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A novel algorithm which combined the merits of the Clustering strategy and the Compressive Sensing-based (CS-based) scheme was proposed in this paper. The lemmas for the relationship between any two adjacent layers, the optimal size of clusters, the optimal distribution of the Cluster Head (CH) and the corresponding proofs were presented firstly. In addition, to alleviate the "Hot Spot Problem" and reduce the energy consumption resulted from the rotation of the role of CHs, a third role of Backup Cluster Head (BCH) as well as the corresponding mechanism to rotate the roles between the CH and BCH were proposed. Subsequently, the Energy-Efficient Compressive Sensing-based clustering Routing (EECSR) protocol was presented in detail. Finally, extensive simulation experiments were conducted to evaluate its energy performance. Comparisons with the existing clustering algorithms and the CS-based algorithm verified the effect of EECSR on improving the energy efficiency and extending the lifespan of WSNs.

A novel energy-efficient clustering algorithm was proposed which aimed at improving the energy efficiency of WSNs via reducing and balancing energy consumption in this paper. The lemma concerning the dual-cluster-head mechanism which was designed to reduce the energy overhead during the process of rotation of Cluster Heads (CHs) was proposed and proven at first. In addition, a non-cooperative game model was presented with the purpose of balancing the energy consumption among the Cluster Heads. Besides, the Nash Equilibrium Point (NEP) of the game model was presented and the corresponding proof was provided. Subsequently, the Energy-efficient Clustering algorithm combined Game theory and Dualcluster-head (ECGD) mechanism was detailed, which took the energy efficiency in both of the intra-cluster and inter-cluster communication into consideration. Finally, extensive experiments were conducted via simulation and the simulation results were compared with the existing Clustering strategies in terms of energy efficiency and network performance. The analyses of results have shown that the ECGD can improve energy efficiency and extend the network lifespan effectively.INDEX TERMS Energy efficiency, dual-cluster-head mechanism, nash equilibrium point, non-cooperative game, network performance.

The features that sensor nodes are powered by battery and have severe energy constraint make the design of energy-efficient protocol a key task for wireless sensor networks (WSNs). Clustering protocols significantly cut down the energy expenditure of each sensor node. However, hot spots problem occurs in locations close to the sink. Besides, it makes things worse if the nodes with less energy are selected as cluster heads (CHs), because they are often loaded heavier traffic than cluster members (CMs) due to their duty. The issues which exist in WSNs are proposed and the primary reason why cluster head election is hard to control is then presented. A mathematical model aiming to ease the hot spots problem via optimizing the cluster size is proposed and an optimal cluster size (OCS) algorithm is given firstly. Subsequently, an evolutionary game model for the sensor nodes to terminate the anarchism during the process of cluster head selection is presented, and a novel routing protocol named Energy Efficient Routing protocol based on Evolutionary Game (EEREG) theory is proposed. Finally, extensive simulation experiments and performance comparisons with the well-known hierarchical routing protocols are conducted. The experiment results show that a significant improvement in energy efficiency as well as lifetime extension is achieved.

A comprehensive analysis on the energy-efficient strategy in static Wireless Sensor Networks (WSNs) which are not equipped with any energy harvesting modules was conducted in this paper. Firstly, a novel generic mathematical definition of Energy Efficiency was proposed, which took the acquisition rate of valid data, the total energy consumption, and the network lifetime of WSNs into consideration simultaneously. To the best of our knowledge, it is for the first time that the Energy Efficiency of WSNs is mathematically defined. The energy consumption characteristics of each individual sensor node and the whole network were expounded at length. Accordingly, the concepts concerning the Energy Efficiency, namely the Energy-efficient Means, the Energy-efficient Tier, and the Energy-efficient Perspective, were proposed. Subsequently, the relevant energy-efficient strategies proposed from 2002 to 2019 were tracked and reviewed. Specifically, they were classified into five categories, i.e., the Energy-Efficient Media Access Control (EEMAC) protocol, the Mobile Node Assistance Scheme (MNAS), the Energy-Efficient Clustering Scheme (EECS), the Energy-Efficient Routing Scheme (EERS), and the Compress Sensing based Scheme (CSS) respectively. A detailed elaboration on both the basic principle and the evolution of them was made. Finally, further analysis on the categories was made and the related conclusion was drawn. To be specific, the interdependence among them, the relationships between each of them and the Energy-efficient Means, the Energy-efficient Tier as well as and the Energy-efficient Perspective were analyzed in detail. Besides, the specific applicable scenarios for each of them and the relevant statistics analysis were detailed. The proportion and the number of citations of each category were illustrated by the statistical chart. In addition, the existing opportunities and challenges facing WSNs in the context of the new computing paradigm, and the feasible direction concerning the energy efficiency in the future were pointed out.

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This is a repository copy of A Fuzzy-logic Based Energy-efficient Clustering Algorithm for the Wireless Sensor Networks.

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