# Questions tagged [network-flow]

Network flows are used to model concepts like traffic or water pipe systems. The basic idea is to move as many units of flow from source to sink nodes via edges with limited capacity.

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### shortest path increases monotonically => a bound on the length of one iteration of Edmons-Karp is then O(E) ... Convince me this is true

I was reading the proof of time-complexity for the Edmonds-Karp algorithm here (https://brilliant.org/wiki/edmonds-karp-algorithm/). Everything in the first part of the proof (The section ...
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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 ...
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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-...
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### Maximum flow in integer flow network

Let's say you have a maximum integer flow function in a network with 7 directed edges, meaning the flow cannot be increased anymore. The capacity of each edge is then increased by one. The capacity of ...
1 vote
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### Dominators when node not reachable

For the definition of domination [Wikipedia], a node $d$ of a control-flow graph dominates a node $n$ if every path from the entry node to $n$ must go through $d$. If node $n$ is not reachable from ...
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### Solving the maximum flow problem in the real world

Is it possible to solve the maximum flow problem in the real world, ie. using water running through physical pipes? So you would have a tap at the source node, pipes of various diameter (depending on ...
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### Show a reduction of max flow to min cost

Show a reduction of max flow to min cost (not min cost max flow!!)
1 vote
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### 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 $S$ ...
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### 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: ...
1 vote
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### 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 ...
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### What does this mean $[X]_1^T$?

I found this in information theory paper, P.3883* the authors states the following Most existing theoretic studies of network coding focus on DAGs due to its simpler structure and dure to the fact ...
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### Possible ways to have cross and full edges in a mincut maxflow

I am trying to solve the following problem about maxflow mincut it seems like my conclusion is incorrect and I am wonder where. There is no graph just following question. An edge e can be (x) ...
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### Max flow algorithm for floating-point weights and E~=10*V

Could you, please, suggest a maximum flow algorithm for a graph with floating-point weights and the number of edges approximately equal to the number of vertices? I.e. ...
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### Looking for an algorithm for multi-path funnel analysis

Suppose we have a dataset with each instance: {uid, action, TS}. The funnel algorithm (e.x https://clickhouse.com/docs/en/sql-reference/aggregate-functions/parametric-functions/#windowfunnel) looks at ...
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### Does a path exist going through each color only once?

I have a directed, colored graph (each node has a color), and I want to find if a path from node A to node B exists such that the path goes through each color at MOST once. I think this problem can ...
1 vote
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### Covering maximal number of sets using fixed number of elements

I've encountered some problem which seems general enough to have already been solved. There is a set of objects $O=\{o_1, o_2,\dots,o_k\}$ and a family of sets $A_1,A_2,\dots,A_t \subseteq O$. For ...
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### Ensure a vertex has the highest flow in max-flow algorithm

Let's suppose we have a supplier, sorting facilities, shipping companies and a target warehouse. We produce n packages of the product, and each goes to a different sorting facility (so every facility ...
1 vote
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### Proof that using residual network from Ford-Fulkerson will get you min-cut

So I'm following this article and they use the following algorithm to find the min-cut. Algorithm: Run Ford-Fulkerson algorithm and consider the final residual graph. Find the set of vertices that ...
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### Lucky Ford Fulkerson

I know that Ford Fulkerson might not terminate. But if we assume we know in advance it terminates for some G, and we always pick the "correct" augmenting path, can we upper bound the number ...
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### Linear programming and network flow

I would like some hint in this homework question. I have to write the max-flow problem (with souce $s$ and sink $t$) as a linear program. I have to do this by defining variables on each $s - t$ path, ...
217 views

### Integral solutions to circulation problem

Suppose we have a circulation problem (with only one commodity), where all lower bounds, upper bounds, and costs are integers. Are we guaranteed that if there is a solution, then there is an integral ...
1 vote
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### Citation for finding node disjoint paths using maximum flow

We can find the maximum number of vertex disjoint paths in a directed graph using maximum flow algorithm keeping the node capacity and edge capacity to one. I could not find the reference paper for ...
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### Edmonds-Karp shortest path vs largest bottleneck

Depending on where I look, some places (https://courses.engr.illinois.edu/cs473/sp2009/notes/19-maxflowalgs.pdf) describe EK algorithm as choosing the st path with ...
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### Which one of the following is NOT a function of transport layer?

A. routing B. flow-control C. congestion control D. All of the above My guess is flow-control only because routing and congestion is part of the network layer. The network layer is the third later and ...
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Let $S= \{ b_{11}, b_{12}, b_{21}, b_{22}, b_{31}, b_{32},\dots, b_{n1}, b_{n2} \}$ be a set of $2n$ balls grouped in $n$ pairs, and $T = \{ B_1, B_2, \dots, B_m\}$ be a set of $m$ bins with ...
The proof that the Edmonds-Karp algorithm will require at most $O(|V||E|)$ uses the fact that when an augmenting path has critical edge $(u, v)$, $\delta_f(u)$ strictly increases. Therefore, that ...