## 1 Introduction
It has shown great energy efficiency and is the basis of various other subsequent routing protocols [17]. It makes use of randomisation for the purpose of evenly distributing the energy load across all the sensing nodes and arranges various sensors into groups, where each group has a special sensor behaving as the leader of the group, coordinating the activities of the group. Here, a few sensors designate  
Figure 1: Typical hierarchical architecture. themselves as cluster heads based on a certain probability and the number of times they have been the cluster head so far. This leader's role is rotated so that it does not drain any single sensor's energy [15]. Since, the deployed battery-operated sensing nodes are energy-constrained, it is important to utilize the energy wisely to extend the network's lifetime. Moreover, the nodes deployed in hostile environments are very prone to faults, which may be related to a harsh environment, energy depletion or hardware failure. Although it is quite evident that a non-CH faulty node will degrade the network performance, a faulty CH node can be much more problematic, as it will hamper the whole data aggregation and dissemination process of this cluster and will make normal working nodes useless. This paper discusses the basic concept of the hierarchical clustering protocols and proposes a base-station-controlled Fault-tolerant Energy-efficient Hierarchical Clustering Algorithm (FEHCA), which focuses on:  
* The issue of energy efficient clustering to enhance the network lifetime;
* The optimal cluster counts for the network;
* The use of k-means clustering that partitions N-nodes into k-clusters, in which each node is associated with the cluster with the nearest mean;
* The election of CHs near the centroids of the respective clusters for effective inter-cluster communication;
* Minimization of energy dissipation by deferring the re-election of new CHs after each round;
* Attempting to make the cluster heads (CHs) fault-tolerant by appointing a secondary cluster head (sCH) in case the current cluster head goes down between two successive rounds. In essence, this paper proposes a centralised cluster formation technique controlled by the base station (BS), where the deployed sensors are divided into an optimal number of clusters. Once the number of clusters is decided and cluster formation is done, the algorithm, instead of electing any arbitrary CH, as shown in Figure 2, elects the CH near the centroid of respective clusters. The algorithm has been developed to be fault-tolerant in the context of the CH and does not require re-cluster formation between two successive rounds if the CH is found to be permanently defective. The work was carried out by considering both friendly and hostile environments; thus, the placement of the BS was assumed to be within the de  
Figure 2: Depiction of random distribution of cluster heads in conventional LEACH protocol. the hostile environment, respectively. The performance of the network highly depends on the placement of the base station. Suppose that a BS is placed within the monitored area (user-friendly environments such homes and offices, etc. ); it will be in close proximity to the cluster heads, as compared to a base station, which is outside the monitored area (generally in the case of hostile deployments such as harsh terrains, border areas, etc. ), where most of the cluster heads generally will be at a distance from the base station. Most of the implementations discuss either friendly environment deployments or hostile environment deployments, but the proposed algorithm was simulated and validated for both scenarios. We also compared our work with some of the state-of-the-art existing technologies with common parameters by positioning the BS within the monitored area.