# An Energy-Efficient Mobile Sink-Based Unequal Clustering Mechanism for WSNs
## 2 Related Works  
As mentioned in the previous section, grouping the nodes into optimal clusters is known as an NP-hard problem [5]. Consequently, one effective method for optimizing the cluster size is to use optimization algorithms. [PERSON] et al. [20] used Particle Swarm Optimization (PSO) in their proposedprotocol in order to determine the optimal cluster size by minimizing the distance between member nodes and CHs and decreasing the energy consumption of the network. [PERSON] [21] used GA to create optimal clusters for energy efficiency in WSNs. [PERSON] [22] proposed a self-clustering method for heterogeneous WSNs using a GA that optimized the network lifetime. In addition, there are other methods which adjust cluster size with different objectives. The designers of the LEACH protocol [23] have obtained an efficient cluster size so that the remarkable amount of energy can be saved. However, their results only determine an interval to which the optimal cluster size belongs. It can be shown that in many network configurations, the analytical results give a long interval and therefore, the optimal number of clusters must be found through simulations for all the numbers that belonged to the aforesaid interval [24]. An unequal cluster size (UCS) was proposed by [PERSON] and [PERSON] [25] in order to balance the energy expenditure among CHs. UCS is the first unequal clustering model in a wireless sensor network to increase network life span, however, this model is not applicable to a larger scale WSN [1]. In [24] a mathematical framework is provided in order to obtain the optimal cluster size which can improve the network lifespan by decreasing the total energy expenditure of the network. The Distance-based Segmentation (DBS) protocol [26] provides a parallel version of the LEACH algorithm to solve the energy imbalance problem which occurs in LEACH. DBS is a cluster-based protocol that divides the network into equal area rings or coronas and applies different clustering rules to each segment to reduce the energy consumption and balance the energy consumption among sensors. In [27], the authors showed that the CH election manner can affect the size of clusters. Therefore, they tried to find the optimal number of clusters by choosing optimal CHs. [PERSON] et al. in [28] attempted to balance the energy consumption of CHs by assigning the larger cluster sizes to CHs that have to forward fewer data in comparison with others. In [29], the authors proposed a cluster-based cooperative spectrum sensing algorithm to save energy consumption. CHs are selected based on a sensor's location with respect to a fusion center (FC), its residual energy, and its signal-to-noise ratio (SNR). An adaptive fuzzy clustering protocol (called LEACH-SF) is proposed in [30] to achieve energy efficiency. They used a fuzzy c-means algorithm to solve the unbalanced clusters problem, and then CHs are elected based on the residual energy of nodes, the distance from the BS, and the distance from the cluster centroid. They used the artificial bee colony algorithm to adjust the fuzzy rules of their proposed protocol. The objective function of the algorithm is defined to enhance the network lifetime, based on the application specifications. In [31] the authors applied a clustering technique on a corona-based WSN. In their model, the cluster size varies with the ring index and the size of clusters is equal in each ring. Their goal is to improve the network lifetime by achieving an energy balance among CHs and decreasing the total energy consumption of the network. However, in their model, the size of clusters is small and this property contrary to allowing the scalability of the network [32]. One goal of clustering is scalability of network management, however, if the cluster size is too small, this goal will not be achieved. On the other hand, if the size of clusters is too large, the intra-cluster energy consumption will increase. [PERSON] et al.