## 2 Related Works  
Recently, several clustering algorithms were proposed to increase stability, routing performance, scalability, bandwidth utilization, and resource allocation in WMASNs. Clustering in WMASNs plays an important role in enhancing their basic network performance parameters like routing delay, congestion, energy consumption, and throughput. The hierarchical routing protocol in the clustering algorithm has been widely used for WMASNs. The existing flooding method [8-10] is the most popular hierarchical routing protocols. In this method, the source node communicates with the destination node irrespective of the movement speed. In WMASNs, the number of control packets for flooding increases exponentially with the number of nodes. A number of clustering algorithms for WMASNs are proposed in the literature [16]. The CBRP (Cluster-Based Routing Protocol) methods were proposed to solve the problem of exponential increase [8]. The CBRP (Cluster-Based Routing Protocol) methods have been widely used to achieve efficient management and extension of distributed nodes. Well-known CBRP methods include LCA (Linked Clustered Algorithm) [17], LID (Lowest-ID) [9], LCC (Least Cluster Change) [18], MCC (Maximum Connectivity) [19], and RCC (Random Competition Clustering) [20]. These existing algorithms have clustering criteria for selecting cluster heads and are based on the minimum cluster overlap method in the formation of clusters [21,22]. These algorithms, however, cannot guarantee stability due to the ambiguity in the selection of cluster heads. Thus, several clustering algorithms were proposed in WMASNs to improve performance and reduce overhead [23,24]. Selecting the cluster head is based on the mobility of nodes in [25], and on the mobility of nodes and power capacity in [26]. In [1], a scenario-based clustering algorithm (SCAM) was proposed, where (k,r)-dominating set was used for selecting the cluster heads and gateway nodes; here, k is the minimum number of cluster heads per node in the network, and r is the maximum number of hops between the node and the cluster head. This is to compute the quality of all dominating nodes. In [3] and [10], the clustering algorithms based on weighting were proposed, which considered link connectivity, power capacity and distance of nodes, and mobility in the selection of cluster head. These algorithms have the advantage of clear selection of the cluster head, but they have the problem of requiring correct information for the attributes and relationships of nodes. Though many clustering algorithms are proposed, few algorithms are dedicated for wireless mobile _ad hoc_ networks. The Lowest-ID method [9], one of the most popular methods for mobile _ad hoc_ networks, has ambiguity in clustering due to selecting the cluster head with the lowest value. In [21], AMCS (Adaptive Multi-hop Clustering Scheme) was proposed as a wireless mobile routing algorithm. The AMCS algorithm reaches the destination node in multi-hop through the cluster head. This algorithm, however, has a problem in that the role of a node is not clear, whether it is the cluster head or the gateway, during the reception of local information from neighbor mobile nodes. A centralized clusterhead selection algorithm was proposed in [27], where the base station assigned the cluster head roles based on the energy level and geographical position of the nodes. In [28], a centralized algorithm based on fuzzy was proposed, where the nodes were selected as cluster heads by the base station based on their distances from each other, energy level, and the concentration of nodes in the region. In [3], a distributed deterministic cluster head selection algorithm based on WCA (Weighted Clustering Algorithm) was proposed. WCA maintains 1-hop clusters with one clusterhead. The weight of each node is used in the selection of the cluster head. WCA considered geographical information and relative distances of nodes for the weight information.