## 2 Cluster Head Selection
### Assisted Schemes
#### 2.2.1.1 Fair Placement of CHs  
To address the shortcomings of LEACH concerning the placement and number of CH nodes, a centralized version of LEACH called LEACH-Centralized (LEACH-C) was presented by [PERSON] _et al_. in [PERSON] _et al_. (2013). In the setup-phase of LEACH-C, each node transmits its location and energy level to the BS, and the average energy level of the network is calculated by the BS and nodes having a remaining energy level below this average cannot be CHs for that round. The initial stages in [PERSON] _et al_. (2013) are also is the same as LEACH-C, but after the initial cluster formation phase, the clusters are steady and the CH role rotates among the nodes with remaining energy over the average energy of the nodes within the cluster. The centralized selection of CHs ensures that energy load is evenly distributed among all the nodes by selecting a predefined number of CHs and dividing the network into optimum equal size clusters.  
Due to the fact that the sensor nodes spend a great proportion of their overall energy in communications, the K-Means Like Minimum Mean Distance Algorithm (KMMDA) proposed in [PERSON] _et al_. (2013) improves the network lifetime by using the K-means algorithm [PERSON] _et al_. (2013) to calculate the minimum mean distance of the nodes as a parameter in CH selection phase. Like other centralized algorithms, the first step in selection of CHs is to transmit the necessary characteristic information of nodes to the BS, while this information, in KMMDA, is the position of the nodes, which is determined by GPS receivers. In the next step, the BS with its high processing capabilities and unlimited source of energy calculates the distances between all the sensor nodes, and the mean distance to all other sensor nodes for each sensor node; and thus the nodes with minimum mean distance are selected for the CH role. The same algorithm is also proposed in [PERSON] _et al_. (2013) that the BS, in addition to finding the mean distance of the nodes, determines zone areas with the diameter less than a threshold value in which two or more nodes are located. Due to sensing area overlap, only one node in active state in each typical zone is sufficient to sense the environment and other nodes within the zone are scheduled by the BS to sleep in the current round. The sensing node duty rotates among other nodes for the subsequent rounds.  
The paper [PERSON] _et al_. (2013) also selects CHs according to the mean distance of the nodes from each other. However, the algorithm first divides the network area into several equal parts based on their location information and distances of the nodes, and then the BS calculates the probability of the nodes for CH role according to the ratio of remained energy and the mean distance of the node from other cluster members. Instead of using localizing devices, the paper proposes to use two nodes with determined position and sink as reference points to locate the sensor nodes within the field. After formation of the network, each node broadcasts a signal and two selected nodes calculate the distances of the nodes with regard of the received signal strength and transmit the gathered information to the BS. By updating the table of distances generated by the BS with the received information from two selected nodes, the BS can calculate the distance of every node from others.  
The paper [46] concentrates on the selection of CHs based on the traffic density of nodes. In this scheme, BS receives Hello packets from nodes and computes the traffic of each node using a trajectory-clustering algorithm. The nodes participating in the data relaying process towards the BS are considered as CHs. Then the BS splits the network into equal size clusters and broadcasts a message including the selected CHs and their cluster members to all nodes.