+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. This chapter concentrates only on area coverage and target coverage problems because it is possible to transform the area coverage problem to target ( or point) coverage problem and vice versa. We have excluded the barrier coverage problem from this discussion about the coverage problems because it is outside the scope of this dissertation. We have focused mainly on the area coverage problem. Therefore, we represent the sensing area of each sensor node in the sensing field as a set of primary points and then achieving full area coverage by covering all the points in the sensing field. The ultimate goal of the area coverage problem is to choose the minimum number of sensor nodes to cover the whole sensing region and prolonging the lifetime of the WSN.
+
+Many centralized and distributed coverage 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. The centralized algorithms have the advantage of requiring very low processing power from the sensor nodes which have usually limited processing capabilities. Indeed, the exchange of packets in large WSNs may consume a considerable amount
+of energy in a centralized approach compared to a distributed one. Moreover, centralized approaches usually suffer from the scalability and reliability problems, making them less competitive as the network size increases.
+
+In a distributed algorithms, on the other hand, the decision process is localized in each individual sensor node, and the 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. Moreover, a recent study conducted in \cite{ref226} concludes that there is a threshold in terms of network size to switch from a distributed to a centralized algorithm. Table~\ref{Table0:ch2} shows a comparison between the centralized coverage algorithms and the distributed coverage algorithms.
+
+
+\begin{table}[h]
+\caption{Centralized Coverage Algorithms vs Distributed Coverage Algorithms}
+\begin{center}
+\begin{tabular}{ |p{3cm}|p{5cm}|p{5cm}|}
+\hline
+
+\textbf{\begin{center} Characteristics \end{center}} & \textbf{\begin{center} Centralized Coverage Algorithms \end{center}} & \textbf{\begin{center} Distributed Coverage Algorithms \end{center}}\\ \hline
+
+\textbf{\begin{center} Computation \end{center}} & Require low processing power where the algorithm is executed only in one elected node. & Require large processing power due to execution the algorithm in every node in WSN. \\ \hline
+
+\textbf{\begin{center} Communication \end{center}} & Require large power consumption for communication. & Require low power consumption for communication. \\ \hline
+
+\textbf{\begin{center} Decision \end{center}} & Ensure optimal (or near-optimal) solution. & Can not ensure optimal (or near-optimal) solution.\\ \hline
+
+\textbf{\begin{center} Redundancy \end{center}} & Provide less redundant active sensor nodes during monitoring the sensing field. & Provide more redundant active sensor nodes during monitoring the sensing field.\\ \hline
+
+\textbf{\begin{center} Energy Consumption \end{center}} & Energy consumption is large especially when the network size and/or density increase. & Energy consumption is low because they have lower communication cost. \\ \hline
+
+\textbf{\begin{center} Scalability \end{center}} & Scalable only with dividing the sensing field into smaller subregions. & More scalable for large networks. \\ \hline
+
+\textbf{\begin{center} Reliability \end{center}} & Less robust against sensor failure. & More robust against sensor failure. \\ \hline
+
+\end{tabular}
+\end{center}
+\label{Table0:ch2}
+\end{table}
+
+
+
+In this dissertation, the sensing field is divided into smaller subregions using divide-and-conquer method. The division continues until the distance between each two sensors inside the subregion is 3 or 2 hops maximum. This division have made our protocols more scalable for the large networks, less energy consumption for communication, less processing power for decision, more reliable against network failure, and a longer lifetime. Our proposed protocols are distributed on the sensor nodes of the subregions. The protocols in each subregion work in independent and simultaneous way with the protocols in the other subregions. If the network disconnected in one subregion, it will not effect on the other subregions of the sensing field. There is no a fixed sensor node in the subregion execute the optimization algorithm. Each period of the network lifetime, the sensor nodes in the subregion cooperate in order to select a sensor node according to a predefined priority metrics to execute the optimization algorithm. The local optimal schedule resulted from the optimization algorithm is applied within the subregion. The elected sensor node sends a packet to every sensor within the subregion to inform him to stay active or sleep during this period. Each optimization algorithm in a subregion provides locally optimal solution, so the solution for all the sensing field is near-optimal.
+
+Several algorithms to retain the coverage and maximize the network lifetime were proposed in~\cite{ref113,ref101,ref103,ref105}. Table~\ref{Table1:ch2} summarized the main characteristics of some coverage approaches in previous literatures.
+
+
+\section{Centralized Algorithms}
+\label{ch2:sec:02}
+The major idea of most centralized algorithms is to divide/organize the sensors into a suitable number of cover sets, where each set completely covers an interest region and to activate these cover sets successively. The centralized algorithms always provide optimal or near-optimal solution since the algorithm has a global view of the whole network. Energy-efficient centralized approaches differ according to several criteria \cite{ref113}, such as the coverage objective (target coverage or area coverage), the node deployment method (random or deterministic), and the heterogeneity of sensor nodes (common sensing range, common battery lifetime).
+
+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~\cite{ref114,ref115,ref116}. For instance, Slijepcevic and Potkonjak \cite{ref116} propose 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. M. Cardei et al.~\cite{ref227}, have suggested a graph coloring technique to achieve energy savings by organizing the sensor nodes into a maximum number of disjoint dominating sets, which are activated successively. They have defined the maximum disjoint dominating sets problem and they have produced a heuristic that computes the disjoint cover sets so as to monitor the area of interest. The dominating sets do not guarantee the coverage of the whole region of interest. Abrams et al.~\cite{ref114} 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{ref116} and the generated cover sets do not provide complete coverage of the monitoring zone.
+
+
+The authors in~\cite{ref115} proposed a heuristic to compute the disjoint set covers (DSC). In order to compute the maximum number of covers, they first transform DSC into a maximum-flow problem, which is then formulated as a mixed integer programming problem (MIP). Based on the solution of the MIP, they design a heuristic to compute the final number of covers. The results show a slight performance improvement in terms of the number of produced DSC in comparison to~\cite{ref116}, but it incurs higher execution time due to the complexity of the mixed integer programming solving. Zorbas et al. \cite{ref228} presented B\{GOP\}, a centralized target coverage algorithm introducing sensor candidate categorization depending on their coverage status and the notion of critical target to call targets that are associated with a small number of sensors. The total running time of their heuristic is $0(m n^2)$ where
+$n$ is the number of sensors and $m$ the number of targets. Compared to algorithm's results of Slijepcevic and Potkonjak \cite{ref116}, their heuristic produces more cover sets with a slight growth rate in execution time. More recently, Deschinkel and Hakem \cite{229} introduced a near-optimal heuristic algorithm for solving the target coverage problem in WSN. The sensor nodes are organized into disjoint cover sets by the resolution an integer programming problem. Each cover set is capable of monitoring all the targets of the region of interest. Those covers sets are scheduled periodically. Their algorithm able to construct the different cover sets in parallel. The results show that their algorithm achieves near-optimal solutions compared to the optimal ones obtained by the exact method.
