%%%The work in~\cite{ref144} addresses the area coverage problem by proposing a Geometrically based Activity Scheduling scheme, named GAS, to fully cover the area of interest in WSNs. The authors deal with a small area, called target area coverage, which can be monitored by a single sensor instead of area coverage, which focuses on a large area that should be monitored by many sensors cooperatively. They explain that GAS is capable to monitor the target area by using the fewest number of sensors and it can produce as many cover sets as possible. A novel area coverage method to divide the sensors called Node Coverage Grouping (NCG) is suggested~\cite{ref147}. The sensors in the connectivity group are within sensing range of each other and the data collected by those in the same group are supposed to be similar. They prove that dividing N sensors via NCG into connectivity groups is an NP-hard problem. So, a heuristic algorithm of NCG with time complexity of $O(n^3)$ is proposed. For some applications, such as monitoring an ecosystem with extremely diversified environment, it might be a premature assumption that sensors near to each other sense similar data.
The problem of k-coverage over the area of interest in WSNs is addressed in~\cite{ref152}. It is mathematically formulated and the spatial sensor density for full k-coverage is determined. The relation between the communication range and the sensing range is constructed by this work to retain the k-coverage and connectivity in WSN. After that, four configuration protocols are proposed for treating the k-coverage in WSNs. Simulation results show that their protocols outperform an existing distributed k-coverage configuration protocol. The work presented in~\cite{ref151} solves the area coverage and connectivity problem in sensor networks in an integrated way. The network lifetime is divided into a fixed number of rounds. A coverage bitmap of sensors of the domain is generated in each round and based on this bitmap, it is decided which sensors stay active or go to sleep. They check the connection of the graph via laplacian of the adjacency graph of active sensors in each round. They define the connected coverage problem as an optimization problem and a centralized genetic algorithm is used to find the solution. Recent studies show an increasing interest in the use of exact schemes to solve optimization problems in WSNs \cite{ref230,ref231,ref121,ref122,ref120}. Column Generation (CG) has been widely used to address different versions of Maximum-network Lifetime Problem (MLP). CG decomposes the problem into a Restricted Master Problem (RMP) and a Pricing Subproblem (PS). The former maximizes lifetime using an incomplete set of columns and the latter is used to identify new profitable columns.
%%%A. Rossi et al.~\cite{ref121} introduce an efficient implementation of a genetic algorithm based on CG to extend the lifetime and maximize target coverage in wireless sensor networks under bandwidth constraints. The authors show that the use of metaheuristic methods to solve PS in the context of CG allows to obtain optimal solutions quite fast and to produce high-quality solutions when the algorithm is stopped before returning an optimal solution. More recently,
%%%The work in~\cite{ref144} addresses the area coverage problem by proposing a Geometrically based Activity Scheduling scheme, named GAS, to fully cover the area of interest in WSNs. The authors deal with a small area, called target area coverage, which can be monitored by a single sensor instead of area coverage, which focuses on a large area that should be monitored by many sensors cooperatively. They explain that GAS is capable to monitor the target area by using the fewest number of sensors and it can produce as many cover sets as possible. A novel area coverage method to divide the sensors called Node Coverage Grouping (NCG) is suggested~\cite{ref147}. The sensors in the connectivity group are within sensing range of each other and the data collected by those in the same group are supposed to be similar. They prove that dividing N sensors via NCG into connectivity groups is an NP-hard problem. So, a heuristic algorithm of NCG with time complexity of $O(n^3)$ is proposed. For some applications, such as monitoring an ecosystem with extremely diversified environment, it might be a premature assumption that sensors near to each other sense similar data.
The problem of k-coverage over the area of interest in WSNs is addressed in~\cite{ref152}. It is mathematically formulated and the spatial sensor density for full k-coverage is determined. The relation between the communication range and the sensing range is constructed by this work to retain the k-coverage and connectivity in WSN. After that, four configuration protocols are proposed for treating the k-coverage in WSNs. Simulation results show that their protocols outperform an existing distributed k-coverage configuration protocol. The work presented in~\cite{ref151} solves the area coverage and connectivity problem in sensor networks in an integrated way. The network lifetime is divided into a fixed number of rounds. A coverage bitmap of sensors of the domain is generated in each round and based on this bitmap, it is decided which sensors stay active or go to sleep. They check the connection of the graph via laplacian of the adjacency graph of active sensors in each round. They define the connected coverage problem as an optimization problem and a centralized genetic algorithm is used to find the solution. Recent studies show an increasing interest in the use of exact schemes to solve optimization problems in WSNs \cite{ref230,ref231,ref121,ref122,ref120}. Column Generation (CG) has been widely used to address different versions of Maximum-network Lifetime Problem (MLP). CG decomposes the problem into a Restricted Master Problem (RMP) and a Pricing Subproblem (PS). The former maximizes lifetime using an incomplete set of columns and the latter is used to identify new profitable columns.
%%%A. Rossi et al.~\cite{ref121} introduce an efficient implementation of a genetic algorithm based on CG to extend the lifetime and maximize target coverage in wireless sensor networks under bandwidth constraints. The authors show that the use of metaheuristic methods to solve PS in the context of CG allows to obtain optimal solutions quite fast and to produce high-quality solutions when the algorithm is stopped before returning an optimal solution. More recently,