# A Novel Connectivity-Based LEACH-MEEC Routing Protocol for Mobile Wireless Sensor Network
## Proposed Framework
### Connectivity  
Two mobile sensors nodes \(N_{i}\) and \(N_{j}\) are connected if they are at \(R_{max}\) radio range. Here, a binary disc model is considered [44]. It is the simplest sensing model that is capable of sensing from any point that is located within its sensing radio range and not from any point beyond it. The sensing ability of the mobile sensor node \(N_{i}\) is with respect to neighboring node \(N_{j}\) within transmission radio range \(R_{max}\). The distance \(D(N_{i},N_{j})\) between two sensor nodes \(N_{i}\) and \(N_{j}\) is given by Euclidean distance \(D(N_{i},N_{j})=\sqrt{(N_{ix}-N_{jx})^{2}+(N_{iy}-N_{jy})^{2})}\). Hence, using above equation, the sensing ability is given by.  
\[S(N_{i},N_{j})=\frac{\Gamma}{D(N_{i},N_{j})^{Z}}, \tag{13}\]  
where \(\Gamma\) and \(Z\) are mobile sensor technology-dependent parameters. The parameter \(\Gamma\) is energy emitted by a target mobile sensor, and \(Z\) is an energy releasing factor, which ranges from 2 to 5 [49]. The sensor node will transmit \"HELLO\" packet [50], in a circular area of \(R\) radius. Using a binary disc sensing model, the node which reply to a \"HELLO\" packet is accumulated to \(NeighN_{i}\) neighboring nodes. Here, we assume a mobile sensor node \(N_{j}\) is in \(R_{max}\) radio range to sensor node \(N_{i}\). If \(S(N_{i},N_{j})=1\), then accumulate \(NeighN_{i}\) to \(NeighN_{i}+1\); otherwise, \(NeighN_{i}\) value remains same. This process will continue until \(N_{i}\) calculates all its neighbors. Algorithm 1 further explains this process.  
```
Result: Declare: Mobile Sensor Nodes\(N_{i}\),\(\forall\cdot(1\leq i\geq n)\) Broadcast: Hello Packet for\(j=to\)\(N-1\)do Procedure:\(Euc_{Dist}(N_{i},N_{j})\) \(/*R_{max}\) radio range \(*\) / \(Net.S(N_{i},N_{j})\longleftarrow Calculate.S(N_{i},N_{j})\) / \(*\)Using Binary disk sensing model \(*\) / Declare: \(NeighN_{i}\longleftarrow 0\) if\(Euc_{Dist}[i]<R_{max}\)then \(NeighN_{i}[i]\longleftarrow NeighN_{i}+1\) / \(*\)Further explained in Section 3.3 \(*\) / else \(NeighN_{i}\)  end if Calculate: Density for all sensor nodes in \(R_{max}\) Net.\(Dn(N_{i})\longleftarrow Calculate.Dn(N_{i})\) \(PC(N_{ki})=(1-e^{-Dn(N_{ki})R_{max}})^{k-1}\) End Procedure end
```  
**Algorithm 1** Connectivity algorithm.  
The density of mobile sensor node \(N_{i}\) with respect to its neighboring nodes in \(R_{max}\) radio range is given by Equation (14) [51], where \(Dn(N_{i})\) is density of sensor node \(N_{i}\) and \(N_{\pi R}{}^{2}\) is the number of nodes located within circular area radio range, which represents the spatial density.  
\[Dn(N_{i})=\frac{(NeighN_{i})}{N_{\pi R}{}^{2}} \tag{14}\]  
A node is set to be \(k\) connected if the removal of \(k-1\) nodes does not disturb its connectivity. Using Equation (15), the probabilistic connectivity of mobile sensor nodes is given by [52].  
\[PC(N_{ki})=(1-e^{-Dn(N_{ki})R_{max}})^{k-1} \tag{15}\]  
The probabilistic connectivity \(PC(N_{ki})\) includes a set of all connected nodes that have at least \(ki\) connected sensor nodes in \(R_{max}\) radio range. Connectivity is further explained in Figure 2, where circular region is assumed on \(R_{max}\) radial range of \(N_{i}\) mobile sensor node. Mobile nodes located within \(R_{max}\) radial range are considered as neighboring nodes.  
Algorithm 1 further presents the steps followed by a mobile sensor nodes to determine connectivity for the selection of CL.