## 2 Cluster Head Selection
### Self-Organized Schemes
#### 2.1.2.2 Density Dispersion  
The dispersion of CHs should conform to the nodes' density in distribution; in other words, selection of the nodes from denser areas leads to conserving more energy. [PERSON] _et al_. in [24] present a mechanism to select the Maximum Energy Cluster-head (MECH) based on the number of neighbours of the node. Every node broadcasts a Hello message to its one-hop neighbours and in this way, each node counts the number of its neighbours. When the number of the received messages reaches a specified value, the node announces its selection as CH by broadcasting an advertisement to its one-hop neighbours. The nodes that receive the advertisement set a back-off timer and never broadcast the same message. By expiring the back-off time, every node selects the nearest CH based on the signal strength. The method ensures the existence of one CH in a region consisting of the neighbouring nodes with a predefined communication range. However, the process of detecting the neighbouring nodes imposes extra control messages to the network and delays the network convergence time in proportion to back-off time.  
[PERSON] [25] focuses on asymmetrical distribution of CHs in network area and changes the probability of being CH in sinusoidal circle around the sink. In this respect, an adjustment function is introduced in Equations (9) and (10) to change the distribution of the threshold value of the nodes within the network. Round number \(r_{c}\), distance of the nodes from the BS (\(\mathrm{d_{BS}}\)) and the optimum cluster radius \(R\) are the variables considered in the adjustment function. Multiplication of T(n) by f(r\({}_{\mathrm{c}}\), \(\mathrm{d_{BS}}\)) gives a new distributed threshold value, which changes symmetrically over the rounds of running the protocol:  
\[\mathrm{f(R_{n},d_{bs})}=\left|\sin(\frac{\pi}{2R}(d\;r_{c}\mathrm{ mod}\left(\frac{1}{p}\right).2 pR\right| \tag{9}\] \[T^{\prime}(n)=\frac{p}{1-p\;*(Rn\mathrm{mod}\;1/p)}*\mathrm{f} (r_{c},d_{BS}) \tag{10}\]  
Since the absolute value of the sinusoidal adjustment-function is always equal or less than one, applying the function to threshold value decreases the number of the CHs over running rounds. Hence, the paper calculates the coefficient of \(\pi/2\) to apply to the desired number of CHs to compensate the diminution of the threshold caused by the adjustment function.  
In [26], the authors propose an Uneven Clustering Scheme based on the Energy and Distribution density of CHs (UCS-ED), which is an application oriented algorithm that especially addresses asymmetric data throughput in underground area in coal mine. Since in a lineway area of a coalmine, the direct transmission of the data from far CHs to the BS is not possible, CHs in addition to data aggregation and transmission to the BS are also a backbone to relay aggregated data of other CHs. Therefore, the CHs nearer to the BS deplete at a faster rate. Hence, to mitigate this issue, the paper proposes a CH selection algorithm that the regions closer to the BS generate more CHs than the further regions. In this respect, at the initial stage, the BS broadcast a \"Hello\" message to all nodes and in this way, each node can evaluate the received signal strength and estimates its approximate distance from the BS. Then, the nodes having the higher remaining energy and closer to the BS have higher chances to be selected as CH and so, the density of the CHs follows the effective density of backbone.