The solution of the minimum cost flow and maximum flow network problems using associative processing

Abstract

The minimum cost flow problem exists in many areas of industry. The problem is defined as: given a network composed of nodes and directed arcs with the arcs having an upper capacity, lower capacity, and a cost per unit of commodity transferred, find the maximum flow at minimum cost between two specified nodes while satisfying all relevant capacity constraints. The classical maximum flow problem is a special case of the general minimum cost flow problem in which all arc costs are identical and the lower capacities of all arcs are zero. The objective in this problem is also to find the maximum flow between two specific nodes. Algorithms exist for the solution of these problems and are coded for running on sequential computers. However, many parts of both of these problems exhibit characteristics that indicate it would be worthwhile to consider their solution by associative processors.