Reduction of the asymptotic complexity of the assignment problem

Abstract

The assignment problem belongs to an extensive class of managerial decision-making tasks. One of the urgent tasks related to this class is the problem of effectively combining various streams (resources). The main purpose of the method modifications is to reduce the asymptotic complexity and to consider the specifics of the subject area. The article describes the solution of the assignment problem on a bipartite sparse graph. The main purpose of the method modifications is to reduce the asymptotic complexity and to consider the specifics of the subject area. A modification of the Hungarian method is proposed. The method is based on the successive shortest path algorithm and Dijkstra’s bidirectional search algorithm. The modification led to a decrease in the asymptotic complexity of the problem.