The choice of non-disjoint or disjoint cover sets (sensors participate or not in many cover sets), coverage type ( area, target, or barrier), coverage ratio, coverage degree (how many sensors are required to cover a target or an area) can be added to the above list.
-Once a sensor nodes are deployed, a coverage algorithm is run to schedule the sensor nodes into cover sets so as to maintain sufficient coverage in the area of interest and extend the network lifetime. The WSN applications require (complete or partial) area coverage and complete target coverage. Many centralized algorithms and distributed algorithms for activity scheduling have been proposed in the literature, and based on different assumptions and objectives. In centralized algorithms, a central controller makes all decisions and distributes the results to sensor nodes. A distributed algorithms, on the other hand, the decision process is localized in each individual sensor node, and only information from neighboring nodes are used for the activity decision. Compared to centralized algorithms, distributed algorithms reduce the energy consumption required for radio communication and detection accuracy whilst increase the energy consumption for computation. Overall, distributed algorithms are more suitable for large-scale networks, but it can not give optimal (or near optimal) solution based only on local information. Several algorithms to retain the coverage and maximize the network lifetime were proposed in~\cite{ref113,ref153,ref103,ref105}.
+Once a sensor nodes are deployed, a coverage algorithm is run to schedule the sensor nodes into cover sets so as to maintain sufficient coverage in the area of interest and extend the network lifetime. The WSN applications require (complete or partial) area coverage and complete target coverage. Many centralized algorithms and distributed algorithms for activity scheduling have been proposed in the literature, and based on different assumptions and objectives. In centralized algorithms, a central controller makes all decisions and distributes the results to sensor nodes. A distributed algorithms, on the other hand, the decision process is localized in each individual sensor node, and only information from neighboring nodes are used for the activity decision. Compared to centralized algorithms, distributed algorithms reduce the energy consumption required for radio communication and detection accuracy whilst increase the energy consumption for computation. Overall, distributed algorithms are more suitable for large-scale networks, but it can not give optimal (or near optimal) solution based only on local information. Several algorithms to retain the coverage and maximize the network lifetime were proposed in~\cite{ref113,ref153,ref103,ref105}. Table~\ref{Table1:ch2} summarized the main characteristics of some coverage approaches in previous literatures.
\subsection{Centralized Algorithms}
A graph theoretical framework for connectivity-based coverage with configurable coverage granularity was proposed~\cite{ref149}. A new coverage criterion and scheduling approach is proposed based on cycle partition. This method is capable of build a sparse coverage set in distributed way by means of only connectivity information. This work considers only the communication range of the sensor is smaller two times the sensing range of sensor.
-The works presented in~\cite{ref134,ref135,ref136} focus on coverage-aware, distributed energy-efficient, and distributed clustering methods respectively, which aim at extending the network lifetime, while the coverage is ensured.
+The works presented in~\cite{ref134,ref135,ref136} focus on coverage-aware, distributed energy-efficient, and distributed clustering methods respectively, which aim at extending the network lifetime, while the coverage is ensured.
-More recently, Shibo et al.~\cite{ref137} 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.
+Shibo et al.~\cite{ref137} 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{ref160} authors transform the area coverage problem to the target
+coverage one taking into account the intersection points among disks of sensors
+nodes or between disk of sensor nodes and boundaries.
+
+
+In \cite{ref133} authors prove that if the perimeters of sensors are sufficiently covered it will be the case for the whole area. They 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 neighboring to a sensor and $n$ is the total number of sensors in the network.
In \cite{ref84}, Xu et al. have described 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. Figure~\ref{gaf1} gives an example of fixed square grid in GAF.
\begin{flushleft}
\centering
-\caption{Centralized approaches for coverage problem in literature.}
+\caption{Main characteristics of some coverage approaches in previous literatures.}
\begin{tabular}{@{} cl*{13}c @{}}
& & \multicolumn{10}{c}{Characteristics} \\[2ex]
- & & \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 Energy-Efficient} & \mcrot{1}{l}{50}{\footnotesize Work in Rounds} & \mcrot{1}{l}{50}{\footnotesize Adjustable Radius} \\
+ & & \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} & \mcrot{1}{l}{50}{\footnotesize Adjustable Radius} \\
\cmidrule[1pt]{2-14}
-& \tiny Z. Abrams et. al. (2004) & & & & & & & & & & & & &\\
+& \tiny Z. Abrams et al. (2004)~\cite{ref114} & \OK &\OK & \OK & & & &\OK & \OK & & \OK & & &\\
+
+& \tiny M. Cardei and D. Du (2005)~\cite{ref115} & & \OK & & \OK & & & \OK & \OK & & \OK & & &\\
+
+& \tiny S. Slijepcevic and M. Potkonjak (2001)~\cite{ref116} & & \OK & \OK & & & & \OK & \OK & & \OK & & &\\
+
+& \tiny Manjun and A. K. Pujari (2011)~\cite{ref117} & & \OK & & \OK & & & \OK & & \OK & & & &\\
+
+& \tiny M. Yang and J. Liu (2014)~\cite{ref118} & & \OK & \OK & & & & \OK & & \OK & & & & \\
+
+& \tiny S. Wang et al. (2010)~\cite{ref144} & & \OK & \OK & & & & \OK & & \OK & & \OK & & \\
+
+& \tiny C. Lin et al. (2010)~\cite{ref147} & & \OK & \OK & & & & \OK & & \OK & & & & \\
-& \tiny M. Cardei and D. Du (2005) & & & & & & & & & & & & &\\
+& \tiny S. A. R. Zaidi et al. (2009)~\cite{ref148} & & \OK & \OK & & & & \OK & & \OK & & & & \\
-& \tiny S. Slijepcevic and M. Potkonjak (2001) & & & & & & & & & & & & &\\
+& \tiny Y. Li et al. (2011)~\cite{ref142} & & \OK & \OK & & & \OK & \OK & \OK & & \OK & & \OK &\\
-& \tiny Manjun and A. KPujari (2011) & & & & & & & & & & & & &\\
+& \tiny H. M. Ammari and S. K. Das (2012)~\cite{ref152} & \OK & \OK & \OK & & \OK & & \OK & & \OK & & \OK & &\\
-& \tiny M. Yang and J. Liu (2014) & & & & & & & & & & & & &\\
+& \tiny L. Liu et al. (2010)~\cite{ref150} & & \OK & & \OK & & \OK & & \OK & & \OK & & &\\
-& \tiny S. Wang et. al. (2010) & & & & & & & & & & & & &\\
+& \tiny H. Cheng et al. (2014)~\cite{ref119} & & \OK & \OK & & & & \OK & & \OK & & & &\\
-& \tiny C. Lin et. al. (2010) & & & & & & & & & & & & &\\
+& \tiny M. Rebai et al. (2014)~\cite{ref141} & & \OK & \OK & & & & \OK & & \OK & & & &\\
-& \tiny S. A. R. Zaidi et. al. (2009) & & & & & & & & & & & & &\\
+& \tiny L. Aslanyan et al. (2013)~\cite{ref151} & & \OK & \OK & & & & \OK & & \OK & \OK & \OK & &\\
-& \tiny Y. Li et. al. (2011) & & & & & & & & & & & &\\
+& \tiny X. Liu et al. (2014)~\cite{ref143} & & \OK & \OK & & & & \OK & & \OK & \OK & \OK & &\\
-& \tiny H. M. Ammari and S. K. Das (2012) & & & & & & & & & & & & &\\
+& \tiny F. Castano et al. (2013)~\cite{ref120} & & \OK & & \OK & & & \OK & & \OK & \OK & & &\\
-& \tiny L. Liu et. al. (2010) & & & & & & & & & & & & &\\
+& \tiny A. Rossi et al. (2012)~\cite{ref121} & & \OK & & \OK & & \OK & \OK & & \OK & \OK & & \OK &\\
-& \tiny H. Cheng et. al. (2014) & & & & & & & & & & & & &\\
+& \tiny K. Deschinkel et al. (2012)~\cite{ref122} & & \OK & & \OK & & & \OK & & \OK & \OK & & &\\
-& \tiny M. Rebai et. al. (2014) & & & & & & & & & & & & &\\
-& \tiny L. Aslanyan et. al. (2013) & & & & & & & & & & & & &\\
-& \tiny X. Liu et. al. (2014) & & & & & & & & & & & & &\\
+& \tiny A. Gallais et al. (2008)~\cite{ref123} & \OK & & \OK & & & \OK & \OK & & \OK & & \OK & \OK &\\
-& \tiny F. Castano et. al. (2013) & & & & & & & & & & & & &\\
+& \tiny D. Tian and N. D. Georganas (2002)~\cite{ref124} & \OK & & \OK & & & & \OK & & \OK & & \OK & &\\
-& \tiny A. Rossi et. al. (2012) & & & & & & & & & & & & &\\
+& \tiny F. Ye et al. (2003)~\cite{ref125} & \OK & & \OK & & & & \OK & & \OK & & & &\\
-& \tiny K. Deschinkel et. al. (2012) & & & & & & & & & & & & &\\
+& \tiny H. Zhang and J. C. Hou (2005)~\cite{ref126} & \OK & & \OK & & & & \OK & & \OK & & \OK & &\\
-\rot{\rlap{Some Proposed Coverage Protocols in literature}}
+& \tiny W. B. Heinzelman et al. (2002)~\cite{ref109} & \OK & & \OK & & & & \OK & & \OK & & \OK & &\\
-& \tiny A. Gallais et. al. (2006) & & & & & & & & & & & & &\\
+& \tiny T. Yardibi and E. Karasan (2010)~\cite{ref127} & \OK & & \OK & & & & \OK & & \OK & & \OK & &\\
-& \tiny D. Tian and N. D. Georganas (2002) & & & & & & & & & & & & &\\
+& \tiny S. K. Prasad and A. Dhawan (2007)~\cite{ref128} & \OK & & & \OK & & & \OK & & \OK & & \OK & &\\
-& \tiny F. Ye et. al. (2003) & & & & & & & & & & & & &\\
+& \tiny S. Misra et al. (2011)~\cite{ref129} & \OK & & \OK & & & & \OK & & \OK & & & &\\
-& \tiny H. Zhang and J. C. Hou (2005) & & & & & & & & & & & & &\\
+& \tiny P. Berman et al. (2005)~\cite{ref130} & \OK & \OK & \OK & & & & \OK & & \OK & \OK & &\\
-& \tiny W. B. Heinzelman et. al. (2002) & & & & & & & & & & & & &\\
+& \tiny J. Lu and T. Suda (2003)~\cite{ref131} & \OK & & \OK & & & & \OK & & \OK & & \OK & &\\
-& \tiny T. Yardibi and E. Karasan (2010) & & & & & & & & & & & & &\\
-& \tiny S. K. Prasad and A. Dhawan (2007) & & & & & & & & & & & & &\\
-& \tiny S. Misra et. al. (2011) & & & & & & & & & & & & &\\
+& \tiny J. Cho et al. (2007)~\cite{ref145} & \OK & & \OK & & & & \OK & & \OK & & & &\\
-& \tiny P. Berman et. al. (2005) & & & & & & & & & & & &\\
+& \tiny V. T. Quang and T. Miyoshi (2008)~\cite{ref146} & \OK & & \OK & & \OK & & \OK & & \OK & & \OK & &\\
-& \tiny J. Lu and T. Suda (2003) & & & & & & & & & & & & &\\
+\rot{\rlap{Some Proposed Coverage Protocols in previous literatures}}
-& \tiny J. Cho et. al. (2007) & & & & & & & & & & & & &\\
+& \tiny D. Dong et al. (2012)~\cite{ref149} & \OK & & \OK & & & & \OK & & \OK & & \OK & &\\
-& \tiny V. T. Quang and T. Miyoshi (2008) & & & & & & & & & & & & &\\
+& \tiny B. Wang et al. (2012)~\cite{ref134} & \OK & & \OK & & & & \OK & & \OK & & \OK & &\\
-& \tiny D. Dong et. al. (2012) & & & & & & & & & & & & &\\
+& \tiny Z. Liu et al. (2012)~\cite{ref135} & \OK & & \OK & & & & \OK & & \OK & & \OK & &\\
-& \tiny B. Wang et. al. (2012) & & & & & & & & & & & & &\\
+& \tiny L. Zhang et al. (2013)~\cite{ref136} & \OK & & \OK & & & \OK & \OK & & \OK & & \OK & &\\
-& \tiny Z. Liu et. al. (2012) & & & & & & & & & & & & &\\
+& \tiny S. He et al. (2012)~\cite{ref137} & \OK & \OK & \OK & & & & \OK & & \OK & & & &\\
-& \tiny L. Zhang et. al. (2013) & & & & & & & & & & & & &\\
+& \tiny Y. Xu et al. (2001)~\cite{ref84} & \OK & & \OK & & & & \OK & & \OK & & & &\\
-& \tiny Y. Xu et. al. (2001) & & & & & & & & & & & & &\\
+& \tiny C. Vu et al. (2006)~\cite{ref132} & \OK & & \OK & & \OK & & \OK & & \OK & & \OK & &\\
+
+& \tiny X. Deng et al. (2012)~\cite{ref160} & \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}{ \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}{ \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}{ \tiny LiCO Protocol (2014)}} & \textbf{\textcolor{red}{\OK}} & & \textbf{\textcolor{red}{\OK}} & & & \textbf{\textcolor{red}{\OK}} & \textbf{\textcolor{red}{\OK}} & & & &\textbf{\textcolor{red}{\OK}} & & \\
\end{flushleft}
-\label{table:1}
+\label{Table1:ch2}
\end{table}
+
\section{Conclusion}
\label{ch2:sec:05}
This chapter has been described some coverage problems proposed in the literature, and their assumptions and proposed solutions.
The coverage problem has been considered an essential requirement for many applications in WSNs, because better
-coverage of an area of interest provides better sensing measurements of the physical phenomenon. So, there are many extensive research have been focused on those problem. these problems aim at designing mechanisms that efficiently manage or schedule the sensors after deployment, since sensor nodes have a limited battery life. 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.
+coverage of an area of interest provides better sensing measurements of the physical phenomenon. So, there are many extensive researches have been focused on those problem. These researches have been aiming at designing mechanisms that efficiently manage or schedule the sensors after deployment, since sensor nodes have a limited battery life.
+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. 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
+
+
+
+% 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.
+
+
+
