Algorithm for finding subcritical paths on network diagrams

Abstract

Objectives . Network diagrams are used as an information support element in planning and project management processes for structuring planned work and calculating project efficiency characteristics. In order to optimize and balance resources used in projects, it becomes necessary to locate in these models not only the critical path of the maximum weighted length, but also the subcritical paths closest to it having a shorter length in relation to it. The aim of the work is to synthesize and analyze an algorithm for finding k -shortest paths between the input and output network vertices, on which basis the above-mentioned subcritical paths can be identified. Methods . The provisions of graph theory and group theory, as well as the method of dynamic programming, were used. Results . An algorithm for finding k- shortest paths in contourless directed graphs having a strict order relation was developed. Abstract elements were defined according to group theory in graphs as p- contours, between which a multilevel structure of relations for implementing the necessary search of paths was then established. For substantiating the efficiency of the constructed algorithm, the validity of the main provisions was demonstrated as follows: firstly, the multilevel system of relations is exhaustive; secondly, there is no loss in the final solution during the operation of the algorithm; thirdly, the paths obtained as a result of the work of the algorithm satisfy the main required relation between them. Numerically, the algorithm was implemented by the dynamic programming method extended by means of an additional functional relationship, implying the presence of suboptimal policies. Conclusions . The conducted runs of computational experiments confirmed the operability and efficiency of the software-implemented algorithm. The performed analysis demonstrated the good convergence characteristics of the proposed algorithm as compared with other algorithms of this class applied to network diagrams. On this basis, it can be recommended for practical use in project management information systems.