# A New Centralized Clustering Algorithm for Wireless Sensor Networks
## 4 Results  
The validity of the skip setting is verified with three different configurations related to BS positions corresponding to the scenarios described in the previous section. With these configurations, the algorithm is tested in the three modes commonly evaluated in the literature. The initial energy of each node is 0.5 J.  
To check the performance of the proposed Centralized Skip Based Algorithm (CSBA), it is compared with other relevant proposals widely used in the literature. The evaluated algorithms are:  
* A distributed stochastic algorithm referred to as LEACH [4]. In this well-known technique, the nodes have a probability of converting into CH. This probability increases with the number of rounds in which the nodes has not been selected as CH (see Section 2 for further detail).
* A centralized Type-2 fuzzy system algorithm known as Clustering Routing Protocol for Wireless Sensor Networks Based on Type-2 Fuzzy Logic and ACO (CRT2 FLACO) [21]. The nodes that will be CH are selected with a fuzzy system in which the input variables are residual energy, distances to the BS and the number of neighbours. Later, the routers between CH are found using ACO to save energy sending data to the BS from the nodes.
* A centralized Type-1 fuzzy algorithm known as Cluster Head Election mechanism using Fuzzy logic (CHEF) [11]. A group of nodes is selected that are converted into CH from the output of the fuzzy system, that has residual energy, centrality and the number of near nodes, as inputs.
* A distributed Type-1 fuzzy system known as EEDCF [12]. In this case, the close nodes coordinate among them to decide the CH. For that operation, they exchange information about the output of the fuzzy system based on the residual energy, the number of close nodes and the average energy of those nodes. These last parameters constitute the inputs of the fuzzy system. The node with the higher output value becomes the CH for the close nodes.
* A distributed Type-2 Fuzzy system algorithm presented in [5]. The Enhanced Unequal Distributed Type-2 Fuzzy Clustering Algorithm (EUDCF) uses the residual energy, BS distance, the average number of nodes connected to the CH and the number of rounds without being CH as input variables.  
These algorithms were implemented in Matlab according to their specifications described in the corresponding papers. The simulations are all run with the same energy model (see Equations (3)-(6)). In order to allow a statistically significant comparison, 30 simulations were made for each of the mentioned algorithms to obtain the average values for \(FND\), \(HND\) and \(LND\).  
For the first set of simulations, the wireless sensor network corresponds to the Scenario 1. The results are shown in Figure 10. As it is observed, centralized methods get better metrics than the distributed ones. Moreover, the methods based on Type-2 fuzzy logic outperform their counterparts of Type-1. The results obtained by our proposal, CSBA, are the best in terms of \(FND\), \(HND\) and \(LND\) when compared with all the other methods. Moreover, the result of \(FND\) in CSBA is greater than the \(LND\) value obtained with most methods. This implies that the network performance was improved in terms of reliability and durability when CSBA was applied.