reading until the end of IV

diff --git a/LiCO_Journal.tex b/LiCO_Journal.tex
index 02be4ac25396654877c281cb78b2a579f4a8521c..7e788d4f6524d030e7276e745ed2a82c4ba02b61 100644 (file)
--- a/LiCO_Journal.tex
+++ b/LiCO_Journal.tex
@@ -64,16 +64,15 @@ this paper,  we propose such an approach  called Lifetime  Coverage Optimization
 protocol (LiCO).   It is a  hybrid of  centralized and distributed  methods: the
 region of interest is first subdivided  into subregions and our protocol is then
 distributed among sensor nodes in each  subregion.
 protocol (LiCO).   It is a  hybrid of  centralized and distributed  methods: the
 region of interest is first subdivided  into subregions and our protocol is then
 distributed among sensor nodes in each  subregion.

-%%RAPH abstract too long
-% 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
-%leader selected after  cooperation between nodes within the  same subregion.
-The novelty  of  our  approach  lies  essentially   in  the  formulation  of  a  new
+% 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 leader selected  after cooperation between
+%nodes within the same subregion.
+The  novelty of  our  approach lies  essentially  in the  formulation  of a  new

 mathematical optimization  model based on  perimeter coverage level  to schedule
 sensors' activities.  Extensive simulation experiments have been performed using
 mathematical 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
+OMNeT++, the  discrete event simulator, to  demonstrate that LiCO  is capable to

 offer longer lifetime coverage for WSNs in comparison with some other protocols.
 \end{abstract} 
 
 offer longer lifetime coverage for WSNs in comparison with some other protocols.
 \end{abstract} 
 


@@ -319,7 +318,7 @@ $R_c$ 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.
 
 proved  that if  the  transmission  range fulfills  the  previous hypothesis,  a
 complete coverage of a convex area implies connectivity among active nodes.
 

-LiCO protocol  uses the  same perimeter-coverage  model than  Huang and
+The LiCO protocol  uses the  same perimeter-coverage  model as  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
 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


@@ -359,17 +358,17 @@ obtained through  the formula: $$\alpha =  \arccos \left(\dfrac{Dist(u,v)}{2R_s}
 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
 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
+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
 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
+from the 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 $3$
 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 $0$.
+(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.
 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.


@@ -428,11 +427,11 @@ above is thus given by the sixth line of the table.
 
 %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.
 
 
 %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
+In the 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
 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 $\infty$
+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.
  
 and  the  corresponding  interval  will  not   be  taken  into  account  by  the
 optimization algorithm.
  


@@ -457,14 +456,14 @@ 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.
 
 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~\ref{fig2}, node  activity  scheduling is  produced by  our
+As  shown in  Figure~\ref{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
 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
+a node failure is discovered before  taking the decision, the corresponding sensor
+node will  not be considered  by the optimization  algorithm. 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
 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


@@ -543,7 +542,7 @@ protocol applied by a sensor node $s_k$ where $k$ is the node index in the WSN.
            }
       
         \emph{$s_k.status$ = COMMUNICATION}\;
            }
       
         \emph{$s_k.status$ = COMMUNICATION}\;

-        \emph{Send $ActiveSleep()$ to each node $l$ in subregion} \;
+        \emph{Send $ActiveSleep()$ to each node $l$ in subregion}\;

         \emph{Update $RE_k $}\;
       }          
       \Else{
         \emph{Update $RE_k $}\;
       }          
       \Else{


@@ -557,20 +556,19 @@ protocol applied by a sensor node $s_k$ where $k$ is the node index in the WSN.
 \label{alg:LiCO}
 \end{algorithm}
 
 \label{alg:LiCO}
 \end{algorithm}
 

-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 their 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.
+In this  algorithm, K.CurrentSize and K.PreviousSize  respectively represent the
+current number and  the previous number of alive nodes in  the subnetwork of the
+subregion.  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 their  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.
 
 
 %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.
 


@@ -592,7 +590,7 @@ First, we have the following sets:
 \end{itemize}
 $I_j$ refers to the set of  coverage intervals which have been defined according
 to the  method introduced in  subsection~\ref{CI}. For a coverage  interval $i$,
 \end{itemize}
 $I_j$ refers to the set of  coverage intervals which have 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
+let $a^j_{ik}$ denotes  the indicator function of whether  sensor~$k$ is involved

 in coverage interval~$i$ of sensor~$j$, that is:
 \begin{equation}
 a^j_{ik} = \left \{ 
 in coverage interval~$i$ of sensor~$j$, that is:
 \begin{equation}
 a^j_{ik} = \left \{ 


@@ -670,7 +668,7 @@ X_{k} \in \{0,1\}, \forall k \in A
 $\alpha^j_i$ 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
 $\alpha^j_i$ 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

-be  given a  relatively larger  magnitude than  weights associated  with another
+be  given by a  relatively larger  magnitude than  weights associated  with another

 region. This  kind of integer program  is inspired from the  model developed for
 brachytherapy    treatment   planning    for   optimizing    dose   distribution
 \cite{0031-9155-44-1-012}. The integer  program must be solved by  the leader in
 region. This  kind of integer program  is inspired from the  model developed for
 brachytherapy    treatment   planning    for   optimizing    dose   distribution
 \cite{0031-9155-44-1-012}. The integer  program must be solved by  the leader in


@@ -872,7 +870,7 @@ rounds and  DiLCO and LiCO  protocols compete perfectly  with only 17.92  \% and
 20.16 \% active  nodes during the same  time interval. As the  number of periods
 increases, LiCO protocol  has a lower number of active  nodes in comparison with
 the three other approaches, while keeping a greater coverage ratio as shown in
 20.16 \% active  nodes during the same  time interval. As the  number of periods
 increases, LiCO protocol  has a lower number of active  nodes in comparison with
 the three other approaches, while keeping a greater coverage ratio as shown in

-figure \ref{fig333}.
+Figure \ref{fig333}.

 
 \begin{figure}[h!]
 \centering
 
 \begin{figure}[h!]
 \centering


@@ -917,14 +915,14 @@ while keeping a good coverage level.
 
 We observe the superiority of LiCO and DiLCO protocols in comparison against the
 two    other   approaches    in    prolonging   the    network   lifetime.    In
 
 We observe the superiority of LiCO and DiLCO protocols in comparison against the
 two    other   approaches    in    prolonging   the    network   lifetime.    In

-figures~\ref{fig3LT}(a)  and (b),  $Lifetime95$ and  $Lifetime50$ are  shown for
+Figures~\ref{fig3LT}(a)  and (b),  $Lifetime95$ and  $Lifetime50$ are  shown for

 different  network  sizes.   As  highlighted  by  these  figures,  the  lifetime
 increases with the size  of the network, and it is clearly  the larger for DiLCO
 and LiCO  protocols.  For instance,  for a  network of 300~sensors  and coverage
 different  network  sizes.   As  highlighted  by  these  figures,  the  lifetime
 increases with the size  of the network, and it is clearly  the larger for DiLCO
 and LiCO  protocols.  For instance,  for a  network of 300~sensors  and coverage

-ratio greater than 50\%, we can  see on figure~\ref{fig3LT}(b) that the lifetime
+ratio greater than 50\%, we can  see on Figure~\ref{fig3LT}(b) that the lifetime

 is about two times longer with  LiCO compared to DESK protocol.  The performance
 is about two times longer with  LiCO compared to DESK protocol.  The performance

-difference    is    more    obvious   in    figure~\ref{fig3LT}(b)    than    in
-figure~\ref{fig3LT}(a) because the gain induced  by our protocols increases with
+difference    is    more    obvious   in    Figure~\ref{fig3LT}(b)    than    in
+Figure~\ref{fig3LT}(a) because the gain induced  by our protocols increases with

 the time, and the lifetime with a coverage  of 50\% is far more longer than with
 95\%.
 
 the time, and the lifetime with a coverage  of 50\% is far more longer than with
 95\%.