Questions tagged [ford-fulkerson]

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2answers
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Flow graph that requires pushing back flow in Ford Fulkerson

Does there exist a flow graph that always requires flow to be pushed back no matter what ordering of augmenting paths is chosen in Ford Fulkerson? Let's assume we use the standard procedure of ...
4
votes
0answers
2k views

Ford–Fulkerson with irrational numbers

I am trying to understand why Ford–Fulkerson Algorithm for finding maximum flows doesn't work with irrational numbers? I tried to draw several examples but it seems to work.
2
votes
0answers
18 views

Find a maximum flow that also maximizes the flow over a specific edge

Let $G=(V,E,c,s,t)$ be a flow-network, where $s$ is the source, $t$ is the target, and $c:E\mapsto [0,\infty)$ defines the capacity of every edge in the network. Let $e=(u,v)$ be an edge in the ...
2
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0answers
636 views

How can we add back edges in Ford - Fulkerson algorithm?

I was going through the Ford-Fulkerson(FF) algorithm. The given graph is directed and there is an edge from A to B with capacity y. Now sending a flow of x units (x < y) from A to B is equivalent ...
1
vote
0answers
72 views

Minimum changes to be made to get Max-flow between each pair of vertices in an undirected graph

I was asked the following problem in an interview: Let M be a N X N matrix, such that: ...
0
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0answers
43 views

Why does the Ford-Fulkerson Maximum flow algorithm not work for irrational capacities?

Can anyone help me understand why the Ford-Fulkerson algorithm does not work in the case of irrational capacities?
0
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0answers
35 views

MaxFlow Problem MinCut

Yesterday I found a question here, that asked, if the value of the flow across the edges of the MinCut is at capacity. I think the question has been deleted. But I want to confirm that for the edges ...
0
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0answers
41 views

The path with the highest sum of weights

Mr. Katsaros owns a rectangular olive grove divided into 5 rows and 4 columns. He notes down the amount of olives (pounds) possibly obtainable from each of 20 square sections. The picking starts from ...
0
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0answers
154 views

Will the Ford-Fulkerson method return any value if the residual network is ignored?

The normal Ford-Fulkerson method finds augmenting paths (as long as one exists) while including "back-flows", but if those back-flows are ignored, does there exist a flow network for which algorithm ...
0
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0answers
276 views

Running Time of Ford Fulkerson where all edges have equal capacity

My intuition says it would simply be the number of edges leaving s. I'm assuming it's a valid flow network so sum of capacities leaving s is the same as the sum of capacities entering t, so a max flow ...
0
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0answers
74 views

Applying Ford-Fulkerson to settle a business lunch

I want to organize a business lunch with two societies $E_1$ (mine) and $E_2$. Each society is made of four people from the Executive management and 6 of the Financial Management. I want to organize ...
0
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0answers
402 views

Ford–Fulkerson algorithm. Counterexamples

Consider Ford–Fulkerson algorithm (FF). Look to wiki : The following example shows the first steps of Ford–Fulkerson in a flow network with 4 nodes, source A and sink D. This example shows the ...