# Minimizing the Number of Distrustful Nodes on the Path of IP Packet Transmission
## 3 Results and Discussion
### Large Topology Scenario  
The topologies of the previous examples of networks were formed by their successive expansion and complication. In the following example, we consider a large network of arbitrary topology, the dimensions of which are chosen from the point of view of the comfortable recognition of its image. The following scenario (Figure 15) depicts the case of the presence of a distrustful node in the center of the AS and several distrustful nodes on its borders. To visually illustrate the potential possibilities of using the proposed solution, it is displayed on the background of the Ukraine map. But note that this is not an illustration of the real network. In general, it can be any Autonomous System of the Internet.  
The distrustful nodes in the network are routers K, Q, R, T, U, and Y. Node K is located in the middle of the network and there are 6 nodes (G, H, J, L, O, N, and M) connected to it. Nodes Q, R, T, U, and Y are located on the periphery of the network and the number of connected nodes is relatively smaller.  
Let us choose router B, for which the routing table should be constructed. So, node B will be the root of the shortest path tree that needs to be built.  
To begin with, consider what the shortest path tree will look like for the classic Dijkstra algorithm (Figure 16).  
Figure 14: The shortest path tree for the (a) classical Dijkstra algorithm and (b) modified Dijkstra algorithm.  
Now, for comparison, consider the shortest path tree built using a modified algorithm (Figure 17).  
Figure 16: The shortest path tree, according to the classical [PERSON] algorithm.  
Figure 15: The topology of a large network.  
As can be seen from Figure 16, the distrustful node K takes part in transporting packets to the trustful nodes M, N, O, P, and L, because the paths through it are the shortest. Distrustful nodes Q, R, and T are the end nodes of the tree branch, so there are no other paths to them. Node U is a transit node to node Y, to which there are also no bypasses.  
Let us now compare the results of our modification of the algorithm (Figure 17) and [PERSON]'s algorithm (Figure 16). Considering the end nodes Y, T, R, and Q, we can conclude that the paths to them have not changed, because there are no bypass paths for them. However, we can see that distrustful node K is no longer a transit node for paths to nodes M, N, O, and L. Now, the distrustful node K is an end node for a branch of this tree. Paths to nodes M, N, O, and L are now safe, but are longer than in the case of the classical algorithm. In the shown example, with the classical algorithm, the path to node M was B\(\rightarrow\)E\(\rightarrow\)H\(\rightarrow\)K\(\rightarrow\)M and was four hops long, but contained a transit distrustful node K. Our modified algorithm found a bypass for this node, which is now B\(\rightarrow\)E\(\rightarrow\)H\(\rightarrow\)J\(\rightarrow\)S\(\rightarrow\)O\(\rightarrow\)N\(\rightarrow\)M and is eight hops long. In delay-tolerant networks [30], the proposed approach can be recommended without any reservations; in time-critical networks, the ratio of security and delay requirements needs to be analyzed.  
The algorithm works optimally for all possible cases of the location of distrustful routers, as follows: when it is possible to bypass the distrustful node; when there is no possibility to bypass the distrustful node and it must be transitive and when distrustful routers are located both in the middle of the autonomous system and on its periphery. The algorithm works optimally regardless of how many neighboring nodes are connected to the distrustful router and what type of safety they have.