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.
In the present work an attempt is being made to reduce the Maximum Flow Network Interdiction Problem (MFNIP) in to the Subset Sum Problem so as to get some algorithms solvable in polynomial time. Previously developed algorithms are either applicable to some special cases of MFNIP or they do not have a constant performance guarantee. Our reduction has paved the way towards the development of fully polynomial time approximation schemes for Maximum Flow Network Interdiction Problem.
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