Development of an Algorithm for all type of Network Flow Problems

Abstract

We develop an algorithm which reduces the arbitrary instance of the network flow problem to a simple path disjoint network in polynomial time. Then the flow in each path is taken as the minimum of the arc capacities of that path from where the flow in each arc can be easily determined. The polynomial time algorithm can determine any instance of the network flow problem faster than the previously existing algorithms . An example has been given to elucidate the process. At the end a MATLAB program based on this algorithm has been given. General TermsNetwork flow problem, computational complexity KeywordsMaximum Flow Network Problem (MFNP), Simple path disjoint network, polynomial time algorithm.

Reduction of Maximum Flow Network Interdiction Problem: Step towards the Polynomial Time Solutions

“…The algorithm was earlier proposed by us in [25], here we present a modified form of that algorithm. A network is 4.…”