# A New Centralized Clustering Algorithm for Wireless Sensor Networks
## 1 Introduction  
Wireless Sensor Networks (WSN) are composed of multiple nodes, which are deployed randomly in most situations. Although there are some commercial solutions for this kind of network in e-health, smart grids or surveillance [1], there are still some technological aspects that could be addressed to improve their performance. Presently, their main failing is the durability of the network in an autonomous and reliable way. For this reason, there are several proposals to reduce the energy consumption of the nodes while it operates correctly. This energy consumption is mainly caused by the data gathering and the data transmission. The formation of groups or clusters in this kind of network helps in the reduction of the energy dissipation during the data transmission especially when considering scalability and robustness [2]. As a consequence, the network autonomous lifetime (without the need for replacing the nodes' batteries) is prolonged when clustering is conveniently applied. In a cluster, there is a node, referred to as the Cluster Head (CH), which is in charge for the communication with other CHs or with the Base Station. It recollects the data from the nodes belonging to its cluster, it aggregates this information and then proceeds to send it to the Base Station (BS). The base station or sink decides the actions to take according to the data. The decision about which nodes are the CHs can be taken centrally by the BS or in a distributed mode by the sensor nodes. Centralized clustering algorithms demonstrated their ability to have an optimal behaviour in comparison with their distributed counterparts as more information can be used to create the clusters appropriately [3]. Another important issue related to clustering is how long the cluster structure is going to be maintained. The initial proposals on clustering algorithms set that the clusters should be periodically formed. In particular, they opted for deciding about the CHs in each round. A round is the interval of time into which the network lifetime is divided. In a round, the inter-cluster communication, the data fusion/aggregation and the intra-cluster communication sequentially take place to send the measurements to the BS. Therefore, the first proposals (e.g., LEACH-C [4]) included the determination of the CHs at the beginning of each round. An alternative and novel approach consists of including the execution of the selection of the CHs only in some rounds. The skip stands for the number of rounds in which the cluster heads will be kept [5]. The work in [5] sets the skip as a constant parameter and equal to 2. However, the appropriate value for this parameter is related to the network density, the nodes' positions and the traffic pattern. In the present paper, we propose a novel centralized clustering algorithm that decides the cluster heads while it sets an optimized skip. The algorithm, named as \"Centralized Skip Based Algorithm\" or CSBA, is based on two hypotheses. The first hypothesis, or H1, relies on the fact that when a CH is conveniently elected, maintaining it during some rounds will make the network lifetime longer as the control information (and the consumption related to the transmission and reception of these frames) does not need to be exchanged. However, the second hypothesis on which CSBA is based, or H2, is that keeping a node as a CH indefinitely degrades the network performance in terms of reliability, that is, not all the measurements are collected from the nodes. This happens because the node acting as CH will receive information from the nodes which are ascribed to it. As a consequence, the energetic dissipation of this node increases, especially when this operation is prolonged over several rounds. The measurements that should be collected by this node cannot be guaranteed to be transmitted. In our proposal, the selection of the cluster heads is modelled by a Type-2 Fuzzy system incorporated into the Base Station.