levels for perimeter of sensor node $0$.}
 \label{expcm}
-\end{figure} 
-
-
-
-
-
-
-
-
+\end{figure*} 
 
 %For example, consider the sensor node $0$ in figure~\ref{pcmfig}, which has 9 neighbors. Figure~\ref{expcm} shows the perimeter coverage level for all left and right points of a segment that covered by a neighboring sensor nodes. Based on the figure~\ref{expcm}, the set of sensors for each left and right point of the segments illustrated in figure~\ref{ex2pcm} for the sensor node 0.
 
@@ -352,25 +396,25 @@ The left and right points of each segment are placed on the line segment $[0,2\p
  \caption{Coverage intervals and contributing sensors for sensor node 0.}
 \begin{tabular}{|c|c|c|c|c|c|c|c|c|}
 \hline
-\begin{tabular}[c]{@{}c@{}}The angle \\ $\alpha$ \end{tabular} & \begin{tabular}[c]{@{}c@{}}Segment \\ Left (L) or\\  Right (R)\end{tabular} & \begin{tabular}[c]{@{}c@{}}Sensor \\ Node Id\end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ Coverage\\  Level\end{tabular} & \multicolumn{5}{c|}{\begin{tabular}[c]{@{}c@{}}The Set of Sensors\\ Involved in Interval \\ Coverage\end{tabular}} \\ \hline
-0.0291    & L                                                                         & 1                                                         & 4                                                                     & 0                     & 1                     & 3                    & 4                    &                      \\ \hline
-0.104     & L                                                                         & 2                                                         & 5                                                                     & 0                     & 1                     & 3                    & 4                    & 2                    \\ \hline
-0.3168    & R                                                                         & 3                                                         & 4                                                                     & 0                     & 1                     & 4                    & 2                    &                      \\ \hline
-0.6752    & R                                                                         & 4                                                         & 3                                                                     & 0                     & 1                     & 2                    &                      &                      \\ \hline
-1.8127    & R                                                                         & 1                                                         & 2                                                                     & 0                     & 2                     &                      &                      &                      \\ \hline
-1.9228    & L                                                                         & 5                                                         & 3                                                                     & 0                     & 2                     & 5                    &                      &                      \\ \hline
-2.3959    & L                                                                         & 6                                                         & 4                                                                     & 0                     & 2                     & 5                    & 6                    &                      \\ \hline
-2.4258    & R                                                                         & 2                                                         & 3                                                                     & 0                     & 5                     & 6                    &                      &                      \\ \hline
-2.7868    & L                                                                         & 7                                                         & 4                                                                     & 0                     & 5                     & 6                    & 7                    &                      \\ \hline
-2.8358    & L                                                                         & 8                                                         & 5                                                                     & 0                     & 5                     & 6                    & 7                    & 8                    \\ \hline
-2.9184    & R                                                                         & 5                                                         & 4                                                                     & 0                     & 6                     & 7                    & 8                    &                      \\ \hline
-3.3301    & R                                                                         & 7                                                         & 3                                                                     & 0                     & 6                     & 8                    &                      &                      \\ \hline
-3.9464    & L                                                                         & 9                                                         & 4                                                                     & 0                     & 6                     & 8                    & 9                    &                      \\ \hline
-4.767     & R                                                                         & 6                                                         & 3                                                                     & 0                     & 8                     & 9                    &                      &                      \\ \hline
-4.8425    & L                                                                         & 3                                                         & 4                                                                     & 0                     & 3                     & 8                    & 9                    &                      \\ \hline
-4.9072    & R                                                                         & 8                                                         & 3                                                                     & 0                     & 3                     & 9                    &                      &                      \\ \hline
-5.3804    & L                                                                         & 4                                                         & 4                                                                     & 0                     & 3                     & 4                    & 9                    &                      \\ \hline
-5.9157    & R                                                                         & 9                                                         & 3                                                                     & 0                     & 3                     & 4                    &                      &                      \\ \hline
+\begin{tabular}[c]{@{}c@{}}Left \\ point \\ angle~$\alpha$ \end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ left \\ point\end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ right \\ point\end{tabular} & \begin{tabular}[c]{@{}c@{}}Maximum \\ coverage\\  level\end{tabular} & \multicolumn{5}{c|}{\begin{tabular}[c]{@{}c@{}}Set of sensors\\ involved \\ in interval coverage\end{tabular}} \\ \hline
+0.0291    & 1L                                                                        & 2L                                                        & 4                                                                     & 0                     & 1                     & 3                    & 4                    &                      \\ \hline
+0.104     & 2L                                                                        & 3R                                                        & 5                                                                     & 0                     & 1                     & 3                    & 4                    & 2                    \\ \hline
+0.3168    & 3R                                                                        & 4R                                                        & 4                                                                     & 0                     & 1                     & 4                    & 2                    &                      \\ \hline
+0.6752    & 4R                                                                        & 1R                                                        & 3                                                                     & 0                     & 1                     & 2                    &                      &                      \\ \hline
+1.8127    & 1R                                                                        & 5L                                                        & 2                                                                     & 0                     & 2                     &                      &                      &                      \\ \hline
+1.9228    & 5L                                                                        & 6L                                                        & 3                                                                     & 0                     & 2                     & 5                    &                      &                      \\ \hline
+2.3959    & 6L                                                                        & 2R                                                        & 4                                                                     & 0                     & 2                     & 5                    & 6                    &                      \\ \hline
+2.4258    & 2R                                                                        & 7L                                                        & 3                                                                     & 0                     & 5                     & 6                    &                      &                      \\ \hline
+2.7868    & 7L                                                                        & 8L                                                        & 4                                                                     & 0                     & 5                     & 6                    & 7                    &                      \\ \hline
+2.8358    & 8L                                                                        & 5R                                                        & 5                                                                     & 0                     & 5                     & 6                    & 7                    & 8                    \\ \hline
+2.9184    & 5R                                                                        & 7R                                                        & 4                                                                     & 0                     & 6                     & 7                    & 8                    &                      \\ \hline
+3.3301    & 7R                                                                        & 9R                                                        & 3                                                                     & 0                     & 6                     & 8                    &                      &                      \\ \hline
+3.9464    & 9R                                                                        & 6R                                                        & 4                                                                     & 0                     & 6                     & 8                    & 9                    &                      \\ \hline
+4.767     & 6R                                                                        & 3L                                                        & 3                                                                     & 0                     & 8                     & 9                    &                      &                      \\ \hline
+4.8425    & 3L                                                                        & 8R                                                        & 4                                                                     & 0                     & 3                     & 8                    & 9                    &                      \\ \hline
+4.9072    & 8R                                                                        & 4L                                                        & 3                                                                     & 0                     & 3                     & 9                    &                      &                      \\ \hline
+5.3804    & 4L                                                                        & 9R                                                        & 4                                                                     & 0                     & 3                     & 4                    & 9                    &                      \\ \hline
+5.9157    & 9R                                                                        & 1L                                                        & 3                                                                     & 0                     & 3                     & 4                    &                      &                      \\ \hline
 \end{tabular}
 
 \label{my-label}
@@ -379,13 +423,18 @@ The left and right points of each segment are placed on the line segment $[0,2\p
 
 %The optimization algorithm that used by LiCO protocol based on the perimeter coverage levels of the left and right points of the segments and worked to minimize the number of sensor nodes for each left or right point of the segments within each sensor node. The algorithm minimize the perimeter coverage level of the left and right points of the segments, while, it assures that every perimeter coverage level of the left and right points of the segments greater than or equal to 1.
 
-In LiCO protocol, scheduling of sensor nodes'activities is formulated with an integer program based on coverage intervals and is detailed in section~\ref{cp}.
-
-In the case of sensor node, which has a part of its sensing range outside the border of the WSN sensing field as in figure~\ref{ex4pcm}, the coverage level for this segment is set to $\infty$, and the corresponding interval will not be taken into account by the optimization algorithm.
-\begin{figure}[ht!]
+In LiCO  protocol, scheduling of sensor  nodes' activities is formulated  with an
+integer program  based on  coverage intervals. 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
+figure~\ref{ex4pcm}, the maximum coverage level for  this arc is set to $\infty$
+and  the  corresponding  interval  will  not   be  taken  into  account  by  the
+optimization algorithm.
+ 
+\begin{figure}[t!]
 \centering
-\includegraphics[width=75mm]{ex4pcm.jpg}  
-\caption{Part of sensing range outside the the border of WSN sensing field.}
+\includegraphics[width=62.5mm]{ex4pcm.jpg}  
+\caption{Sensing range outside the WSN's area of interest.}
 \label{ex4pcm}
 \end{figure} 
 %Figure~\ref{ex5pcm} gives an example to compute the perimeter coverage levels for the left and right points of the segments for a sensor node $0$, which has a part of its sensing range exceeding the border of the sensing field of WSN, and it has a six neighbors. In figure~\ref{ex5pcm}, the sensor node $0$ has two segments outside the border of the network sensing field, so the left and right points of the two segments called $-1L$, $-1R$, $-2L$, and $-2R$.
@@ -396,42 +445,67 @@ In the case of sensor node, which has a part of its sensing range outside the bo
 %\label{ex5pcm}
 %\end{figure} 
 
-
 \subsection{The Main Idea}
-\noindent The area  of  interest can  be  divided into smaller areas called subregions and
-then our protocol will be implemented in each subregion simultaneously. LiCO protocol works into periods fashion as shown in figure~\ref{fig2}.
-\begin{figure}[ht!]
+
+\noindent The  WSN area of  interest is, in a  first step, divided  into regular
+homogeneous subregions  using a divide-and-conquer  algorithm. In a  second step
+our  protocol  will  be  executed  in   a  distributed  way  in  each  subregion
+simultaneously to schedule nodes' activities for one sensing period.
+
+As shown  in figure~\label{fig2},  node activity scheduling  is produced  by our
+protocol in a periodic manner. Each period is divided into 4 stages: Information
+(INFO)  Exchange,  Leader Election,  Decision  (the  result of  an  optimization
+problem),  and  Sensing.   For  each  period there  is  exactly  one  set  cover
+responsible for  the sensing task.  Protocols  based on a periodic  scheme, like
+LiCO, are more  robust against an unexpected  node failure. On the  one hand, if
+node failure is discovered before  taking the decision, the corresponding sensor
+node will  not be considered  by the optimization  algorithm, and, on  the other
+hand, if the sensor failure happens after  the decision, the sensing task of the
+network will be temporarily affected: only  during the period of sensing until a
+new period starts, since a new set cover will take charge of the sensing task in
+the next period. The energy consumption and some other constraints can easily be
+taken  into  account since  the  sensors  can  update  and then  exchange  their
+information (including their  residual energy) at the beginning  of each period.
+However, the pre-sensing  phases (INFO Exchange, Leader  Election, and Decision)
+are energy consuming, even for nodes that will not join the set cover to monitor
+the area.
+
+\begin{figure}[t!]
 \centering
-\includegraphics[width=85mm]{Model.pdf}  
+\includegraphics[width=80mm]{Model.pdf}  
 \caption{LiCO protocol}
 \label{fig2}
 \end{figure} 
 
-Each period is divided into 4 stages: Information (INFO) Exchange, Leader  Election, Optimization Decision,  and  Sensing.  For  each  period there  is exactly one set cover responsible for the sensing task. LiCO is more powerful against an unexpected node failure because it works in periods. On the one hand, if the node failure is discovered before taking the decision of the optimization algorithm, the sensor node would not involved to current stage, and, on the other hand, if the sensor failure takes place after the decision,  the sensing task of the network will be temporarily affected: only during the period of sensing until a new period starts, since a new set cover will take charge of the sensing task in the next period.  The energy consumption and some other constraints can easily be taken into account since the sensors can update and then exchange their information (including their residual energy) at the beginning of each period.  However,   the  pre-sensing  phases   (INFO  Exchange,  Leader Election, and  Decision) are energy  consuming for  some sensor nodes,  even when they do not join the network to monitor the area. 
-
-We define two types of packets to be used by LiCO protocol.
+We define two types of packets to be used by LiCO protocol:
 %\begin{enumerate}[(a)]
 \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 inform them to be Active or Sleep during the sensing phase.
+\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.
 \end{itemize}
 %\end{enumerate}
 
-There are five status for each sensor node in the network :
+Five status are possible for a sensor node in the network:
 %\begin{enumerate}[(a)] 
 \begin{itemize} 
-\item LISTENING: Sensor is waiting for a decision (to be active or not)
-\item COMPUTATION: Sensor applies the optimization process as leader
-\item ACTIVE: Sensor is active
-\item SLEEP: Sensor is turned off
-\item COMMUNICATION: Sensor is transmitting or receiving packet
+\item LISTENING: waits for a decision (to be active or not);
+\item COMPUTATION: executes the optimization algorithm as leader to
+  determine the activities scheduling;
+\item ACTIVE: node is sensing;
+\item SLEEP: node is turned off;
+\item COMMUNICATION: transmits or recevives packets.
 \end{itemize}
 %\end{enumerate}
 %Below, we describe each phase in more details.
 
 \subsection{LiCO Protocol Algorithm}
-The pseudo-code for LiCO Protocol is illustrated as follows:
 
+The  pseudocode  implementing the  protocol  on  a  node  is given  below.  More
+precisely, Algorithm~\label{alg:LiCO} gives a  brief description of the protocol
+applied by a sensor node $s_k$ where $k$ is the node index in the WSN.
 
 \begin{algorithm}[h!]                
  % \KwIn{all the parameters related to information exchange}
@@ -441,8 +515,8 @@ The pseudo-code for LiCO Protocol is illustrated as follows:
   
   \If{ $RE_k \geq E_{th}$ }{
       \emph{$s_k.status$ = COMMUNICATION}\;
-      \emph{Send $INFO()$ packet to other nodes in the subregion}\;
-      \emph{Wait $INFO()$ packet from other nodes in the subregion}\; 
+      \emph{Send $INFO()$ packet to other nodes in subregion}\;
+      \emph{Wait $INFO()$ packet from other nodes in subregion}\; 
       \emph{Update K.CurrentSize}\;
       \emph{LeaderID = Leader election}\;
       \If{$ s_k.ID = LeaderID $}{
@@ -453,12 +527,12 @@ The pseudo-code for LiCO Protocol is illustrated as follows:
          % \emph{ Determine the segment points using perimeter coverage model}\;
       }
       
-      \If{$ (s_k.ID $ is the same Previous Leader) AND (K.CurrentSize = K.PreviousSize)}{
+      \If{$ (s_k.ID $ is the same Previous Leader) And (K.CurrentSize = K.PreviousSize)}{
       
       	 \emph{ Use the same previous cover set for current sensing stage}\;
       }
       \Else{
-            \emph{ Update $a^j_{ik}$ and prepare data to Algorithm}\;
+            \emph{Update $a^j_{ik}$; prepare data for IP~Algorithm}\;
             \emph{$\left\{\left(X_{1},\dots,X_{l},\dots,X_{K}\right)\right\}$ = Execute Integer Program Algorithm($K$)}\;
             \emph{K.PreviousSize = K.CurrentSize}\;
            }
@@ -481,16 +555,29 @@ The pseudo-code for LiCO Protocol is illustrated as follows:
 
 \end{algorithm}
 
-\noindent Algorithm 1 gives a brief description of the protocol applied by each sensor node (denoted by $s_k$ for a sensor node indexed by $k$). In this algorithm, the K.CurrentSize and K.PreviousSize refer to the current size and the previous size of sensor nodes still alive in the subregion respectively.
-Initially, the sensor node checks its remaining energy $RE_k$, which must be greater than a threshold $E_{th}$ in order to participate in the current period. Each sensor node determines its position and its subregion based Embedded GPS  or Location Discovery Algorithm. After that, all the sensors collect position coordinates, remaining energy, sensor node id, and the number of its one-hop live neighbors during the information exchange. The sensors inside a same region cooperate to elect a leader. The selection criteria for the leader in order  of priority  are: larger number of neighbors,  larger remaining  energy, and  then in  case of equality, larger index. Thereafter the leader collects information to formulate and solve the integer program which allows to construct the set of active sensors in the sensing stage.  
-
+\noindent  In this  algorithm,  K.CurrentSize and  K.PreviousSize  refer to  the
+current  size  and  the  previous  size  of  the  subnetwork  in  the  subregion
+respectively.   That  means   the  number  of  sensor  nodes   which  are  still
+alive. Initially, the sensor node checks its remaining energy $RE_k$, which must
+be greater  than a  threshold $E_{th}$  in order to  participate in  the current
+period. Each  sensor node  determines its  position and  its subregion  using an
+embedded GPS  or a  location discovery  algorithm. After  that, all  the sensors
+collect position coordinates,  remaining energy, sensor node ID,  and the number
+of  its one-hop  live neighbors  during  the information  exchange. The  sensors
+inside a same region cooperate to elect a leader. The selection criteria for the
+leader, in order of priority, are:  larger number of neighbors, larger remaining
+energy, and  then in case  of equality, larger  index.  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 stage.
 
 %After the cooperation among the sensor nodes in the same subregion, the leader will be elected in distributed way, where each sensor node and based on it's information decide who is the leader. The selection criteria for the leader in order  of priority  are: larger number of neighbors,  larger remaining  energy, and  then in  case of equality, larger index. Thereafter,  if the sensor node is leader, it will execute the perimeter-coverage model for each sensor in the subregion in order to determine the segment points which would be used in the next stage by the optimization algorithm of the LiCO protocol. Every sensor node is selected as a leader, it is executed the perimeter coverage model only one time during it's life in the network.
 
 % The leader has the responsibility of applying the integer program algorithm (see section~\ref{cp}), which provides a set of sensors planned to be active in the sensing stage.  As leader, it will send an Active-Sleep packet to each sensor in the same subregion to inform it if it has to be active or not. On the contrary, if the sensor is not the leader, it will wait for the Active-Sleep packet to know its state for the sensing stage.
 
+% MICHEL TO BE CONTINUED
 
 \section{Lifetime Coverage problem formulation}
+
 \label{cp}
 In this section, the coverage model is mathematically formulated.
 For convenience, the notations are described first. 
@@ -501,7 +588,6 @@ For convenience, the notations are described first.
 \noindent $I_j :$ the set of coverage intervals (CI)  for sensor $j$.\\
 \noindent $I_j$ refers to the set of intervals which have been defined for each sensor $j$ in section~\ref{sec:The LiCO Protocol Description}.
 \noindent For a coverage interval  $i$,  let  $a^j_{ik}$ denote the indicator function of whether the sensor $k$ is involved in the coverage interval $i$ of sensor $j$, that is:
-
 \begin{equation}
 a^j_{ik} = \left \{ 
 \begin{array}{lll}
@@ -543,9 +629,8 @@ Note that $a^k_{ik}=1$ by definition of the interval.\\
 
 
 
-\noindent Our coverage optimization problem can be mathematically formulated as follows: \\
+\noindent Our coverage optimization problem can be mathematically formulated as follows: 
 %Objective:
-
 \begin{equation} \label{eq:ip2r}
 \left \{
 \begin{array}{ll}
@@ -791,7 +876,7 @@ We denote by Protocol/50, Protocol/80, Protocol/85, Protocol/90, and Protocol/95
 \section{\uppercase{Conclusion and Future Works}}
 \label{sec:Conclusion and Future Works}
 In this paper we have studied the problem of lifetime coverage optimization in
-WSNs. We designed a protocol LiCO that schedules node activities (wakeup and sleep) with the objective of maintaining a good coverage ratio while maximizing the network lifetime. This protocol is applied on each subregion of the area of interest. It works in periods and is based on the resolution of an integer program to select the subset of sensors operating in active mode for each period. Our work is original in so far as it proposes for the first time an integer program scheduling the activation of sensors based on their perimeter coverage level instead of using a set of targets/points to be covered.
+WSNs. We designed a protocol LiCO that schedules node' activities (wakeup and sleep) with the objective of maintaining a good coverage ratio while maximizing the network lifetime. This protocol is applied on each subregion of the area of interest. It works in periods and is based on the resolution of an integer program to select the subset of sensors operating in active mode for each period. Our work is original in so far as it proposes for the first time an integer program scheduling the activation of sensors based on their perimeter coverage level instead of using a set of targets/points to be covered.
 
  
 
