Application of the Ford-Falkerson algorithm to detect excess information

Abstract

The object of the article is the network maximum flow algorithm, mainly the Ford-Fulkerson algorithm. The algorithm began to be developed by two scientists: Ford and Fulkerson. This algorithm was proposed in order to find the maximum flow in the network. They began to be actively studied by scientists from the middle of the last century. The first report of "Maximum Network Flow" dates back to 1954. The authors of the report, Ford and Fulkerson had proved the theorem on the maximum flow and the minimum cross section for non-oriented graphs: the value of the maximum flow in the network is equal to the minimum throughput capacity of the section. The interest in the solution of these tasks was primarily due to practical needs, for that time construction of routes for the transportation of raw materials was not optimal and transported more raw materials than can transfer the connection between points. Such problems often arise when constructing connections that transport oil through pipes or transport coal through special excavators. The subject of the article is the problem of finding the maximum flow in the network. In graph theory, the transport network is an indicative graph in which each arc has no negative throughput and flow. Two peaks are distinguished: source and drain - such that any other vertex in the network lies on the way from source to drain. The article consists of two sections. In the first section we consider the mathematical formulation of the problem and concrete examples of problems. The second section examines the classic Ford-Fulkerson algorithm, the modified Ford-Fulkerson algorithm to find excess information on the network, and the work of a modified algorithm on a specific example from the first section. The considered problems are relevant both from a theoretical and a practical point of view.