Experimental Analysis of the Multidimensional-Matrix Approach to Construct Routes in a Graph

— The algorithms for calculating the weights of routes between all pairs of graph vertices have polynomial computational complexity. However, the construction of the routes themselves belongs to the NP class. The heuristic algorithms that allow reducing the computational complexity of this problem, as a rule, require careful statistical analysis to prove their effectiveness, are focused on specific types of graphs, and require artificial tricks for their parallel implementation. In this paper, an experimental analysis of the approach to construct routes in a graph based on the algebra of multidimensional matrices is carried out. The proposed approach, based on the (1, 0)-convoluted product of multidimensional matrices, makes it possible to find all possible routes in a graph and implement parallel computations due to the natural parallelism inherent in matrix algebra. In addition, since the algebra of multidimensional matrices is isomorphic to relational algebra under the conditions of the problem of constructing routes, the possibility of parallel implementation of work with sparse matrices using database technology is shown. An experimental analysis of the implementation of the proposed approach based on the software developed in the programming environment using C++ and the relational database tools PostgreSQL and Microsoft SQL Server is presented. The proposed approach allows us to set up a one-to-one correspondence between the data model and the computational model.