Is Ford-Fulkerson algorithm unique?

Necessity Suppose there is a different flow than the original one (with the same total value), with at least one of the edges flowing a different amount. Say that, for each edge, the flow in the alternative solution is not less than the flow in the original solution.

What is Ford-Fulkerson algorithm used for?

The Ford-Fulkerson algorithm is used to detect maximum flow from start vertex to sink vertex in a given graph. In this graph, every edge has the capacity. Two vertices are provided named Source and Sink.

Does Ford-Fulkerson always terminate?

The max-flow min-cut theorem along with the above observation ensures that with integral capacities, Ford-Fulkerson must always terminate and the number of iterations is at most: C = the sum of edge capacities leaving s. Hence complexity is O(m + nC).

What happens when the sink is Labelled in Ford-Fulkerson algorithm?

If we ever label the sink, then we will have discovered an augmenting path, and the flow will be suitably updated.

Does Ford-Fulkerson run in polynomial time?

1 Answer. Yes, the Ford-Fulkerson algorithm is a pseudopolynomial time algorithm. Its runtime is O(Cm), where C is the sum of the capacities leaving the start node. Since writing out the number C requires O(log C) bits, this runtime is indeed pseudopolynomial but not actually polynomial.

What is the termination criterion for Ford-Fulkerson algorithm?

Since ˆG has finite edge capacities, we already know that any execution of the Ford- Fulkerson algorithm on input ˆG will terminate with a flow f whose value is equal to the minimum cut capacity in ˆG.

What is an augmenting path?

Given a flow network , an augmenting path is a simple path from the source to the sink in the corresponding residual network . Intuitively, an augmenting path tells us how we can change the flow on certain edges in. so that we increase the overall flow from the source to the sink.