## 5 Methods and Materials  
Now, we present a set of experiments designed to characterize the performance of the _balanced_, _direct_, and _inverse_ strategies. As baseline, we consider the intuitive strategy of covering locations following the order of popularity. Most popular cell gets covered first. We refer to this strategy as _dl_ (densest locations). It receives as input the volume of traffic per cell (\(V\)), and the number of cells to be covered, returning the set of \(\alpha\) cells presenting higher volume of traffic, as presented in Algorithm 2. ```
0:\(V,\alpha\);
0:\(Y\); \(\triangleright\) Cells to be covered
1:\(V^{\prime}\leftarrow\text{sort}(V)\); \(\triangleright\) Sort cells according to volume of traffic
2:\(Y\leftarrow\text{get\_initial\_elements}(V^{\prime},\alpha)\); \(\triangleright\) Gets the \(\alpha\) initial elements of \(V^{\prime}\)
3:return Y;
```  
**Algorithm 2** Strategy _dl_: Covering the most popular cells firstly. Strategy balanced: Uniform Distribution of Weights, Regardless of the Percentage Trip Duration under Coverage: An Alternative to Maximize the Area under the Delta Curve  
By using an uniform distribution of weights across the entire range of \"trip duration under coverage\" (\(\rho_{1}\)), we intend to maximize the area under the Delta curve. The area is computed using  
Figure 4: Figure shows the distribution of weights used for computing the _score_ indicating the next cell to be covered by Algorithm 1. (**a**) Shows the distribution used for the strategy _balanced_. All ranges of “percentage trip duration under coverage” receive the same weight, and the goal is to maximize the area under the Delta curve. (**b**) Shows the distribution used for the strategy _direct_, where weights are directly proportional to the “percentage trip duration under coverage” shown in the \(x\)-axis. By using such distribution, we intend to increase the share of highly connected vehicles. (**c**) Shows the distribution used for the strategy _inverse_, where weights are inversely proportional to the “percentage trip duration under coverage”. By using such distribution, we intend to democratize the coverage. the trapezoidal rule [55], a technique for approximating the definite integral. Computing the integral demands partitioning the integration interval, applying the trapezoidal rule to each sub-interval, and summing the results. The approximation becomes more accurate as the resolution of the partition increases. In this work, we consider 1000 partitions dividing the \(x\)-axis (that has range [0...1]). In order to be more didactic, now we present an illustrative example: Let us suppose that we have only two vehicles traveling along the road network divided into 5 cells. Let us also assume that such vehicles remain the same amount of time inside each cell, and we have communication devices for covering only two cells (\(\alpha=2\)). Vehicle \(v_{1}\) crosses cells [1,2], while vehicle \(v_{2}\) crosses cells [1,3,4,5]. \[ \begin{array}{l}v_{1}=\{1,2\};\\ v_{2}=\{1,3,4,5\};\end{array} \]  
Since _cell 1_ is crossed by both vehicles, it intuitively maximizes the area under the Delta curve. After covering _cell 1_, we have vehicle \(v_{1}\) covered during 50% of the trip, and vehicle \(v_{2}\) covered during 25% of the trip. Figure 5a plots the Delta Network for this hypothetical scenario. Point \(A\) is (\(\rho_{1}=0.00\), \(\rho_{2}=1.00\)), i.e., 100% of vehicles are covered during 0% of the trip duration (true, vehicles \(v_{1}\) and \(v_{2}\)). Point \(B\) is (\(\rho_{1}=0.25\), \(\rho_{2}=1.00\)), i.e., 100% of vehicles are covered during 25% of the trip duration (true, vehicles \(v_{1}\) and \(v_{2}\)). Point \(C\) is (\(\rho_{1}=0.50\), \(\rho_{2}=0.50\)), i.e., 50% of vehicles are covered during 50% of the trip duration (true, vehicle \(v_{1}\)). Point \(D\) is (\(\rho_{1}=0.50\), \(\rho_{2}=0.00\)), i.e., no vehicle is covered more than 50% of the trip duration. Moreover, the plot indicates that covering _cell 1_ leads to area = 0.375.