## 3 Problem Description
We assume a speed of 60 km/h for the UAVs to allow for a good exploration of the road network. Figures 5 and 6 show the difference a refueling station at a victim location can make. Figure 5 shows the situation with only the DMC is working as a refueling station, while in Figure 6, victim node 1 is a potential refueling station. This refueling station can be used in case victim location 1 is connected to the DMC by functional roads. In Figures 5 and 6, the UAV starts at the DMC. It first explores the road to road crossing 5 (0,5). Next, the UAV tries to reach victim location 6 using (5,6). However, a disruption is detected, and the UAV returns to the DMC directly using an aerial edge. Starting again at the DMC, the UAV explores the edges (0,2) and (2,1). It has now reached victim node 1. It now wants to explore the edge (1,3). However, there is not enough fuel left to reach road crossing 3 and return to the DMC. Figure 5 shows that the UAV returns directly to the DMC on an aerial edge due to the fuel shortage. In Figure 6, there is a different solution to the fuel shortage. Victim location 1 is a potential refueling stations. It is already established that there are functional roads (0,2) and (2,1) connecting it to the DMC. Thus, the UAV can refuel at victim node 1 and then continue by exploring (1,3). Figure 4: Example of the relationship between networks involved in the on-line UAV routing problem. For the tackled problem, we made the following assumptions:  
1. The road and the aerial network are undirected networks. 2. Both the road and the aerial network are used: if an interruption is detected on a road, the route of the UAV is redirected using the aerial network. 3. The UAV route starts and ends at the DMC. 4. In the pre-disaster stage, all roads of the known network work. No initial information about the road network state after the disaster is given. The exploration of the road network starts under this assumption. 5. The length of each edge on the road and the aerial network is known. 6. The disruptions are not known in advance and might occur on any edge of the road network after the disaster. 7. We assume a constant speed of the UAV. 8. A pilot on the ground monitors the flight progress at the DMC. 9. The pilot determines if a road is disrupted or not. 10. Based on the extracted real-time information, it is determined if a victim location is reachable by road or not. 11. The DMC and a certain percentage of the victim locations can operate as refueling stations. Victim locations that can operate as refueling stations must be connected to the DMC by road. 12. Staff to refuel the UAV are available at refueling stations. 13. The exploration duration is defined as the flying time and the refueling time of the UAV. 14. The type of UAV to use depends on the characteristics of the known road network to be explored. The flying range of the UAV should be at least the distance of the longest aerial edge connecting the DMC to the farthest node in the network. Figure 5: Example of the flying range limitation with only the DMC working as a refueling station. Figure 6: Example of the flying range limitation with the DMC and victim location 1 working as a refueling station. Assumptions 11 to 14 extend [PERSON] et al. [4].