Graph Clustering for Application to the Shortest Path Search Problem

The application of shortest path algorithms remains relevant despite the historical bulkiness of these approaches. This topic is also related to the need to not only consider the computational complexity of algorithms as theoretical aspects of time based on the traversal of vertices and edges, but also practical estimation of the running time of the software implementing the algorithm. This study describes the proposed graph clustering method for application in the problem of finding the shortest path and increasing the speed of the Bellman-Ford algorithm by reducing the set of considered vertices. The mathematical formalization of the graph clustering method is described, including the steps of the algorithm operation under the conditions of the modified graph utilization method, the unconditionality of such an approach in the process of use in the shortest path search problem is evaluated. The effectiveness of the proposed graph clustering method for reducing the execution time of the Bellman-Ford algorithm due to the reduction of the considered vertices in the graph is analyzed. A software implementation is proposed to perform graph clustering for further use in the shortest path search method based on the Bellman-Ford algorithm. An experiment is also conducted to compare the speed of performing the shortest path search by the Bellman-Ford algorithm under different graph utilization approaches, which results that the graph clustering method is 75% faster than the classical algorithm and also faster than the maximum distance constraint method obtained by restricting the area of the considered vertices by 38.89%.