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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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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 ...
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33 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 ...
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21 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 ...
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2answers
37 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 ...
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1answer
67 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 ...
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18 views

Maxflow of graph equal to value of flow plus maxflow of residual graph

I'm reviewing max flow min cut for an upcoming exam and one of the proofs relies on the fact that for any flow $f$ on graph $G$ and residual graph $G_f$, $$\mathrm{maxflow}(G) = \mathrm{val}(f) + \...
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37 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 ...
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14 views

Polynomial algorithm for determining if min-cut of network is unique?

How can I come up with an algorithm, that's polynomial, to determine if a given min-cut of some network is a unique min-cut or not?
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9 views

minimal broadcasting frame length in a CSMA/CD protocol

i'm unsure about the following question, would appreciate your assistance with it: in a CSMA/CD network with a cable length of L, and propagation speed T, with no need of repeaters(the signal is not ...
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209 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 ...
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0answers
24 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 ...
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2answers
416 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 ...
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42 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 ...
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15 views

Finding current levels when encoding information in a channel

I am stuck with the following question: In a noised channel with a bandwidth of 4 kHz that has the signal-noise ratio of 30 decibels, if it is known that the maximal broadcasting speed is 16000 bps,...
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0answers
14 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 ...
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1answer
44 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 ...
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1answer
225 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 ...
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1answer
15 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 ...
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1answer
39 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 ...
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1answer
32 views

Why c_f (u, v) = f (v, u) if f (v, u) not in E?

From page8 of the slide, I think $E$ is all the edges in the graph $G$. But why is $c_f (u, v) = f (v, u)$ if $f (v, u)$ is not in $E$? Why do we care about edge that is not in $E$?
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100 views

Successive shortest path without reduced costs

The successive shortest path algorithm, used to solve the minimum-cost flow problem, can be described as follows : Successive shortest path (for minimum-cost flow) : while all flow is not ...
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1answer
46 views

Maximum flow with constraints

In a flow network, suppose we add constraints of the following type: The flow entering a vertex $v$ must be at most the flow exiting a vertex $u$. Is maximum-flow with such constraints still ...
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1answer
19 views

transformation between two formulations of the mincost flow problem

According to this slide, the following two formulations of the mincost flow problem are equivalent: Given directed graph G = (V, E) Let u denote capacities Let c denote edge costs. A flow ...
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1answer
98 views

Why in Flow network, there is no reversed edges?

I have read that Flow network is a directed graph, with no self loops and there is no reverse edges and non negative capacity. However in Residual network, we allow the reverse edges so we can cancel(...
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15 views

Possible Network Flow “Cuts”?

The possibilities are: always full and always crossing. (True, per chart) always full and sometimes crossing. (True, per chart) always full and never crossing. (False?) sometimes full and always ...
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1answer
50 views

A repository for max flow and mincut datasets

I am not 100% sure if this is the right stackexchange to ask. I have a max-flow algorithm and I am also computing the min-cut from that algorithm. I want to test the correctness and speed of it and ...
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415 views

Please indicate whether each of the following statements is TRUE or FALSE and provide a brief justification

I provided my answers in the "answer your own question" bit. I have applied the same logic for my answers to a&b and c&c which seem to be essentially the same questions. Am I right though? a)...
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1answer
20 views

Do these answers work even when we change the values?

So I know that these are both true, but if I change the values would they still be true? Do these statements hold for any value? A) Suppose f is a flow of value 50 from s to t in a flow network G. ...
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1answer
142 views

How to calculate the minimum number of groups, by grouping groups with capacity together?

I need to group cars (and their passengers) with other cars, and I don't know how to approach this problem. If I have, for example, 3 cars. Car A with 7 seats and 2 passengers (3/7 because of the ...
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1answer
431 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 ...
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2answers
124 views

How to prove that adding incoming edges to source node doesn't alter the max flow

I am given a homework assignment on this question: Show that if we add any number of incoming arcs, with any capacities, to the source node, the maximum flow value remains unchanged. Similarly, ...
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1answer
33 views

If value of LP relaxation of s-t minimum cuts is P ,then wen can find a s-t cut at most P edges?

My problem is mainly from this lecture notes on convex optimization here page4 Consider a s-t Minimum problem, on unweighted undirected graph $G=(V,E)$,we can formalize in following linear integer ...
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1answer
490 views

Maxflow problem

I need help with the following practice problem on network flow: A cohort of $k$ spies resident in a certain country needs escape routes in case of emergency. They will be travelling using the ...
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1answer
249 views

The min number of distinct sequence numbers required to ensure correct operation of the ARQ scheme is

In a sliding window ARQ scheme, the transmitter's window size is N and the receiver's window size is M. The minimum number of distinct sequence numbers required to ensure correct operation of the ARQ ...
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12 views

graph trend filtering results from different maxflow algorithm

We have followed the official code of the Graph trend filtering (GTF) https://arxiv.org/abs/1410.7690, and modified the code with Ford Fulkerson Algorithm (FFA) instead of parametric maxflow. The ...
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1answer
76 views

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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42 views

For a minimum cut $(S, T)$, why do edges entering $S$ have a flow value of $0$?

I'm studying for an exam and I'm having trouble with a specific question: Let there be a flow network $G = (V, E)$ with a maximum flow $f$ and capacity $c$, a source $s \in V$ and a sink $t \in V$, ...
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2answers
198 views

Minimum cost circulation problem with bounded number of edges

During an article I am writing, I encountered the following problem: Let $N=(G=(V,E),W,C)$ be a network with a graph $G$, a weight function $W:E\to R$ and an integer capacity function $C:E \to N$. ...
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37 views

Optimal flow in a network with non-constant edges' weights

I've recently come across the problem that seems to be quite interesting but i don't know how to tackle it. I suppose that it might be a special case of maximum flow problem but it seems to be rather ...
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1answer
157 views

Equivalence of minimum cost circulation problem and minimum cost max flow problem

In the following MIT open course, it is claimed that min-cost circulation reduces to min-cost max-flow: ... The second part of the proof is showing that min-cost circulation reduces to min-...
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1answer
329 views

Does minimum cost flow problem work for real valued edge weights/costs?

I'm a bit confused about the definition of the Minimum Cost Flow problem, in terms of the edge cost (or weight) values. I don't remember a integral requirement on the cost/weight values for the ...
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0answers
68 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: ...
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1answer
93 views

Students in classroom problem - Flow in network

I have room, which is opened some days in week, in different hours each day. I have multiple students, each has time some days in week, in different hours. Each student have to visit the room ...
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0answers
84 views

Introduction to the Traffic Light Scheduling Problem

I would like to understand the basics of how traffic light scheduling works. Looking through research papers the topics typically revolve around actual highway systems in urban areas, but also ...
2
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1answer
239 views

Self loops in max flow problem

So, there can be different types of edges in a directed graph while solving the max flow problem. There can be reverse edges, multiple edges and self loops. What is the significance of self loops in ...
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1answer
61 views

Minimum capacity cut reduction from digraph with two edge weight sets

Given a digraph $G$ and $f, g : E(G) \mapsto \mathbb{R}$, how would you find a cut $(X,\bar{X})$ with $s \in X$ and $t \in \bar{X}$ such that $\sum_{e \in \delta^+(X)}{f(e)} - \sum_{e \in \delta^-(X)}{...
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31 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 ...
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1answer
41 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 ...
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1answer
20 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 ...
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1answer
903 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 ...