use of its limited energy provision, so that it can fulfill its monitoring task
as long as possible. Among known available approaches that can be used to
improve power management, lifetime coverage optimization provides activity
-scheduling which ensures sensing coverage while minimizing the energy cost. In
-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
+scheduling which ensures sensing coverage while minimizing the energy cost. In
+this paper, we propose such an approach called Perimeter-based Coverage Optimization
+protocol (PeCO). 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.
% 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
+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
-OMNeT++, the discrete event simulator, to demonstrate that LiCO is capable to
+OMNeT++, the discrete event simulator, to demonstrate that PeCO is capable to
offer longer lifetime coverage for WSNs in comparison with some other protocols.
\end{abstract}
deviations.
\item We have conducted extensive simulation experiments, using the discrete event
simulator OMNeT++, to demonstrate the efficiency of our protocol. We have compared
- our LiCO protocol to two approaches found in the literature:
+ our PeCO protocol to two approaches found in the literature:
DESK~\cite{ChinhVu} and GAF~\cite{xu2001geography}, and also to our previous
work published in~\cite{Idrees2} which is based on another optimization model
for sensor scheduling.
\end{enumerate}
-%Two combined integrated energy-efficient techniques have been used by LiCO protocol in order to maximize the lifetime coverage in WSN: the first, by dividing the area of interest into several smaller subregions based on divide-and-conquer method and then one leader elected for each subregion in an independent, distributed, and simultaneous way by the cooperation among the sensor nodes within each subregion, and this similar to cluster architecture;
+%Two combined integrated energy-efficient techniques have been used by PeCO protocol in order to maximize the lifetime coverage in WSN: the first, by dividing the area of interest into several smaller subregions based on divide-and-conquer method and then one leader elected for each subregion in an independent, distributed, and simultaneous way by the cooperation among the sensor nodes within each subregion, and this similar to cluster architecture;
% the second, activity scheduling based new optimization model has been used to provide the optimal cover set that will take the mission of sensing during current period. This optimization algorithm is based on a perimeter-coverage model so as to optimize the shared perimeter among the sensors in each subregion, and this represents as a energu-efficient control topology mechanism in WSN.
The rest of the paper is organized as follows. In the next section we review
-some related work in the field. Section~\ref{sec:The LiCO Protocol Description}
-is devoted to the LiCO protocol description and Section~\ref{cp} focuses on the
+some related work in the field. Section~\ref{sec:The PeCO Protocol Description}
+is devoted to the PeCO protocol description and Section~\ref{cp} focuses on the
coverage model formulation which is used to schedule the activation of sensor
nodes. Section~\ref{sec:Simulation Results and Analysis} presents simulations
results and discusses the comparison with other approaches. Finally, concluding
\label{sec:Literature Review}
\noindent In this section, we summarize some related works regarding the
-coverage problem and distinguish our LiCO protocol from the works presented in
+coverage problem and distinguish our PeCO protocol from the works presented in
the literature.
The most discussed coverage problems in literature can be classified in three
provide an algorithm in $O(nd~log~d)$ time to compute the perimeter-coverage of
each sensor, where $d$ denotes the maximum number of sensors that are
neighbors to a sensor and $n$ is the total number of sensors in the
-network. {\it In LiCO protocol, instead of determining the level of coverage of
+network. {\it In PeCO protocol, instead of determining the level of coverage of
a set of discrete points, our optimization model is based on checking the
perimeter-coverage of each sensor to activate a minimal number of sensors.}
activated in succession to achieve the desired network lifetime. Vu
\cite{chin2007}, Padmatvathy {\em et al.}~\cite{pc10}, propose algorithms
working in a periodic fashion where a cover set is computed at the beginning of
-each period. {\it Motivated by these works, LiCO protocol works in periods,
+each period. {\it Motivated by these works, PeCO protocol works in periods,
where each period contains a preliminary phase for information exchange and
decisions, followed by a sensing phase where one cover set is in charge of the
sensing task.}
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 is, the
higher the communication and thus the energy cost are. {\it In order to be
- suitable for large-scale networks, in the LiCO protocol, the area of interest
+ suitable for large-scale 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 selecting the active sensors for the current
period. Thus our protocol is scalable and is a globally distributed method,
energy constraints. Column generation techniques, well-known and widely
practiced techniques for solving linear programs with too many variables, have
also been
-used~\cite{castano2013column,rossi2012exact,deschinkel2012column}. {\it In the LiCO
+used~\cite{castano2013column,rossi2012exact,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 the undercoverage
of the perimeter of each sensor.}
%\uppercase{\textbf{shortcomings}}. In spite of many energy-efficient protocols for maintaining the coverage and improving the network lifetime in WSNs were proposed, non of them ensure the coverage for the sensing field with optimal minimum number of active sensor nodes, and for a long time as possible. For example, in a full centralized algorithms, an optimal solutions can be given by using optimization approaches, but in the same time, a high energy is consumed for the execution time of the algorithm and the communications among the sensors in the sensing field, so, the full centralized approaches are not good candidate to use it especially in large WSNs. Whilst, a full distributed algorithms can not give optimal solutions because this algorithms use only local information of the neighboring sensors, but in the same time, the energy consumption during the communications and executing the algorithm is highly lower. Whatever the case, this would result in a shorter lifetime coverage in WSNs.
-%\uppercase{\textbf{Our Protocol}}. In this paper, a Lifetime Coverage Optimization Protocol, called (LiCO) in WSNs is suggested. The sensing field is divided into smaller subregions by means of divide-and-conquer method, and a LiCO protocol is distributed in each sensor in the subregion. The network lifetime in each subregion is divided into periods, each period includes 4 stages: Information Exchange, Leader election, decision based activity scheduling optimization, and sensing. The leaders are elected in an independent, asynchronous, and distributed way in all the subregions of the WSN. After that, energy-efficient activity scheduling mechanism based new optimization model is performed by each leader in the subregions. This optimization model is based on the perimeter coverage model in order to producing the optimal cover set of active sensors, which are taken the responsibility of sensing during the current period. LiCO protocol merges between two energy efficient mechanisms, which are used the main advantages of the centralized and distributed approaches and avoids the most of their disadvantages.
+%\uppercase{\textbf{Our Protocol}}. In this paper, a Lifetime Coverage Optimization Protocol, called (PeCO) in WSNs is suggested. The sensing field is divided into smaller subregions by means of divide-and-conquer method, and a PeCO protocol is distributed in each sensor in the subregion. The network lifetime in each subregion is divided into periods, each period includes 4 stages: Information Exchange, Leader election, decision based activity scheduling optimization, and sensing. The leaders are elected in an independent, asynchronous, and distributed way in all the subregions of the WSN. After that, energy-efficient activity scheduling mechanism based new optimization model is performed by each leader in the subregions. This optimization model is based on the perimeter coverage model in order to producing the optimal cover set of active sensors, which are taken the responsibility of sensing during the current period. PeCO protocol merges between two energy efficient mechanisms, which are used the main advantages of the centralized and distributed approaches and avoids the most of their disadvantages.
-\section{ The LiCO Protocol Description}
-\label{sec:The LiCO Protocol Description}
+\section{ The PeCO Protocol Description}
+\label{sec:The PeCO Protocol Description}
\noindent In this section, we describe in details our Lifetime Coverage
Optimization protocol. First we present the assumptions we made and the models
proved that if the transmission range fulfills the previous hypothesis, a
complete coverage of a convex area implies connectivity among active nodes.
-The LiCO protocol uses the same perimeter-coverage model as Huang and
+The PeCO 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
\end{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 PeCO 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 the LiCO protocol, scheduling of sensor nodes' activities is formulated with an
+In the PeCO 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
(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
+PeCO, are more robust against an unexpected node failure. On the one hand, if
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
\begin{figure}[t!]
\centering
\includegraphics[width=80mm]{Model.pdf}
-\caption{LiCO protocol.}
+\caption{PeCO protocol.}
\label{fig2}
\end{figure}
-We define two types of packets to be used by LiCO protocol:
+We define two types of packets to be used by PeCO protocol:
%\begin{enumerate}[(a)]
\begin{itemize}
\item INFO packet: sent by each sensor node to all the nodes inside a same
%\end{enumerate}
%Below, we describe each phase in more details.
-\subsection{LiCO Protocol Algorithm}
+\subsection{PeCO Protocol Algorithm}
\noindent The pseudocode implementing the protocol on a node is given below.
-More precisely, Algorithm~\ref{alg:LiCO} gives a brief description of the
+More precisely, Algorithm~\ref{alg:PeCO} 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!]
}
}
\Else { Exclude $s_k$ from entering in the current sensing stage}
-\caption{LiCO($s_k$)}
-\label{alg:LiCO}
+\caption{PeCO($s_k$)}
+\label{alg:PeCO}
\end{algorithm}
In this algorithm, K.CurrentSize and K.PreviousSize respectively represent the
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 PeCO 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.
\subsection{Simulation Results}
In order to assess and analyze the performance of our protocol we have
-implemented LiCO protocol in OMNeT++~\cite{varga} simulator. Besides LiCO, two
+implemented PeCO protocol in OMNeT++~\cite{varga} simulator. Besides PeCO, two
other protocols, described in the next paragraph, will be evaluated for
comparison purposes. The simulations were run on a laptop DELL with an Intel
Core~i3~2370~M (2.4~GHz) processor (2 cores) whose MIPS (Million Instructions
optimization solver GLPK (GNU linear Programming Kit available in the public
domain) \cite{glpk} through a Branch-and-Bound method.
-As said previously, the LiCO is compared with three other approaches. The first
+As said previously, the PeCO is compared with three other approaches. The first
one, called DESK, is a fully distributed coverage algorithm proposed by
\cite{ChinhVu}. The second one, called GAF~\cite{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~\cite{Idrees2}, is an improved version
of a research work we presented in~\cite{idrees2014coverage}. Let us notice that
-LiCO and DiLCO protocols are based on the same framework. In particular, 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 chosen because
it corresponds to the configuration producing the better results for DiLCO. 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 LiCO protocol objective is to reach a desired level of coverage for each
+whereas PeCO protocol objective is to reach a desired level of coverage for each
sensor perimeter. In our experimentations, we chose a level of coverage equal to
one ($l=1$).
Figure~\ref{fig333} shows the average coverage ratio for 200 deployed nodes
obtained with the four protocols. DESK, GAF, and DiLCO provide a little better
coverage ratio with respectively 99.99\%, 99.91\%, and 99.02\%, against 98.76\%
-produced by LiCO for the first periods. This is due to the fact that at the
+produced by PeCO for the first periods. This is due to the fact that at the
beginning DiLCO protocol puts in sleep status more redundant sensors (which
slightly decreases the coverage ratio), while the three other protocols activate
more sensor nodes. Later, when the number of periods is beyond~70, it clearly
-appears that LiCO provides a better coverage ratio and keeps a coverage ratio
+appears that PeCO provides a better coverage ratio and keeps a coverage ratio
greater than 50\% for longer periods (15 more compared to DiLCO, 40 more
-compared to DESK). The energy saved by LiCO in the early periods allows later a
+compared to DESK). The energy saved by PeCO in the early periods allows later a
substantial increase of the coverage performance.
\parskip 0pt
\label{fig333}
\end{figure}
-%When the number of periods increases, coverage ratio produced by DESK and GAF protocols decreases. This is due to dead nodes. However, DiLCO protocol maintains almost a good coverage from the round 31 to the round 63 and it is close to LiCO protocol. The coverage ratio of LiCO protocol is better than other approaches from the period 64.
+%When the number of periods increases, coverage ratio produced by DESK and GAF protocols decreases. This is due to dead nodes. However, DiLCO protocol maintains almost a good coverage from the round 31 to the round 63 and it is close to PeCO protocol. The coverage ratio of PeCO protocol is better than other approaches from the period 64.
-%because the optimization algorithm used by LiCO has been optimized the lifetime coverage based on the perimeter coverage model, so it provided acceptable coverage for a larger number of periods and prolonging the network lifetime based on the perimeter of the sensor nodes in each subregion of WSN. Although some nodes are dead, sensor activity scheduling based optimization of LiCO selected another nodes to ensure the coverage of the area of interest. i.e. DiLCO-16 showed a good coverage in the beginning then LiCO, when the number of periods increases, the coverage ratio decreases due to died sensor nodes. Meanwhile, thanks to sensor activity scheduling based new optimization model, which is used by LiCO protocol to ensure a longer lifetime coverage in comparison with other approaches.
+%because the optimization algorithm used by PeCO has been optimized the lifetime coverage based on the perimeter coverage model, so it provided acceptable coverage for a larger number of periods and prolonging the network lifetime based on the perimeter of the sensor nodes in each subregion of WSN. Although some nodes are dead, sensor activity scheduling based optimization of PeCO selected another nodes to ensure the coverage of the area of interest. i.e. DiLCO-16 showed a good coverage in the beginning then PeCO, when the number of periods increases, the coverage ratio decreases due to died sensor nodes. Meanwhile, thanks to sensor activity scheduling based new optimization model, which is used by PeCO protocol to ensure a longer lifetime coverage in comparison with other approaches.
\subsubsection{\bf Active Sensors Ratio}
energy consumption and so maximize the network lifetime. Figure~\ref{fig444}
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 LiCO protocols compete perfectly with only 17.92 \% and
+rounds and DiLCO and PeCO 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
+increases, PeCO 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}.
computation, listening, active, and sleep status for different network densities
and compare it for the four approaches. Figures~\ref{fig3EC}(a) and (b)
illustrate the energy consumption for different network sizes and for
-$Lifetime95$ and $Lifetime50$. The results show that our LiCO protocol is the
+$Lifetime95$ and $Lifetime50$. The results show that our PeCO protocol is the
most competitive from the energy consumption point of view. As shown in both
-figures, LiCO consumes much less energy than the three other methods. One might
+figures, PeCO consumes much less energy than the three 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
\label{fig3EC}
\end{figure}
-%The optimization algorithm, which used by LiCO protocol, was improved the lifetime coverage efficiently based on the perimeter coverage model.
+%The optimization algorithm, which used by PeCO protocol, was improved the lifetime coverage efficiently based on the perimeter coverage model.
%The other approaches have a high energy consumption due to activating a larger number of sensors. In fact, a distributed method on the subregions greatly reduces the number of communications and the time of listening so thanks to the partitioning of the initial network into several independent subnetworks.
\subsubsection{\bf Network Lifetime}
-We observe the superiority of LiCO and DiLCO protocols in comparison against the
+We observe the superiority of PeCO 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
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
+and PeCO 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
-is about twice longer with LiCO compared to DESK protocol. The performance
+is about twice longer with PeCO 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
the time, and the lifetime with a coverage of 50\% is far more longer than with
\label{fig3LT}
\end{figure}
-%By choosing the best suited nodes, for each period, by optimizing the coverage and lifetime of the network to cover the area of interest and by letting the other ones sleep in order to be used later in next rounds, LiCO protocol efficiently prolonged the network lifetime especially for a coverage ratio greater than $50 \%$, whilst it stayed very near to DiLCO-16 protocol for $95 \%$.
+%By choosing the best suited nodes, for each period, by optimizing the coverage and lifetime of the network to cover the area of interest and by letting the other ones sleep in order to be used later in next rounds, PeCO protocol efficiently prolonged the network lifetime especially for a coverage ratio greater than $50 \%$, whilst it stayed very near to DiLCO-16 protocol for $95 \%$.
Figure~\ref{figLTALL} compares the lifetime coverage of our 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 $50\%$, $80\%$, $85\%$, $90\%$, and $95\%$
-respectively, where Protocol is DiLCO or LiCO. Indeed there are applications
-that do not require a 100\% coverage of the area to be monitored. LiCO might be
+respectively, where Protocol is DiLCO or PeCO. Indeed there are applications
+that do not require a 100\% coverage of the area to be monitored. PeCO might be
an interesting method since it achieves a good balance between a high level
-coverage ratio and network lifetime. LiCO always outperforms DiLCO for the three
+coverage ratio and network lifetime. PeCO always outperforms DiLCO for the three
lower coverage ratios, moreover the improvements grow with the network
-size. DiLCO is better for coverage ratios near 100\%, but in that case LiCO is
+size. DiLCO is better for coverage ratios near 100\%, but in that case PeCO is
not so bad for the smallest network sizes.
\begin{figure}[h!]
\label{figLTALL}
\end{figure}
-%Comparison shows that LiCO protocol, which are used distributed optimization over the subregions, is the more relevance one for most coverage ratios and WSN sizes because it is robust to network disconnection during the network lifetime as well as it consume less energy in comparison with other approaches. LiCO protocol gave acceptable coverage ratio for a larger number of periods using new optimization algorithm that based on a perimeter coverage model. It also means that distributing the algorithm in each node and subdividing the sensing field into many subregions, which are managed independently and simultaneously, is the most relevant way to maximize the lifetime of a network.
+%Comparison shows that PeCO protocol, which are used distributed optimization over the subregions, is the more relevance one for most coverage ratios and WSN sizes because it is robust to network disconnection during the network lifetime as well as it consume less energy in comparison with other approaches. PeCO protocol gave acceptable coverage ratio for a larger number of periods using new optimization algorithm that based on a perimeter coverage model. It also means that distributing the algorithm in each node and subdividing the sensing field into many subregions, which are managed independently and simultaneously, is the most relevant way to maximize the lifetime of a network.
\section{Conclusion and Future Works}
sensors based on their perimeter coverage level, instead of using a set of
targets/points to be covered.
-%To cope with this problem, the area of interest is divided into a smaller subregions using divide-and-conquer method, and then a LiCO protocol for optimizing the lifetime coverage in each subregion. LiCO protocol combines two efficient techniques: network
+%To cope with this problem, the area of interest is divided into a smaller subregions using divide-and-conquer method, and then a PeCO protocol for optimizing the lifetime coverage in each subregion. PeCO protocol combines two efficient techniques: network
%leader election, which executes the perimeter coverage model (only one time), the optimization algorithm, and sending the schedule produced by the optimization algorithm to other nodes in the subregion ; the second, sensor activity scheduling based optimization in which a new lifetime coverage optimization model is proposed. The main challenges include how to select the most efficient leader in each subregion and the best schedule of sensor nodes that will optimize the network lifetime coverage
%in the subregion.
%The network lifetime coverage in each subregion is divided into
%(ii) Leader Election, (iii) a Decision based new optimization model in order to
%select the nodes remaining active for the last stage, and (iv) Sensing.
We have carried out several simulations to evaluate the proposed protocol. The
-simulation results show that LiCO is more energy-efficient than other
+simulation results show that PeCO is more energy-efficient than other
approaches, with respect to lifetime, coverage ratio, active sensors ratio, and
energy consumption.
%Indeed, when dealing with large and dense WSNs, a distributed optimization approach on the subregions of WSN like the one we are proposed allows to reduce the difficulty of a single global optimization problem by partitioning it in many smaller problems, one per subregion, that can be solved more easily. We have identified different research directions that arise out of the work presented here.
