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Edmonds-Karp algorithm says that shortest distance between source s and sink t is increases monotonically every time shortest path is augmented. With this assumption distance between source s and sink t is going to be not more then |V| - 1. I think it means that there would be no more path between source S and sink T after |V| - 1 augmentation. If this is true , then complexity of finding maximum flow would be (|V| - 1) * E.

I know i wrongly assumed something above. But couldn't understand what it is. Can anyone help me ?

rishabh mittal
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In my copy of Introduction to Algorithms (probably an early edition) they say "increases monotonically" in lemma 27.8 but what they really prove is that if it decreases there is a contradiction. Where they refer to this lemma in theorem 27.9 they just say since DELTAf(x,v) <= DELTAf'(S,v) so it looks like when they say increases monotonically they really mean "does not decrease" or "increases or remains the same". If it can remain the same, you cannot use it to bound the number of iterations as you have done.

mcdowella
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