Abstract
Maximum Flow Problem (MFP) discusses the maximum amount of flow that can be sent from the source to sink. Edmonds-Karp algorithm is the modified version of Ford-Fulkerson algorithm to solve the MFP. This paper presents some modifications of Edmonds-Karp algorithm for solving MFP. Solution of MFP has also been illustrated by using the proposed algorithm to justify the usefulness of proposed method.
Highlights
The maximum amount of commodities that can be shipped through any network from source to sink is called maximum flow and this problem is called Maximum Flow Problem (MFP), which is a classical network flow problem
A modified Edmonds-Karp algorithm is proposed to compute maximum amount of flow from source to sink for a MFP
Given a flow network and a flow, the residual network consists of edges that can admit more flow
Summary
The maximum amount of commodities that can be shipped through any network from source to sink is called maximum flow and this problem is called MFP, which is a classical network flow problem. Network flows problem has got a vast application in the field of Mathematics, Computer Science, Management and Operations Research. At first the effective solution procedure to obtain the maximum flow in a flow network was introduced by Lester R. The improvement of the Ford-Fulkerson method is Edmonds-Karp algorithm [3] which observed that augmenting along shortest paths leads to a polynomial-time algorithm, and performs better than the previous one. (2016) Modified EDMONDSKARP Algorithm to Solve Maximum Flow Problems. Very recently, Ahmed, F. et al [17] and Khan, Md. A. et al [18] proposed new approaches for finding maximum flow problem. A modified Edmonds-Karp algorithm is proposed to compute maximum amount of flow from source to sink for a MFP. Numerical illustration of the proposed algorithm is done by solving a good number of examples to test the effectiveness and usefulness of the proposed algorithm
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