For questions about networks that inhibit source and sink nodes and a notion of flow.

# Questions tagged [network-flow]

377 questions

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### Belt Balancer problem (Factorio)

So this question is inspired by the following thread: https://forums.factorio.com/viewtopic.php?f=5&t=25008
In it, the poster is examining an $8$-belt balancer (more on that to come) which he shows fails to satisfy a desirable property, which he…

Justin Benfield

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### Finding the max flow of an undirected graph with Ford-Fulkerson

Given the following undirected graph, how would I find the max-flow/min-cut?
Now, I know that in order to solve this, I need to redraw the graph so that it is directed as shown below. However, after this, I'm stuck. I chose the olive-colored path…

audiFanatic

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### Probability of global epidemic

Consider $\mathbb{Z}^2$ as a graph, where each node has four neighbours. 4 signals are emitted from $(0,0)$ in each of four directions (1 per direction) . A node that receives one signal (or more) at a timestep will re-emit it along the 4 edges to…

TROLLHUNTER

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### Max flow min-cut after a change in edges of capacity 1

I have been asked the following question:
Let G be an input graph to the max flow problem. Let (A, B) be a minimum capacity s−t cut in the graph. Suppose we add 1 to the capacity of every edge in the graph. Is it necessarily true that A is still a…

jam

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### Definition of capacity of cut in a flow network

In the flow network below, an S-T cut is made.
The net flow across the cut is $12-4+11=19$.
The capacity of the cut is $12+14=26$. The "backwards" edge $(v_3,v_2)$ is not counted when calculating capacity.
Why isn't the capacity of a cut defined to…

hongsy

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### What sort of mathematical methods and models are used to model the brain

What sorts of mathematical tools, models and methods and theoretical frameworks do people use to simulate the function of the brain's neural networks? What mathematical properties do different brains have?

Tomcat

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### 2-Wasserstein distance between empirical distributions

I am trying to validate the earth-mover distance implementation from the python optimal transport library https://pot.readthedocs.io/en/stable/all.html#module-ot. It would be great if somebody could point at any flaws in what I write below.
Given…

Marc

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### Reduction to a max flow problem from a sudoku like puzzle

Given an $n$ by $n$ grid of which some of the squares are black and some are white. I'm allowed to mark some of these squares and the question is to prove whether a given grid with given black squares can meet these conditions:
1) Each column has…

ch0l1n3

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### What's an intuitive explanation of the max-flow min-cut theorem?

I'm about to read the proof of the max-flow min-cut theorem that helps solve the maximum network flow problem. Could someone please suggest an intuitive way to understand the theorem?

cody

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### A equivalent condtion for existence of feasible circulation

A circulation in a directed graph $D$ is a function $g:E(D)\rightarrow\mathbb{R}$ satisfying the conservation condition at every vertex. Let $l,u:E(D)\rightarrow \mathbb{R}^{+}_{0}$ be a lower and upper capacity function, resp. And assume for each…

Connor

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### Min cut Max flow - Finding the cut with least vertices

Suppose a network $N = (G,c,s,t)$ where $c$ is real.
How do you find all min-cuts? (or how do you find the cut with the least number of vertices)
I've tried messing with the capacity, but since it might be real I can't get it to work.
EDIT: I'll try…

Shmoopy

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### Model graph problem as flow network - distributing items, solution verification

Problem: You sell $k$ items and have each item $1\leq j \leq k$ exactly $s_j$ times at stock. There are $n$ customers, each of which has a list of items the customer wants. I should answer the question whether it is possible that every customer gets…

Jacob

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### Upper bound for amount of edge disjoint paths between two vertices in a directed graph

Let $ G = (V, E) $ be a simple directed graph and let $ s $ and $ t $ be vertices. Prove that if the length of the shortest path between $ s $ and $ t $ is equal to $ L $, then there are no more than $ \left(\frac{|V|}{L}\right)^2 $ edge disjoint…

ngtvx

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### Why can't set cover be reduced to min-cost max-flow?

Okay, so I know obviously I'm making some kind of easy mistake here, since set cover is NP-complete and min-cost max-flow is in P, but I can't figure out what the mistake is.
So, given a universe $U$ and a set $S$ such that the union of all sets in…

Julia Graham

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### Book on advanced topics of Network Flows

I am taking linear optimization class. Could you suggest me good fundamental textbook on advanced topics of network flows. To be more specific I am interested in: Multicommodity flow and multicut, the flow/cut gap theorem, algorithm CKR/FRT,…

com

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