Analysis algorithm of shortest paths in dynamically reconfigurable graph structures with variable topology: evaluation of the average number of transformations to reach target nodes

This article addresses the problem of finding the shortest paths in dynamically changing graphs with variable topology. The relevance of the research is driven by the need to develop algorithms capable of operating in changing environments, such as warehouses with movable shelves or mazes with shifting walls. The scientific novelty lies in the proposal of a greedy algorithm that selects the optimal graph transformation at each step to approach the target vertex. The algorithm is implemented in C# and tested on randomly generated graphs. Experimental results show that the average number of transformations depends on the graph configuration. The algorithm demonstrated high efficiency in solving problems related to logistics optimization, robotics, and complex systems modeling. Future work will focus on improving the algorithm to handle more complex graphs and topologies.