Distributed algorithms typically operate in rounds for a predetermined duration. At the beginning of each round, a sensor exchanges information with its neighbors and makes a decision to either remain turned on or to go to sleep for the round. This decision is basically made on simple greedy criteria like the largest uncovered area \cite{ref130} or maximum uncovered targets \cite{ref131}.
Cho et al.~\cite{ref145} propose a distributed node scheduling protocol, which can retain sensing coverage needed by applications and increases network lifetime via putting in sleep mode some redundant nodes. In this work, the Effective Sensing Area (ESA) concept of a sensor node is used, which refers to the sensing area that is not overlapping with another sensor's sensing area. A sensor node can determine whether it will be active or turned off by computing its ESA. The suggested work permits sensor nodes to be in sleep mode opportunistically whilst fulfilling the needed sensing coverage.
-Bahi et al. \cite{ref236,ref237} propose a distributed localisation algorithm and a scheduling method to maintain the coverage and improve the network lifetime. They suggest a mobile beacon to divide the area of interest into unit squares using Hilbert space filling curve method. They exploit the localization phase to construct sets of active nodes. They provide a local activity scheduling approach for the sensor nodes in the region to ensure the area coverage and to prolong the network lifetime. The experiment results show an improvement in the network lifetime due to reducing the energy consumed by the localisation and coverage algorithms.
+J. M. Bahi et al. \cite{ref236,ref237} propose a distributed approach which consists of two steps: nodes localization and coverage scheduling. They suggest a mobile beacon to divide the area of interest into unit squares using Hilbert space filling curve method. They exploit the localization phase to construct sets of active nodes. They provide a local activity scheduling approach for the sensor nodes to ensure the area coverage and to prolong the network lifetime. The experiment results show an improvement in the network lifetime using their proposed distributed approach.
The authors in~\cite{ref146} define a Maximum Sensing Coverage Region problem (MSCR) in WSNs and then propose a distributed algorithm to solve it. The maximum observed area is fully covered by a minimum active sensors. In this work, the major property is to get rid of the redundant sensors in high-density WSNs and putting them in sleep mode. In addition, a smaller number of active sensors is chosen so as to ensure the full area is k-covered, and all events appearing in that area can be precisely and timely detected. This algorithm minimizes the total energy consumption and increases the network lifetime. The Distributed Adaptive Sleep Scheduling Algorithm (DASSA) \cite{ref127} does not require location information of sensors while maintaining connectivity and satisfying a user-defined coverage target. In DASSA, nodes use 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.
A graph theoretical framework for connectivity-based area coverage with configurable coverage granularity is proposed~\cite{ref149}. A new coverage criterion and scheduling approach is proposed based on cycle partition. This method is able to build a sparse coverage set in distributed way by means of only connectivity information. This work only considers that the communication range of the sensor is two times smaller than the sensing one. Shibo et al.~\cite{ref137} express the area coverage problem as a minimum weight submodular set cover problem and propose 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. The authors in \cite{ref160} design an energy-efficient approach to area coverage problems by transforming the area coverage problem to the target coverage problem taking into account the intersection points among disks of sensors nodes or between disc of sensor nodes and boundaries. They propose two mechanisms for the converted target coverage problems to produce cover sets covering the sensing
field completely. Simulations results show that this approach can prolong the lifetime of the network compared with other works.
\label{gaf1}
\end{figure}
-For two adjacent squares grids, (for example, A and B in figure~\ref{gaf1}) all sensor nodes inside A can communicate with sensor nodes inside B and vice versa. Therefore, all the sensor nodes are equivalent from the point of view the routing. The size of the fixed grid is based on the radio communication range $R_c$. It is supposed that the fixed grid is square with $r$ units on a side as shown in figure~\ref{gaf1}. The distance between the farthest sensor nodes in two adjacent squares, such as B and C in figure~\ref{gaf1}, should not be greater than the radio communication range $R_c$. For instance, the sensor node \textbf{2} of grid B can communicate with the sensor node \textbf{5} of square grid C. Thus,
+For two adjacent squares grids, (for example, A and B in Figure~\ref{gaf1}) all sensor nodes inside A can communicate with sensor nodes inside B and vice versa. Therefore, all the sensor nodes are equivalent from the point of view the routing. The size of the fixed grid is based on the radio communication range $R_c$. It is supposed that the fixed grid is square with $r$ units on a side as shown in Figure~\ref{gaf1}. The distance between the farthest sensor nodes in two adjacent squares, such as B and C in Figure~\ref{gaf1}, should not be greater than the radio communication range $R_c$. For instance, the sensor node \textbf{2} of grid B can communicate with the sensor node \textbf{5} of square grid C. Thus,
\begin{eqnarray}
DESK is a novel distributed heuristic to ensure that the energy consumption among the sensors is balanced and the lifetime maximized while the coverage requirement is satisfied~\cite{DESK}. This heuristic works in rounds, it requires only one-hop neighbor information, and each sensor decides its status (Active or Sleep) based on the perimeter coverage model from~\cite{ref133}.
%DESK is based on the result from \cite{ref133}.
-In DESK \cite{ref133}, the whole area is K-covered if and only if the perimeters of all sensors are K-covered. The coverage level of a sensor $s_i$ is determined by calculating the angle corresponding to the arc that each of its neighbors covers its perimeter. Figure~\ref{figp}~(a) illuminates such arcs whilst Figure~\ref{figp}~(b) shows the angles corresponding with those arcs in the range [0,2$ \pi $]. According to figure~\ref{figp}~(a) and (b), the coverage level of sensor $s_i$ can be calculated as follows.
+In DESK \cite{ref133}, the whole area is K-covered if and only if the perimeters of all sensors are K-covered. The coverage level of a sensor $s_i$ is determined by calculating the angle corresponding to the arc that each of its neighbors covers its perimeter. Figure~\ref{figp}~(a) illuminates such arcs whilst Figure~\ref{figp}~(b) shows the angles corresponding with those arcs in the range [0,2$ \pi $]. According to Figure~\ref{figp}~(a) and (b), the coverage level of sensor $s_i$ can be calculated as follows.
%via traversing the range from 0 to 2$ \pi $.
For each sensor $s_j$ such that $d(s_i,s_j)$ $<$ $2R_s$, we calculate the angle of $s_i$'s arc, denoted by [$\alpha_{j,L}$, $\alpha_{j,R}$], which is perimeter covered by $s_j$, where $\alpha= arccos(d(s_i, s_j)/2R_s)$ and $d(s_i,s_j)$ is the Euclidean distance between $s_i$ and $s_j$. After that, we locate the points $\alpha_{j,L}$ and $\alpha_{j,R}$ of each neighboring sensor $s_j$ of $s_i$ on the line segment $[0, 2\pi]$. These points are sorted in ascending order into a list L. We traverse the line segment from 0 to $2\pi$ by visiting each element in the sorted list L from the left to the right and determine the perimeter coverage of $s_i$. Whenever an element $\alpha_{j,L}$ is traversed, the level of perimeter coverage should be increased by one. Whenever an element $\alpha_{j,R}$ is traversed, the level of perimeter coverage should be decreased by one.
\multicolumn{2}{c}{\footnotesize Coverage Approach} & \mcrot{1}{l}{50}{\footnotesize Distributed} & \mcrot{1}{l}{50}{\footnotesize Centralized} & \mcrot{1}{l}{50}{ \footnotesize Area coverage} & \mcrot{1}{l}{50}{\footnotesize Target coverage} & \mcrot{1}{l}{50}{\footnotesize k-coverage} & \mcrot{1}{l}{50}{\footnotesize Heterogeneous nodes}& \mcrot{1}{l}{50}{\footnotesize Homogeneous nodes} & \mcrot{1}{l}{50}{\footnotesize Disjoint sets} & \mcrot{1}{l}{50}{\footnotesize Non-Disjoint sets} & \mcrot{1}{l}{50}{\footnotesize SET K-COVER } & \mcrot{1}{l}{50}{\footnotesize Work in Rounds or Periods} & \mcrot{1}{l}{50}{\footnotesize Adjustable Radius} \\
\cmidrule[1pt]{2-14}
+& \tiny J. M. Bahi et al. (2008)~\cite{ref236,ref237} & \OK & & \OK & & & & \OK & \OK & & & & &\\
%& \tiny Z. Abrams et al. (2004)~\cite{ref114} & \OK &\OK & \OK & & & &\OK & \OK & & \OK & & &\\
& \tiny X. Deng et al. (2005)~\cite{ref133} & \OK & & \OK & & \OK & & \OK & & \OK & & & &\\
-&\textbf{\textcolor{red}{ \tiny DiLCO Protocol (2014)}} & \textbf{\textcolor{red}{\OK}} & & \textbf{\textcolor{red}{\OK}} & & & \textbf{\textcolor{red}{\OK}} & \textbf{\textcolor{red}{\OK}} & & \textbf{\textcolor{red}{\OK}} & &\textbf{\textcolor{red}{\OK}} & & \\
+&\textbf{\textcolor{red}{ \tiny DiLCO Protocol (2015)}} & \textbf{\textcolor{red}{\OK}} & & \textbf{\textcolor{red}{\OK}} & & & \textbf{\textcolor{red}{\OK}} & \textbf{\textcolor{red}{\OK}} & & \textbf{\textcolor{red}{\OK}} & &\textbf{\textcolor{red}{\OK}} & & \\
-&\textbf{\textcolor{red}{ \tiny MuDiLCO Protocol (2014)}} & \textbf{\textcolor{red}{\OK}} & & \textbf{\textcolor{red}{\OK}} & & & \textbf{\textcolor{red}{\OK}} & \textbf{\textcolor{red}{\OK}} & & \textbf{\textcolor{red}{\OK}} & \textbf{\textcolor{red}{\OK}} &\textbf{\textcolor{red}{\OK}} & & \\
+&\textbf{\textcolor{red}{ \tiny MuDiLCO Protocol (2015)}} & \textbf{\textcolor{red}{\OK}} & & \textbf{\textcolor{red}{\OK}} & & & \textbf{\textcolor{red}{\OK}} & \textbf{\textcolor{red}{\OK}} & & \textbf{\textcolor{red}{\OK}} & \textbf{\textcolor{red}{\OK}} &\textbf{\textcolor{red}{\OK}} & & \\
&\textbf{\textcolor{red}{ \tiny PeCO Protocol (2015)}} & \textbf{\textcolor{red}{\OK}} & & \textbf{\textcolor{red}{\OK}} & & & \textbf{\textcolor{red}{\OK}} & \textbf{\textcolor{red}{\OK}} & & \textbf{\textcolor{red}{\OK}} & &\textbf{\textcolor{red}{\OK}} & & \\
-%Many coverage algorithms for maintaining the coverage and improving the network lifetime in WSNs were proposed. On one hand, the centralized coverage algorithms provide optimal or near optimal solution with low computation power but they deplete the battery power due to the communication overhead, as well as they are not scalable for large size networks. On the other hand, the distributed coverage algorithms provide a lower quality solution in comparison with centralized approaches and consume more power for computation but they are reliable, scalable, and provide low communication overhead on the WSNs.
- %none of them ensure the coverage for the sensing field with optimal minimum number of active sensor nodes, and for a long time as possible. In full centralized algorithms, the 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. Therefore, the full centralized approaches are not a good candidate to be used especially in large WSNs. Whilst, a fully distributed algorithms can not give optimal solutions because these 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
-
-
-% Several centralized approaches have been demonstrated, where they are concentrated on modeling the coverage problem and provide the maximum cover set so as to extend the network lifetime. The proposed algorithms are executed in a central node and based on global information. The central node transmits the resulted schedule to other nodes in the network. Even if the centralized algorithms have been produced optimal or near optimal solutions, It seems to be difficult and unpractical to apply the full centralized approaches in WSNs. On the other hand, many distributed algorithms have been described. These approaches seem to be more realistic to be used in WSNs from point of view of designer, but they can not assure optimal or near optimal solutions so as to extend the network lifetime as long time as possible.
