## 5 Methods and Materials
Instead of assigning the same weight for all classes of coverage (as done by the strategy _balanced_), _direct_ assumes weights equal to the value to the percentage of trip duration under coverage (weight = \(\rho_{1}\)), as presented in Figure 4b. By doing so, the strategy increases the reward for covering highly connected vehicles (instead of maximizing the area under the Delta curve). Figure 8 shows the comparison between _dl_ and _direct_. In Figure 8a-c, we notice that _direct_ reduces the coverage for low connected vehicles, increasing the coverage for highly connected ones, as indicated by marks \(H\), \(I\), and \(J\) in such figures. We notice a distinct shape of coverage, different than the one presented by strategy _balanced_ in the previous section. Such distinct shape of coverage is highlighted in Figure 8d-f, where the first half of the green area is negative (indicating the reduction of coverage for low connected vehicles), and the second half is highly positive (indicating increase of coverage of highly connected vehicles). Such shape of coverage is interesting when the applications running on top of the vehicular network demand highly connected vehicles (such as streaming delivery). Figure 9a-d show the layout of roadside units provided by _direct_. Just like the strategy _balanced_, the strategy _direct_ also deploy roadside units in circles from the epicenter of traffic. However, the layout provided by _direct_ is much more concentrated around the epicenter of traffic (assuring more connectivity to highly connected vehicles). The pattern is characterized by connected islands of coverage along the core of the road network, an interesting topology when we intend high connectivy of vehicles in special zones, such as commercial zones in the city. Figure 7: Layout of roadside units deployed by _dl_ and _balanced_. (**a**) Shows the Cologne traffic. The darker the area, the more intense is the flow. (**b–e**) Show the layout of roadside units deployed by _dl_ for covering 5%, 10%, 15%, and 20% (respectively) of the road network. Similarly, (**f–i**) present the layout of roadside units deployed by _balanced_ for covering the same scenarios. Strategy inverse: Distribution of Weights Inversely Proportional to the Percentage of Trip Traveled under Coverage: An Alternative to Prioritize Vehicles with Low Coverage  
Strategy _inverse_ assumes weights inversely proportional to the \"trip duration under coverage\" (i.e., weight = \(1-\rho_{1}\)), as presented in Figure 4c. It increases the reward for covering low connected vehicles, an interesting strategy when we intend to provide small contact opportunities for a large share of vehicles. Figure 10 characterizes the strategy _inverse_ using _dl_ as baseline. We notice that _inverse_ provides more connectivity than _dl_ for all three scenarios presented in Figure 10a-c. When considering the shape of coverage, Figure 10d,e show better coverage when compared to other strategies in the first half of the \(x\)-axis (indicating that _inverse_ is prioritizing the coverage of vehicles with small connectivity along the trip), while Figure 10e,f show the green curve negative for \(\rho_{1}>0.80\), showing reduction in terms of highly connected vehicles. Figure 8: Strategy _dl_ deploys roadside units at the most popular locations (red color), while _direct_ assumes a distribution of weights equal to \(\rho_{1}\) (color blue). The \(y\)-axis indicates the share of vehicles (\(\rho_{2}\)), while the \(x\)-axis indicates percentage of trip under coverage (\(\rho_{1}\)). (**a–c**) Consider coverage ranging from 5% up to 15% of the road network. (**d–f**) Represent the difference _“direct_ minus _dl_”. Figure 9: (**a–d**) Show the layout of roadside units deployed by _direct_ for covering 5%, 10%, 15%, and 20% (respectively) of the road network. We notice that _direct_ presents a denser distribution of roadside units around the epicenter of traffic when compared to strategy _balanced_ (Figure 7f–i). Figure 11a-d Show the layout of roadside units provided by _inverse_.