# Gathering Big Data in Wireless Sensor Networks by Drone +
## 4 Modeling the GBD Problem  
Since the monitored area is composed of an infinite set of points (\(M\)), we defined \(P_{grid}\) as a finite set of points where the drone can hover to gather data. These points are named Possible Drone Points (_PDP_), such that \(P_{grid}=\{PDP_{1},PDP_{2},\ldots,PDP_{|P_{grid}|}\}\) and \(P_{grid}\subset M\). The _PDPs_ form a grid inside the monitored area. The distance between two adjacent _PDPs_ horizontally or vertically is \(r\sqrt{2}\) meters, where \(r\) is the radio range of the sensor nodes (same as the drone). Figure 3 illustrates a monitored area, a set of _PDPs_ forming a grid and the radio range. In this way, if a drone hovers over all _PDPs_ in \(P_{grid}\), we guarantee that the drone can establish direct communication with all sensor nodes inside the monitored area. \begin{table}
\begin{tabular}{c l} \hline \hline
**Notation** & **Description** \\ \hline \(b\) & The bandwidth of a link between sensor nodes or between a drone and a sensor node \\ \hline \(CG\) & Connecting Graph, \(CG=(V,E)\) such that \(V\) is the set of vertices representing PDPs and the sensor nodes, and \(E\) is the set of edges representing communication links between the sensor nodes and the drone over a PDP \\ \hline \(d_{i\in i+1}\) & Subset of sensor nodes that send data to the drone when it is flying between two consecutive hovering points \(p_{i}\) and \(p_{i+1}\) in a tour \\ \hline \(D_{mov}\) & Set of subsets of sensor nodes that have to send data to the drone when it is moving \\ \hline \(dist_{i}\) & The Euclidean Distance of the sensor node \(s_{i}\) to the path (line) between two consecutive hovering points in a tour \\ \hline \(E\) & Set of edges representing communication links between the sensor nodes and the drone over a PDP in the Connecting Graph \\ \hline \(F\) & Set of edges representing the shortest distance between every pair of _PDPs_ in the Trip Graph \\ \hline \(m\) & Amount of data stored in the memory of each sensor node \\ \hline \(M\) & 2D rectangular monitored area \\ \hline \(N_{j}\) & Subset of sensor nodes that have to send data to the drone when it is over the hovering point \(p_{j}\) \\ \hline \(p_{0}\) & Initial and final point in the drone tour, \(p_{0}=0,0\) \\ \hline \(p_{j}\) & Hovering point in the drone tour, \(p_{j}\in P\) \\ \hline \(P\) & Sequence of hovering points forming a tour, \(P\subseteq P_{grid}\) \\ \hline \(P_{grid}\) & Set of all PDPs forming a grid \\ \hline _PDP_ & Possible Drone Points where the drone can hover to gather data \\ \hline \(r\) & Radio range of the sensor nodes and the drone \\ \hline \(R_{i}\) & The \(i\)-th tour created in the \(i\)-th iteration of the heuristics \\ \hline \(s_{i}\) & A sensor node, \(s_{i}\in S\) \\ \hline \(S\) & Set of all sensor nodes \\ \hline \(S_{subsets}\) & Set of subsets of sensor nodes; a set for each hovering point in \(P\) \\ \hline \(T_{allnodes}\) & Time to drones receive data from all sensor nodes, without considering the drone movement \\ \hline \(T_{colltering}\) & Collecting time: it is the time the drone spends hovering to gather data \\ \hline \(T_{moving}\) & Time the drone spends receiving data when it is moving \\ \hline \(T_{total}\) & Overall data gathering time \\ \hline \(T_{trip}\) & Trip time, is the time the drone spend in movement \\ \hline \(TG\) & Trip Graph, \(TG=(P_{grid},F)\). \(F\) is the set of edges linking PDPs, the weights are the Euclidean distance \\ \hline \(trs\) & The minimal distance the drone has to fly inside the area covered by the radio of a sensor node to enable this node to send all \(m\) bits of data to the drone or to relay nodes \\ \hline \(V\) & Vertices representing all sensor nodes and the PDPs in the Connecting Graph \\ \hline \(w_{j}\) & Weight attributed to \(\text{PDP}_{j}\) according to Equation (3) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Problem Notation. The problem of gathering big data in WSNs was modeled by [PERSON] and [PERSON] [12] using two graphs, named _Trip Graph_ (\(TG\)) and _Connectivity Graph_ (\(CG\)).