## 2 Cluster Head Selection
### Assisted Schemes
#### 2.2.2 Energy Expenditure Mitigation in Re-Clustering  
Although re-clustering is proposed to increase network lifetime by distributing the heavy load of CH roles among the sensor nodes evenly, re-clustering itself is an energy consuming procedure, which imposes extra transmission of control messages on the network. Re-clustering also hinders the real-time transmission of data at initial stages of each round. In this respect, some solutions are proposed in papers [52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62] to mitigate the issues pertaining to re-clustering while exploiting the positive aspects of round-based clustering schemes. In [52], a selective CH selection scheme is proposed to minimize the energy dissipation by reducing the frequent communication of conserved nodes in previous cluster with assistance of the current CH. The paper highlights the idea that a great proportions of the nodes around the previous CH have a high possibility of belonging to the same cluster formed by the new CH, therefore, the unchanged nodes of the former cluster can be eliminated from the setup phase and set to sleep mode instead, while only newly added nodes exchange necessary control packets. To select effective CH, besides two common factors of distance and residual energy, the paper proposes to use two other factors of density and transmission cost (_cost_). Both factors are calculated by the number of neighbouring nodes (_Node neighbour_) in the same cluster and the number of foreign nodes (_Node foreign_) located in other clusters, as presented in Equations (12) and (13):  
\[\text{Density}=\frac{Node\,neighbour}{Node\,neighbour\,+\,Node\, foreign} \tag{12}\]  
Figure 4: Selection of the next CHs towards balancing the cluster size. \[Cost = \frac{1}{\alpha_{c}\,.Density +(1-\alpha_{c}\,)\cdot\frac{E_{r}}{E_{\max}}} \tag{13}\]  
After selection of new CH based on the aforementioned factors, the current CH provides the information of the selected CH to the cluster members and each node determines its status using this information to learn whether its cluster is changed or not. The papers [53; 54; 55; 56] address the issue by eliminating dispensable re-clustering rounds by replacing the time-based CH role rotation in LEACH algorithm with an energy-threshold-triggering scheme. LEACH-ET [53] triggers the re-clustering phase on a network scale whenever any of CHs' energy levels drops below the predefined threshold level. The algorithm presumes that each node calculates and transmits \(n\) bits with \(P\) probability in every round and thus the ET is calculated as _n.p.E.CH_, where ECH is the energy dissipation rate of the CH per bit. The BS calculates and broadcasts the ET in initial round and each node records the value, accordingly. [PERSON] _et al._ in [54] also propose using of energy threshold for triggering the re-clustering phase, but only CHs having remaining energy level below the threshold value participate in the CH selection process and other CHs ignore this stage and continue as CH for the subsequent round. Therefore, a great proportion of energy expenditure of CHs having energy level above the threshold level is saved. Instead of demolishing all the constructed clusters, the authors of [55] propose that after the initial cluster construction phase, the cluster boundaries remain constant for a predefined number of rounds, but instead, the responsibility of CH role keeps rotating randomly among the nodes within the cluster until the next scheduled re-clustering round. In RRCH [56] and LEACH-F [23] similar solutions are used that distribute the CH role among the nodes of each cluster. Instead of random rotation of the CH role, the rotation sequence in RRCH and LEACH-F is coordinated either by the CHs or by the BS, respectively. In this way, the energy consumption is balanced among the sensor nodes and the coordinator can select the next round CH based on the energy metrics or any other criteria desired by the user.