## 2 Cluster Head Selection
### Self-Organized Schemes
#### 2.1.1 Fixed Probabilistic Schemes  
In absolute probabilistic schemes, nodes make autonomous decisions without any centralized control. CHs are selected for initial and subsequent rounds only based on the evaluation of an expression that includes some fixed parameters like number of CHs, current round number, time interval or Node ID. The first and the most popular self-organizing clustering protocol for WSNs, called Low-Energy Adaptive Clustering Hierarchy (LEACH) [10] takes advantages of randomization to evenly distribute the energy expenditure among the nodes within the network. In LEACH, each node creates a random number between [0, 1] and compares it with a threshold value T(n), calculated by the Equation (1), to determine whether it is chosen as CH role in current round or not. The node becomes a CH if this number is lower than T(n). If a node is selected as CH, it broadcasts the CH advertisement messages within the network and other nodes join the cluster based on the received signal strength.  
\[\textit{T(n)}=\begin{array}{c}\textit{p}_{CH}\\ \textbf{1-}\textit{p}_{CH}\ast\left(\textit{r}_{c}\textit{mod}\textit{1/p}_{CH} \right)\end{array} \tag{1}\]  
where \(\textit{p}_{CH}\) is the desired percentage of CHs, \(\textit{r}_{c}\) is the current round, and \(n\) is the nodes that have not been CH in the last 1/p rounds [10].  
Keeping the stochastic notion of CH selection strategy in LEACH, Time-Based CH selection (TB-LEACH) [11] proposes that the competition for CH position no longer be dependent on a random number but a random time interval, in which nodes having the shortest time interval win the competition for the CH role. According to the scheme, every node sets a random-interval timer at the outset of each round, when the timer expires, the nodes, which have not received the predefined number of CH advertisement messages, broadcast a CH advertisement throughout the network. To have constant number of CHs, a counter is also set that stops the CH competition when the number of selected CHs reaches the desired value. However, the counter works precisely only if all nodes are in the broadcast range of CH advertisement of all the CHs, which may not be a true presupposition in large scenarios with far distances between nodes.  
Unique identifier (ID) of the nodes and desired number of CHs are the parameters considered by [12] to present two deterministic schemes of Algorithm of Cluster-head Election by Counting (ACE-C) and Location (ACE-L). In ACE-C, the CH selection for a network consisting of \(N\) sensor nodes is based on round-robin fashion. Where number of desired CHs is supposed as \(C\), the sensor nodes with ID's from 0 to \(C-\textit{1}\) in first round, and nodes with ID's from \(C\) to \(2C-\textit{1}\) in next round are selected CHs. The same procedure continues for following rounds until all the nodes become CH once and whole process starts again from the node with ID = 0, ultimately. To make the CH decision approach distributed, each node considers the total number of selected CHs and its ID in each round to announce its selection as CH in its turn. ACE-L, which is especially proposed for mobile sensor nodes, uses location information presented as some fixed reference points to select the predefined number of CHs. The algorithm selects constant number of reference points equal to the desired number of CHs, and each node selects the closest reference point as its main reference point (MRP). The nodes with the same MRP contend a channel for the CH role based on the metric of the _delay time_, which is directly proportional to distance of the nodesto reference point. In other words, the node closer to the reference point broadcasts a beacon of being CH earlier and other nodes by receiving the beacon stop the competition.