## 2 Related Work
The node with the highest weight among its neighbors is chosen as a cluster-head. Note that all of the above algorithms generate one-hop clusters, which may be suitable only for small networks. The authors of [16] generalize the clustering heuristics such that an ordinary node can be at most \(d\) hops away from its clusterhead, which allows more control and flexibility in the determination of clusterhead density. However, clusters are formed heuristically without taking node mobility and their mobility pattern into consideration. [37] designs a clustering algorithm (DDCA) that adaptively changes its clustering criteria based on the current node mobility. As a multi-hop clustering, DDCA normally forms clusters with larger size compared with 1-hop clusters, which may result in increased control overhead for cluster maintenance. In [38], an adaptive clustering protocol is proposed to maintain a network structure based on load-balancing clustering. In order to reorganize the cluster, the proposed scheme sets upper and lower limits on the cluster size. However, it does not describe the procedures of cluster formation and how to select proper values for the upper and lower bounds of the cluster parameters. Reference [3] describes a self-organizing, multihop, mobile radio network which relies on a code-division access scheme for multimedia support. A distributed algorithm with a limited number of hops in the cluster is applied to control the network topology. However, this algorithm does not put any restriction on clusters size, which may increase the difficulty of cluster maintenance and lead to performance degradation in dense networks. [PERSON] _et al._[39] study node connectivity and node ID as two particular weights to generalize the cluster definition and formation algorithm so that a cluster contains all nodes that are at distance at most \(k\) hops from the clusterhead (for \(k=1\) and \(k=2\)). Nevertheless, this proposed scheme forms 1-hop and 2-hop clusters without taking into account the cluster size. \(K\)-clustering frameworks [40, 41] are proposed to divide the wireless network into non-overlapping clusters, and where every two wireless nodes in a cluster are at most \(k\) hops from each other. Thus, the cluster structure is controlled by hop distance. Although these algorithms have polynomial time and message complexity, unbalanced clusters may be formed due to the lack of information regarding cluster diameter and cluster size. LCC [42] is designed to minimize clusterhead changes. However, with the increasing node speed, the migration of the cluster members towards others clusters and the role reassignment between two neighboring clusterheads may lead to frequent clusterhead changes. Moreover, a ripple effect may be generated due to the propagation of clusterhead changes in the LCC scheme. In the purpose to generate balanced clusters, [43] restricts both diameter and size of the cluster. Two thresholds are used to control the size of generated clusters and the distances between cluster members and their corresponding clusterhead are at most two hops. However, the logic behind the setting of the two thresholds and the process of achieving inter-cluster communication are not provided. Comprehensive surveys of recently proposed clustering algorithms for mobile ad-hoc and sensor networks can be found in [44, 45]. In our previous works, the sensors are assumed to be fixed and the cluster size is not specified for cluster formation [8]. Moreover, we focus on only the procedures of clusterhead re-selection [46], not the operations of cluster maintenance and distributed gateway selection. In order to manage cluster members and minimize the overhead of intra-cluster communications in a mobile network, the appropriate design of cluster size and the procedures for cluster maintenance are crucial.