## 2 Related Work  
Low-Energy Adaptive Clustering Hierarchy (LEACH) [18] provides an elegant clustering routing approach that has inspired many varied solutions. After the CHs are randomly selected, they will broadcast their information to all the sensors in the network. Based on the received information, each sensor decides which CH it wants to join. Instead of using random CH election scheme, Hybrid Energy-Efficient Distributed (HEED) [19] can select the sensors with high battery levels to be CHs through the proposed iteration CH election scheme. In the iteration CH election scheme, CHs are classified into two types: \(\mathit{tentative}\) and \(\mathit{final}\) CHs. Some initial CHs are selected randomly as \(\mathit{tentative}\) CHs. After each iteration, every sensor increases their probabilities to become a CH. In this algorithm, they set this probability to be the CH self election threshold and the threshold value is 1. Since the probability is increased twice after each iteration, once the probability is 1, the sensor will claim itself as a \(\mathit{final}\) CH. For example, initially this probability for a sensor to become a CHis 0.3. After the first iteration, it increases to 0.6, and then after the second iteration it increases to 1 (the real value is 1.2 but cut to 1). A _tentative_ CH will give up being a CH if it discovers a \(final\) CH in its communication range. The sensors are not covered by any \(final\) CHs will elect themselves to be CHs. This iteration CH election scheme guarantees that the probability of the phenomena that two sensors, within each other's communication range, both become CHs is rare. Therefore, it is can be deduced that the CHs are well distributed over the network and thus all the clusters have similar size. HEED involves significant overhead due to the heavy broadcast in each iteration. As the number of iterations required in the initial phase increases, the overhead and network delays are also increased. LEACH and HEED are two typical Voronoi structure based clustering algorithms that have inspired many other algorithms. DWEHC [20] made an improvement on HEED by using sensors' location information. It can achieve more balanced cluster size, and consequently achieve more balanced power consumption on each sensor. However, the location information of the sensors used in this algorithm is not always available. DWEHC also improved HEED by supporting multihop inter-cluster and multihop intra-cluster communication. In PEGASIS [21], every sensor in the network transmits its data to one of its neighbours. In this way, the gathered data is transferred from one node to another through a chain. A designated node (a node receives data from both sides) will send the assembled data back to the BS. PEGASIS is claimed as a distributed algorithm. However, every single node needs to obtain the global topology map of the network. CCS [22] is a centralised clustering algorithm based on PEGASIS. Instead of using a single chain structure, CCS utilises a multihop chain structure. Regarding the BS as the centre of the network, each sensor assigns itself a level number according to the signal strength received from the BS. Through this way, the sensors in the network are organised into a hierarchical structure. For each level, the sensors perform transmission and fusion in the same way as that in PAGASIS. The sensor that is elected as the CH will gather data from all the other sensors on the same level and then transmit the assembled data to the CH in the 1-lower level. Once being assigned a level, a sensor will not change its level unless the location of the BS changes. This structure suffers from a problem that the sensors near the BS can die soon from forwarding packets for the sensors in the higher levels. Only total power consumption of the network is measured to evaluate this algorithm. There is no evidence showing a balanced power usage throughout the network. In a spectrum structure based network, the sensors are partitioned based on both the distance and the angle to the BS.