Questions tagged [ford-fulkerson]

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Edge connectivity using flow network

Find an algorithm for edge connectivity in undirected graph using flow networks. Try to use $O(m)$ edges. So basically the flow network should be used as a "helper function" and the graph ...
popcorn's user avatar
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122 views

Why in Edmonds Karp or Ford Fulkerson Algorithm the time complexity of BFS or DFS respectively is O(E) rather than O(V+E)?

For these algorithms, the time complexity of BFS and DFS is O(E). I have gone through many websites and even the algorithm books, but I never got a clear idea of why it is O(E). It just says it's O(E) ...
CaptainHow's user avatar
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1 answer
138 views

How to find the subsets S and T and the min-cut of this graph?

I get the residual graph by Ford-Fulkerson Algorithm: I get that the minimum cut can be found by the residual graph, and when traversing this residual network from the source to all reachable nodes, ...
waxyao's user avatar
  • 3
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0 answers
106 views

Network flow - properties of a vertex that belong to any minimum cut

while solving some questions about network flow I was wondering about the following statement: Given a network flow (a graph $G=(V,E)$ with a source $s \in V$ and sink $t \neq s \in V$) > and an ...
Yarin's user avatar
  • 275
2 votes
1 answer
79 views

Will the Ford-Fulkerson Algorithm always return the same min-cut for any source-sink from one side of the min-cut to the other?

I was playing around with https://visualgo.net/en/maxflow when I realized a pattern: Take this graph, for example. We notice that the min-cut divides the graph into two sets of nodes: {0, 2, 3, 6} ...
Green Ideology's user avatar
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1 answer
188 views

Finding the nodes in the source and sink side of a min-cut

We are learning of the Ford-Fulkerson Algorithm for max-flow/min-cut, and I have been wondering of the following question: How do we exactly find which nodes are on the "sink" side of the ...
Green Ideology's user avatar
-1 votes
1 answer
511 views

Maximum Flow algorithm. How to prove the following statements

Good Evening, So I am trying to solve this exercise which is a paticular case of maximum flow algorithm. Here the graph must have all even edges and 1 odd edge and it must have a maximum flow that is ...
ConScience's user avatar
1 vote
1 answer
84 views

Can distance from source to any of the vertex decrease during the run of Ford Fulkerson algorithm?

During the run of Ford Fulkerson algorithm if we label each vertex with d(v) where it means the shortest path distance from source to vertex v in residual graph. Is it possible that for some vertex ...
AmacOS's user avatar
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1 answer
2k views

How to find a crticial edge in a flow network?

The complete question is as follows: An edge of a flow network is called critical if decreasing the capacity of this edge results in a decrease in the maximum flow. Give an efficient algorithm that ...
Jash Shah's user avatar
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1 answer
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Max flow bottleneck approach flow after k iterations

This is a question from a previous exam in Graph theory and algorithms, the correct answer is E but I don't understand why. Given a network flow $(G,c)$ over graph $G(V,E) $. Assume we run Edmonds-...
Danny Blozrov's user avatar
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1 answer
70 views

Finding source-like nodes in a flow notework

Let $G$ be a flow network, where $c(e)$ is the capacity of an edge, and the source is $s$ and sink $t$. Define a node $v$ to be "source-like" if for every min-cut $(S,T)$ of $G$ where $S$ ...
Addem's user avatar
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0 answers
190 views

How to solve a specific dining problem with max flow network?

n people named i are invited to a party. They are a(i) years old. We want to position them on some tables by obeying the following criteria: Each guest must sit around a table. Each table should have ...
AriyaDey's user avatar
0 votes
1 answer
110 views

How to find the maximum number of square groups in a board

I'm stuck with the following problem: Given an n*m board, find the maximum number of square groups that can be positioned on the board. What are square groups? They contain 4 distinct squares named: ...
AriyaDey's user avatar
1 vote
1 answer
672 views

find edges such that if decreased by one unit, the max flow decreases as well

We are given a flow network $G = (V,E,c)$, where $c$ is the capacity function as well as a maximum flow $f_m: E\rightarrow \mathbb R$ from $s$ to $t$. The goal is to find edges such that if decreased ...
emma funkhouser's user avatar
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Min cut with smallest number of edges [duplicate]

Cormen's Algorithms 3rd edition Exercise 26.2-13 Page 731: Suppose that you wish to find, among all minimum cuts in a flow network G with integral capacities, one that contains the smallest number of ...
chesslad's user avatar
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How to find all minimum cuts in network flow [duplicate]

In a network flow graph, using the Ford–Fulkerson algorithm, we can find a residual graph G_f which no augmenting paths. This gives us a way of finding one minimum ...
Charlie Brown's user avatar
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1 answer
234 views

Multi Source/Sink Max Flow Alternative Reduction

When solving a multi source/sink max flow problem, the classic reduction to the single source/sink problem is to add a new source and sink node with infinite capacities that connect to/from the ...
gowrath's user avatar
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1 answer
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Flow graph with non zero lower bound or 0 capacity

I am afraid the question title might not be sufficiently accurate but I could not come up with something more accurate Here is the problem Given 'n' machines Each machine has a set of capabilities ...
Peter Coppens's user avatar
3 votes
1 answer
304 views

How to apply the Ford Fulkerson algorithm to the assignment problem

I am quite familiar with Ford-Fulkerson algorithm but I am having a trouble to apply the algorithm to the following problem. Can someone please give me some hints or better instructions how to use FF ...
Alex C's user avatar
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1 answer
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Minimum cost flow and Ford-Fulkerson

I have a question concerning the use of the Ford-Fulkerson algorithm. Since a minimum cost flow problem is a linear programming problem, it has a dual problem. That dual would be to maximize a certain ...
rak81's user avatar
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2 votes
0 answers
97 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 ...
Ido's user avatar
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0 answers
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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?
Shruti Katpara's user avatar
1 vote
2 answers
311 views

Find max flow in a network with all capcities of $\sqrt 2$ and one with 2

Given a graph $G(V, E)$ with capacities on the edges such that all edges have a capacity of $\sqrt2$ apart from one edge with a capacity of 2. need to find max flow efficiently. I can run Dinic on ...
BOB123's user avatar
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2 votes
1 answer
1k views

Ford-Fulkerson pseudo-polynomial

Can somebody explain please why Ford-Fulkerson Algorithm has pseudo-polynomial complexity? I understand that the complexity in this case strongly depends on the capacities of the edges of the network, ...
user12632521's user avatar
3 votes
1 answer
270 views

is it possible to find the maximal min cut in polynomial time?

A maximal minimum cut is a minimum capacity cut with the largest number of edges.
42069walrus's user avatar
14 votes
2 answers
1k views

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 ...
ryan's user avatar
  • 4,451
1 vote
1 answer
1k views

Min-cut in a network with zero flow from source to sink

The max-flow min-cut theorem guarantees that the min-cut of a directed network equals the maximum flow. And we can compute $S$ and $T$, are disjoint subsets containing source node and sink node ...
Ozymandais's user avatar
1 vote
1 answer
88 views

What is a flow through the cut in the Ford-Fulkerson algorithm?

In page 12 of the slide, it states flow across a cut $(S, T)$ is $f(S, T) = \sum_{u\in S} \sum_{v\in T} f(u,v) - \sum_{u\in S} \sum_{v\in T} f(v,u)$. I think the first part $\sum_{u\in S} \sum_{v\in ...
user8314628's user avatar
1 vote
1 answer
40 views

Flow value over edges in Max flow/Min Cut Ford Fulkerson

Is it true that if a given edge e is in the min cut of a graph that there exists a max flow of the graph that has e with its full capacity?
Adi Lapp's user avatar
0 votes
1 answer
339 views

Which flow algorithm on a graph is used when the capacity is a rational number?

Does ford fulkerson only use whole numbers? I tried to understand this but without success Thank you
Adi Lapp's user avatar
1 vote
1 answer
3k views

Given max-flow determine if edge is in a min-cut

We were given an exam question of: Given a flow network G=(V,E) with integer edge capacities, a max-flow f in G, and a specific edge e in E, design a linear time algorithm that determines whether or ...
Scooter2000's user avatar
2 votes
1 answer
826 views

Minimum cost node cut

I am interested in solving the following problem: Given an undirected graph whose vertices are weighted, find a subset of vertices of minimal weight whose removal disconnects the graph. Is there ...
SaRa's user avatar
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1 vote
0 answers
95 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: ...
Nakul Ram's user avatar
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0 answers
36 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 ...
S K's user avatar
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0 answers
45 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 ...
trill.o.beat's user avatar
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0 answers
167 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 ...
Dr C's user avatar
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0 answers
554 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 ...
SleekPanther's user avatar
2 votes
1 answer
392 views

Question on pseudocode for Ford-Fulkerson in Kleinberg-Tardos Text

I am looking at the following pseudocode from the Kleinberg-Tardos text "Algorithm Design". ...
ClownInTheMoon's user avatar
0 votes
1 answer
544 views

Maximum flow properties

I was trying to solve problems in max flow algorithms. And I came across this MIT Lecture Quiz. http://people.csail.mit.edu/moitra/docs/6854hw4.pdf solution : http://people.csail.mit.edu/moitra/docs/...
learner's user avatar
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0 answers
81 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 ...
Revolucion for Monica's user avatar
3 votes
1 answer
6k views

Checking if a given flow is a maximum flow

I'm curious as to if there's any way to check (without having to run a 'whole' maximum-flow-algorithm) whether a given flow $f_e$ is the maximum flow of the flow graph $G$ in $O(|E|)$ time complexity. ...
Nyfiken Gul 's user avatar
1 vote
1 answer
301 views

Operation of the Ford–Fulkerson algorithm given an almost maximum flow [closed]

I have been assigned the question: Let $G$ be a flow network and $f^*$ be the maximum flow computed by the Ford-Fulkerson algorithm. Consider a new flow network $G'$ constructed by increasing the ...
Eric Nelson's user avatar
4 votes
1 answer
5k views

Algorithm for solving incremental max flow problem

I am working on a project where I need to be able to compute the maximum flow between two nodes in a graph after one of the edge weights has been incremented or decremented by 1. The graph is directed ...
flapdoodle's user avatar
1 vote
1 answer
506 views

Can max-flow with mutually exclusive edges be reduced to standard max-flow problem?

I'm working with a flow network like the following: The source s has four edges, each with capacity 1, out to the nodes A, B, C, and D. All of A, B, C, and D have edges to two other nodes, X and Y, ...
Jeremy's user avatar
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1 answer
2k views

Multiple matching in Maximum Flow problem?

I'm sorry if this has already been asked before, but I couldn't find any similar questions. The situation is as such: Assume there are x restaurants, each with a capacity q, and y people, each of ...
podington's user avatar
5 votes
0 answers
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.
Dvir Samuel's user avatar
3 votes
1 answer
1k views

Ford-Fulkerson Algorithm not "pushing back" flow

I am told that with every flow network, the Ford-Fulkerson algorithm produces an execution that never decreases the value of the flow on any of the edges (i.e. never “pushes back” the flow on any of ...
jacobybryant23's user avatar
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0 answers
519 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 ...
Sergey Kopeliovich's user avatar
5 votes
1 answer
3k views

Will the Ford-Fulkerson algorithm always find the max flow if we start from a valid flow?

I stumbled across this question and answer (source): Question: Suppose someone presents you with a solution to a max-flow problem on some network. Give a linear time algorithm to determine ...
Michal Tenenberg's user avatar
2 votes
0 answers
758 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 ...
harun_a's user avatar
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