## 2 WSN Basic Concepts and Preliminaries  
### Preliminary Definitions  
There are several types of coverage and connectivity problems in WSN, so depending on the application requirements, we distinguish: area coverage where the goal is to cover an area, point coverage that aims to monitor only a set of points with known locations, and path or barrier coverage, where a barrier must be fully covered to detect any intruders that attempt to penetrate a protected area. An area is fully covered only if every point of the RoI is within the sensing range of at least one sensor node. The network is said to be connected only when every sensor can reach and transmit data to the desired destination. Each and every WSN application requires a certain degree of coverage and connectivity. An area is k-coverage if each physical point in the area is covered by at least k (k \(\geq\) 1) active sensor nodes. The term k-connectivity (k \(\geq\) 1) means that there are at least k disjoint paths between any pair of nodes in the network [8; 16].  
Based on the type of nodes, WSN can be heterogeneous or homogeneous. Heterogeneous WSN contains sensor nodes with different abilities such as battery energy and sensing range, while in homogeneous WSN all nodes are similar [6; 9]. Sensor nodes can be static or mobile. Static nodes are fixed and can't move after deployment, while the mobile nodes possess all the features of the fixed nodes, and can relocate themselves after deployment [6; 17]. Deployment is either deterministic or random. Deterministic solvers can guarantee the best possible sensor placement is found only for a small sized WSN, but they have difficulty with large-scale network cases. By contrast, heuristic solvers cannot generally guarantee the optimal solution but are known to quickly find a near-optimal solution [18]. In [10], the authors developed a classification scheme for sensor node deployment strategies. The primary classification of static deployments is based on non-corona-based and corona-based deployments. Further classification is based on the desired objectives. The first category non-corona based sensor node deployment strategies are categorized as follows:  
* A random-uniform deployment, where sensor nodes are uniformly distributed;
* Engineered-uniform deployment strategy where the sensor nodes are distributed in an engineered-uniform fashion;
* Random-Gaussian deployment strategy considers an incremental deployment model such that the number of sensor nodes keeps on increasing near the sink vicinity.  
In a corona based sensor node deployment, the sensor nodes are arranged in a circular fashion of radius r with a static sink positioned at the center. The classification of each corona based deployment strategy is based on the required objectives.  
* Engineered Gaussian deployment strategy, where the density of sensor nodes in the first corona is higher than the other coronas, treats the energy hole problem;
* In the second Engineered corona-based sensor node deployment strategy, the sensor node distribution should achieve the maximum coverage using the minimum number of sensor nodes;
* For optimized, balanced energy consumption, the third and the fourth categories use, respectively, arithmetic/geometric proportion, to find the optimum number of nodes in Corona;
* Finally, the engineered corona-based sensor nodes deployment strategy, using relay nodes for transmission that aim to reduce redundant data transmission.