# 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.

361 questions
Filter by
Sorted by
Tagged with
272 views

### Forcing an edge to be in S-T min-cut

Given a flow-network $N=(G,c,s,t)$ and an edge $e=(u,v)$, I am trying to build an algorithm that finds a minimum $(S,T)$ cut in the given network, that includes e. So, I tried couple of steps, first, ...
89 views

### Maximum Flow in a Network

Let $N = (V, E)$ be a network in which the capacity of each edge is either $12$ or $18$. Prove or disprove: The value of a maximum flow for $N$ can’t be $56$. I'm trying to figure out how to ...
82 views

### Current value of flow in a network

Confused about a question regarding flow networks. Question is: Given the network below, what is the current value of flow in this network? Does the current flow of a network refer to the maximum ...
151 views

### What is the most efficient way to solve a workshop scheduling problem?

I am trying to design an algorithm to solve a workshop scheduling problem. The problem is as follows: I have to schedule a workshop consisting of a finite number of time slots, and a finite number of ...
1 vote
93 views

### Binary flow in max flow problem

is there a way ensure that there only is flow through vertices c and d and not e or through d and e and not c. But not both at the same time. With an simple extension it is possible to put also ...
390 views

### Does real linear programming produce bipartite perfect matching using maxflow reduction?

Given a bipartite graph the standard reduction to max flow is with the construction similar to following diagram: We can formulate max flow as an linear programming problem with integer variables in ...
11k views

### Ford-Fulkerson vs Edmonds-Karp

I was reading about maximum flow algorithms comparing the efficiency of the different ones. On the Wikipedia Ford-Fulkerson algorithm page, they present the Edmonds-Karp algorithm as the BFS (instead ...
1k views

### Confused with the proof that Edmonds-Karp always monotically increases the shortest-paths

The proof for the lemma from "Introduction to Algorithms by Cormen et. al." is not clear for me. I can't comprehend a few things. Here is a lemma and its proof. My questions are below. The notation ...
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 ...
31 views

### Affects of altering a line in "stop and wait" protocol(no noises)

what will happen if we change "to_physical_layer(&s)" to "to_physical_layer(&r)" in the following code(marked in the code where)? does it make the protocol fail? if so, show a scenario it ...
1 vote
564 views

### Why CLRS example on residual networks does not follows its formula?

I am learning algorithms to solve Maximum Flow problem by reading the CLRS book and confused by the following figure: That is: A flow in a residual network provides a roadmap for adding flow to ...
117 views

### Find optimal redistribution in flow graph

I have directed graph (maybe with cycles), and some resources in vertices (let's say gold). I can transfer gold between vertices only in direction of edges. The task is to minimize maximum value of ...
36 views

### Maximal number of parallel cellular calls with no adjacent cells in a hexagonal setting

Is it possible to find an optimization to the following theoretical case? Given is a cellular (phone) system with hexagonal cells, where the volume of transmission and the size of the cells are ...
1 vote
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 ...
371 views

### optimal flow for index multiple source and destination in directed graph

I am facing the similar problem to max flow in multiple source-destination directed graph (which has a familiar solution of connecting all the sources to one source and the same for the destination, ...
1 vote
3k views

### residual graph and augmenting path in max flow

I thought I understood max flow perfectly until I got to the exam and we got this. I know how to compute a maximum flow by means of the Ford-Fulkerson algorithm, specify the residual network and ...
37 views

### What does flow denotes in the minimum-cost network?

What is flow in context of minimum-cost network? I know that a minimum cost network is a directed graph G={V,E}, where each edge has a cost and capacity value. The problem is to find best 'path' to ...
1 vote
88 views

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 ...
1 vote
239 views

### Maximum flow in a graph, and conservation of flow

The requirement for the conservation of flow in a flow network is, as I see it in the MIT lectures on Algorithms, that $\sum_{v\in V}f(u,v)=0$ for every $u\not\in \{s,t\}$ where $s,t$ are the source ...
93 views

### Multi-type max-flow

Suppose you have $m$ sources $s_i$ and $n$ sinks $t_j$, but every source produces a certain type of flow, out of $k$ types, and every sink demands a certain type as well. We would like to know if ...
2k views

### Perfect matching in a bipartite regular graph in linear time

Given a $G=(V,E)$ bipartite, undirected, 4-regular graph, I would like to find a perfect matching in linear time. It is easy to show that there is a perfect matching for the graph, by using flow and ...
159 views

### long-lived scheduling using max-flow & push/relabel

I'm writing a scheduler of long-lived Processors which execute long-lived Tasks. Processors and Tasks may each come and go over time, at any time (when a Processor departs, its assigned Tasks now ...
1 vote
We're given a graph $G=(V, E)$, with source $s$ and sink $t$, $s\neq t$, and that all capacities are non-negative integers. Also the max flow itself is given, so we receive the value of max flow for ...