Graphical algorithms for solving minimal cost network flow problems and applications

This paper presents two algorithms, based on the simplex algorithm, which can be used to minimize linear functions of flow in a directed network or digraph. These algorithms can be preformed directly on the graph, and hence eliminate the need for simplex tableaus, and increase solution speed. In addition, the paper gives several examples of important applications for both of the algorithms. These include the minimal cost network flow problem, the shortest path problem, the traveling salesman problem, and a scheduling problem (longest path problem).