for the related work shoudl be reduced and there are too much toto and titi have...

[JournalMultiPeriods.git] / article.tex

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@@ -199,25 +199,25 @@ size increases.
 
 The first algorithms proposed in the literature consider that the cover sets are
 disjoint: a sensor node appears in exactly one of the generated cover sets.  For
 
 The first algorithms proposed in the literature consider that the cover sets are
 disjoint: a sensor node appears in exactly one of the generated cover sets.  For

-instance, Slijepcevic  and Potkonjak \cite{Slijepcevic01powerefficient} proposed
-an  algorithm, which  allocates sensor  nodes  in mutually  independent sets  to
-monitor an area divided into several fields.  Their algorithm builds a cover set
-by including in  priority the sensor nodes which cover  critical fields, that is
-to say  fields that  are covered by  the smallest  number of sensors.   The time
+instance,  Slijepcevic  and  Potkonjak  \cite{Slijepcevic01powerefficient}  have
+proposed an algorithm, which allocates sensor nodes in mutually independent sets
+to monitor an area divided into  several fields.  Their algorithm builds a cover
+set by including in priority the  sensor nodes which cover critical fields, that
+is to say fields  that are covered by the smallest number  of sensors.  The time

 complexity of  their heuristic is $O(n^2)$  where $n$ is the  number of sensors.
 complexity of  their heuristic is $O(n^2)$  where $n$ is the  number of sensors.

-Abrams et al.~\cite{abrams2004set} designed three approximation algorithms for a
-variation of  the set k-cover problem,  where the objective is  to partition the
-sensors into covers such that the  number of covers that include an area, summed
-over  all   areas,  is  maximized.    Their  work  builds  upon   previous  work
+Abrams et al.~\cite{abrams2004set}  have designed three approximation algorithms
+for a variation of the set  k-cover problem, where the objective is to partition
+the sensors  into covers such  that the number  of covers that include  an area,
+summed  over all  areas, is  maximized.  Their  work builds  upon  previous work

 in~\cite{Slijepcevic01powerefficient}  and  the  generated  cover  sets  do  not
 provide complete coverage of the monitoring zone.
 
 in~\cite{Slijepcevic01powerefficient}  and  the  generated  cover  sets  do  not
 provide complete coverage of the monitoring zone.
 

-\cite{cardei2005improving} proposed a method  to efficiently compute the maximum
-number of disjoint  set covers such that each set can  monitor all targets. They
-first transform the problem into a  maximum flow problem, which is formulated as
-a mixed integer  programming (MIP). Then their heuristic uses  the output of the
-MIP to compute disjoint set covers.  Results show that this heuristic provides a
-number      of     set      covers     slightly      larger      compared     to
+In \cite{cardei2005improving}, the authors have proposed a method to efficiently
+compute the maximum number of disjoint set covers such that each set can monitor
+all targets. They first transform the problem into a maximum flow problem, which
+is formulated  as a mixed integer  programming (MIP). Then  their heuristic uses
+the output  of the MIP to compute  disjoint set covers.  Results  show that this
+heuristic  provides  a  number  of   set  covers  slightly  larger  compared  to

 \cite{Slijepcevic01powerefficient}, but with a  larger execution time due to the
 complexity of the mixed integer programming resolution.
 
 \cite{Slijepcevic01powerefficient}, but with a  larger execution time due to the
 complexity of the mixed integer programming resolution.
 


@@ -286,27 +286,27 @@ its status by a  rule named off-duty eligible rule, which tells  him to turn off
 if its sensing area is covered by its neighbors. A back-off scheme is introduced
 to let each sensor  delay the decision process with a random  period of time, in
 order  to avoid  simultaneous conflicting  decisions between  nodes and  lack of
 if its sensing area is covered by its neighbors. A back-off scheme is introduced
 to let each sensor  delay the decision process with a random  period of time, in
 order  to avoid  simultaneous conflicting  decisions between  nodes and  lack of

-coverage  on  any  area.    \cite{prasad2007distributed}  defines  a  model  for
-capturing the  dependencies between different cover sets  and proposes localized
+coverage on any area.  In \cite{prasad2007distributed} a model for capturing the
+dependencies between different  cover sets is defined and  it proposes localized

 heuristic based  on this  dependency. The algorithm  consists of two  phases, an
 initial setup phase during which each sensor computes and prioritizes the covers
 and a  sensing phase during which  each sensor first decides  its on/off status,
 and then remains on or off for the rest of the duration.
 
 heuristic based  on this  dependency. The algorithm  consists of two  phases, an
 initial setup phase during which each sensor computes and prioritizes the covers
 and a  sensing phase during which  each sensor first decides  its on/off status,
 and then remains on or off for the rest of the duration.
 

-The  authors in \cite{yardibi2010distributed}  developed a  Distributed Adaptive
-Sleep Scheduling Algorithm  (DASSA) for WSNs with partial  coverage.  DASSA does
-not require  location information of sensors while  maintaining connectivity and
-satisfying a  user defined  coverage target.  In  DASSA, nodes use  the residual
-energy levels  and feedback from the  sink for scheduling the  activity of their
-neighbors.  This  feedback mechanism reduces  the randomness in  scheduling that
-would  otherwise  occur  due  to   the  absence  of  location  information.   In
-\cite{ChinhVu},  the  author  proposed  a novel  distributed  heuristic,  called
-Distributed  Energy-efficient Scheduling  for k-coverage  (DESK),  which ensures
-that  the energy  consumption among  the sensors  is balanced  and  the lifetime
-maximized while the coverage requirement is maintained.  This heuristic works in
-rounds, requires only one-hop neighbor  information, and each sensor decides its
-status  (active or  sleep) based  on the  perimeter coverage  model  proposed in
-\cite{Huang:2003:CPW:941350.941367}.
+The  authors  in  \cite{yardibi2010distributed}  have  developed  a  Distributed
+Adaptive  Sleep Scheduling  Algorithm (DASSA)  for WSNs  with  partial coverage.
+DASSA  does  not  require  location  information of  sensors  while  maintaining
+connectivity and satisfying a user defined coverage target.  In DASSA, nodes use
+the  residual  energy levels  and  feedback from  the  sink  for scheduling  the
+activity of their neighbors.  This  feedback mechanism reduces the randomness in
+scheduling  that  would   otherwise  occur  due  to  the   absence  of  location
+information.   In  \cite{ChinhVu},  the  author have proposed  a  novel  distributed
+heuristic, called Distributed Energy-efficient Scheduling for k-coverage (DESK),
+which ensures that the energy consumption  among the sensors is balanced and the
+lifetime maximized while the coverage requirement is maintained.  This heuristic
+works in  rounds, requires  only one-hop neighbor  information, and  each sensor
+decides  its status  (active or  sleep) based  on the  perimeter  coverage model
+proposed in \cite{Huang:2003:CPW:941350.941367}.

 
 %Our Work, which is presented in~\cite{idrees2014coverage} proposed a coverage optimization protocol to improve the lifetime in
 %heterogeneous energy wireless sensor networks. 
 
 %Our Work, which is presented in~\cite{idrees2014coverage} proposed a coverage optimization protocol to improve the lifetime in
 %heterogeneous energy wireless sensor networks. 


@@ -315,19 +315,20 @@ status  (active or  sleep) based  on the  perimeter coverage  model  proposed in
 The  works presented in  \cite{Bang, Zhixin,  Zhang} focuses  on coverage-aware,
 distributed energy-efficient,  and distributed clustering  methods respectively,
 which aims  to extend the network  lifetime, while the coverage  is ensured.  S.
 The  works presented in  \cite{Bang, Zhixin,  Zhang} focuses  on coverage-aware,
 distributed energy-efficient,  and distributed clustering  methods respectively,
 which aims  to extend the network  lifetime, while the coverage  is ensured.  S.

-Misra et al.  \cite{Misra} proposed a localized algorithm for coverage in sensor
-networks. The algorithm conserve the  energy while ensuring the network coverage
-by activating the subset of sensors  with the minimum overlap area. The proposed
-method preserves the network connectivity  by formation of the network backbone.
-More recently,  Shibo et  al. \cite{Shibo} expressed  the coverage problem  as a
-minimum weight submodular set cover problem and proposed a Distributed Truncated
-Greedy Algorithm (DTGA) to solve it.  They take advantage from both temporal and
-spatial  correlations between  data sensed  by different  sensors,  and leverage
-prediction,  to   improve  the  lifetime.   In   \cite{xu2001geography},  Xu  et
-al. proposed  an algorithm, called  Geographical Adaptive Fidelity  (GAF), which
-uses geographic location  information to divide the area  of interest into fixed
-square grids. Within each grid, it keeps only one node staying awake to take the
-responsibility of sensing and communication.
+Misra et al.   \cite{Misra} have proposed a localized  algorithm for coverage in
+sensor networks.  The  algorithm conserve the energy while  ensuring the network
+coverage by activating the subset of  sensors with the minimum overlap area. The
+proposed method preserves  the network connectivity by formation  of the network
+backbone.  More recently, Shibo et  al. \cite{Shibo} have expressed the coverage
+problem  as  a  minimum weight  submodular  set  cover  problem and  proposed  a
+Distributed Truncated Greedy Algorithm (DTGA)  to solve it.  They take advantage
+from both  temporal and  spatial correlations between  data sensed  by different
+sensors,   and    leverage   prediction,   to   improve    the   lifetime.    In
+\cite{xu2001geography},   Xu  et   al.  have   proposed  an   algorithm,  called
+Geographical Adaptive Fidelity (GAF), which uses geographic location information
+to divide  the area of  interest into fixed  square grids. Within each  grid, it
+keeps only  one node  staying awake  to take the  responsibility of  sensing and
+communication.

 
 Some  other  approaches (outside  the  scope  of our  work)  do  not consider  a
 synchronized and  predetermined period of time  where the sensors  are active or
 
 Some  other  approaches (outside  the  scope  of our  work)  do  not consider  a
 synchronized and  predetermined period of time  where the sensors  are active or