Finding the Maximum Flow in a Network with Simple Paths

An efficient method is developed to obtain the maximum flow for a network when its simple paths are known. Most of the existing techniques need to convert simple paths into minimal cuts, or to determine the order of simple paths to be applied in the process to reach the correct result. In this paper, we propose a method based on the concepts of signed simple path and signed flow defined in the text. Our method involves a fewer number of arithmetic operations at each iteration, and requires fewer iterations in the whole process than the existing methods. Our method can be easily extended to a mixed network with a slight modification. Furthermore, the correctness of our method does not depend on the order of simple paths to be applied in the process.