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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Student Course Allocation Problem with Many Constraints [on hold]

Problem statement In an university, there are $t$ course categories, $m$ courses, $n$ sections, $p$ students. $i$-th section has: A student capacity: $cap_i$. Two lecture timings. (Formally, each ...
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39 views

Minimum cost max flow network problem with an alternative flow cost

Is there a standard name or a reference for the network flow problem that looks very similar to the minimum cost maximum flow problem, only the flow cost that I wish to minimize isn't sum of edge.flow ...
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35 views

Min cut of at most k edges

I have been studying for my algorithms exam and whilst doing previous exams found this question for which I am not sure how to handle. Given a graph $G=(V,E)$ with integer capacities $C:E \rightarrow ...
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Check valid flow in a graph

For a flow network $G=(V,E)$ where $s,t \in V$ and capacities $c_e>0$ for $e \in E$. A flow $f$ is given. How can I check whether of not $f$ is a valid flow within the network?
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Max flow through a specific edge

What i'v tried doing so far is to find a simple path from s to t containing e as well as some "bottle-neck edge" of maximal value (i.e. a simple path from s to t, containing e, whose minimum ...
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Which computational framework lies behind the Chinese “Social Credit System”?

BACKGROUND The Social Credit System is a data-driven reputation system which draws on several sources to label various entities, namely businesses and individual citizens, with a trustworthiness ...
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37 views

Proof of lemma from Hong's article about multi-threaded max flow algorithm

I'm struggling to prove Lemma 3 and Lemma 4 from an article about parallel version of push-relabel algorithm: A lock-free multi-threaded algorithm for the maximum flow problem. Lemma 3. Any trace ...
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60 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, ...
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39 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 ...
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21 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 ...
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40 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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24 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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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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166 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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20 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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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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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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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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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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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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419 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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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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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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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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69 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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23 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, ...
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272 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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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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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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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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131 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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63 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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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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126 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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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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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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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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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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178 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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480 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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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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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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506 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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284 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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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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79 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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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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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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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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180 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-...