# A Cluster-Based Dual-Adaptive Topology Control Approach in Wireless Sensor Networks
## 3 The Improved Clustering Scheme
### Overview  
The term \"topology control\" has been used with the different meanings in the literatures for wireless sensor networks. Some typical topology control methods (e.g., works in [24; 25; 26; 27; 28]) only control a flat network topology, but clustering algorithms (e.g., LEACH [29], HEED [30], and the vehicular clustering scheme in [31]) can control a hierarchical network topology. Therefore, several authors also regard clustering algorithms as topology control techniques. However, according to the informal definition of topology control in [32] (i.e., this definition is to dynamically change the nodes' transmitting range in order to maintain some property of the communication graph), they cannot be classified as topology control mechanisms since the transmit power of nodes is usually not modified by conventional clustering algorithms. With the evolution of clustering mechanisms, the transmit powers in both inter-cluster and intra-cluster should be adjusted adaptively. In a sense, it is basically consistent with the definition in [32].  
Our clustering scheme aims at not only minimizing the total energy consumption (transmission plus circuit energies) in inter-cluster communications and improving fair energy consumption in intra-cluster communication but also determine adaptively the inter-cluster transmission modes and the clustering ranges. An example for cluster-based network topology is shown in Figure 1, where each cluster is managed by at most three Cluster Heads (CHs) (i.e., A master CH (MCH), a slave CH (SCH), and a data fusion CH (FCH)), big circles indicate transmission ranges of MCHs, the lines between the nodes are wireless links, and some arrows in links only show the transmission direction of data collection in an intra-cluster.  
The MCH and SCH operate as a cooperative multi-antenna node for inter-cluster communications, and the operation consists of three main phases: cluster formation, power adjustment for intra-cluster communications, and determination of inter-cluster transmission modes.  
Each cluster sets a FCH to collect data within the cluster. In brief, cluster formation is a distributed process for selecting the CHs of each cluster (the MCH and FCH are mandatory whereas the SCH may or may not be present) and associating non-CH nodes with the corresponding MCH/SCH pairs, where one of the associated non-CH nodes is selected as the FCH. During intra-cluster communications, the FCH is responsible for aggregating data sent by other nodes in its cluster and sending the aggregated data to the corresponding MCH/SCH pairs that may operate as a cooperative multi-antenna node. The inter-cluster communications are carried out by forwarding data from the MCH/SCH pairs of one cluster to those of a neighboring cluster (or directly to the sink/base station),  
Figure 1: Example for cluster-based network topology.  
which is built on the basis of inter-cluster topology construction. As mentioned in the CMIMO scheme, an energy-efficient routing algorithm is executed over the topology of virtual nodes to determine an end-to-end inter-cluster path that minimizes the total energy consumption, which is done by running [PERSON]'s algorithm with the weight of a link taken as its total energy consumption. Also, like the CMIMO scheme, each virtual MIMO link, the MCH (or the MCH and SCH) of the receiving cluster selects the optimal transmission mode and transmission power for communication with other CHs, where the mode and power can be different for different hops, depending on the distances between the CHs of neighboring clusters.