## 2 Related Work  
A survey of clustering algorithms for WSNs was presented by [PERSON] _et al._[32]. The authors of that survey presented a taxonomy and classification of typical clustering schemes, then summarized different clustering algorithms for WSNs based on classification of variable convergence time protocols and constant convergence time algorithms, and highlighted their objectives, features, complexity, _etc._ Finally, these clustering approaches were compared based on a few metrics such as convergence rate, cluster stability, cluster overlapping, location-awareness and support for node mobility. [PERSON] _et al_. [33] presented a comparison survey between different clustering protocols. The authors of the survey discussed some basic concepts related to the clustering process, such as cluster structure, cluster types, clustering advantages, and briefly analyzed LEACH-based protocols as well as proactive and reactive algorithms in WSNs. The main characteristics of these protocols were compared and the evidences where they can be used currently were outlined. [PERSON] _et al_. [34] surveyed the clustering algorithms available for WSNs and classified them based on the cluster formation parameters and CH election criteria. The authors of the survey also studied the key design challenges and discussed the performance issues related clustering protocols based on the classification of identity-based clustering algorithms, neighborhood information based clustering algorithms, probabilistic clustering algorithms and biologically inspired clustering algorithms. Different clustering schemes are discussed by [PERSON] _et al_. [35], with special emphasis on their CH selection strategies based on the classification of deterministic scheme, adaptive scheme and combined metric scheme. The costs of CH selection were compared with respect to cluster formation, distribution of CHs and creation of clusters. Besides, a need of more scalable, energy efficient and stable clustering scheme for data gathering in WSNs was put forward. [PERSON] _et al_. [36] discussed a total of three prominent advantages of clustering methods for WSNs, such as more scalability, less overheads, and easy maintenance, and then present a classification of WSN clustering schemes based on a total of eight clustering attributes. The authors also analyzed altogether six popular WSN clustering algorithms, such as LEACH, PEGASIS, HEED, EEUC, and _etc._, and compared these WSN clustering algorithms, including various attributes. [PERSON] _et al_. [37] considered clustering routing protocols to achieve energy efficiency in WSNs and presented a review on clustering algorithms from the perspective of data routing. A simple classification of clustering routing protocols is proposed in the review. Totally nine typical clustering protocols including two classes, pre-established clustering routing algorithms and on-demand clustering routing algorithms, are summarized in respectively. Besides, some future research directions are presented in the review. The operations of some clustering protocols were discussed in the survey presented in [38], and the advantages and limitations of each one of these algorithms were analyzed in brief. The authors of the survey selected only seven popular clustering algorithms for WSNs, such as LEACH, TL-LEACH, EECS, TEEN, APTEEN, and _etc._ Additionally, the survey compared these clustering protocols in terms of energy consumption and network lifetime. A survey on clustering algorithms for WSNs was presented by [PERSON] _et al_. [39]. The main challenges for clustering algorithms were discussed and altogether nine popular clustering algorithms for WSNs such as LEACH, TL-LEACH, EECS, HEED, EEUC, _etc._ were simply summarized in the survey. The authors also compared these clustering algorithms based on metrics such as residual energy, uniformity of CH distribution, cluster size, delay, hop distance and cluster formation methodology.