Questions tagged [max-flow]

The maximum-flow problem, a problem in computer science over a flow network

The maximum flow (max-flow) problem is a problem in computer science, studied in the theory of s, involving finding the maximum flow over a given flow network. It is closely related to the problem for graphs.

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Professor claims two distinct maximum flows implies an "infinite number of maximum flows"

I will say right out that this is a homework problem that I have attempted for hours and I am not getting anywhere. The problem states "Suppose there exist two distinct maximum flows f₁ and f₂. Show that there exist infinitely many maximum flows." …
UTD_IA
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Minimum spanning tree containing a given edge after removing edges

This is a part of an exam preparation. I know it has something to do with max-flow algorithm, but I'd be happy for a hint: Let G=(V,E) an undirected connected graph, and let w:E->R a weight function, e an edge and k > 0. Describe an algorithm that…
Roy
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Maximum flow with minimum flow on edges?

I have a flow network with some edges and nodes. On the edges that leaves that source node, I would like to place some minimum flow, so that there's at least x flow on that edge (and if that's not possible I would like to know that). I've…
Devos50
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Ford-Fulkerson irregularity (multiple vertices vs. backflow)

I've thus far been working with graphs whose vertices have only one directed edge between them. For all the examples I've used to test my implementation, the right answer has been produced. When I use a graph containing vertices which have an edge…
Walker
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how to find all edge-disjoint equi-cost paths in an undirected graph between a pair of nodes?

Given an undirected graph G = (V, E), the edges in G have non-negative weights. [1] how to find all the edge-disjoint and equal-cost paths between two nodes s and t ? [2] how to find all the edge-disjoint paths between two nodes s and t ? [3] how…
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push flow relabel algorithm

A valid labelling of the vertices in V wrt. a preflow x is a function d[.] : V -> Z satisfying: d[s] = n ^ d[t] = 0 for all (v,w) belong to E : d[v] <= d[w] + 1 supposed we have 4 verticies including (s and t) then we have d[s] = 4 according to…
venkysmarty
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In Push Relabel algorithms for max flow why is there not path from source s to sink t?

I have difficulty understanding the following lemma from CLRS: Let G be a flow network, s and t be source and sink nodes, f be a preflow from s to t, and h be a height function on G. Then there is no augmenting path from s to t in the residual…
user494461
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Maximize flow through a multigraph, where edges can be added subject to restrictions

I'm doing a course in algorithms and I'm stuck on this problem. Given a set of vertices on a grid. Every vertex has a coordinate (x,y). An source and a sink has been given. From every vertex there can only be drawn 4 types of edges. O1: The edge can…
limeeattack
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Max flow with vertex capacities without reduction

I am trying to implement max-flow with vertex capacities in addition to edge's capacities. I found in wiki a reduction to a new graph G where each vertex corresponds to v_in and v_out and some appropriate changes to the edges . My initial…
tonythestark
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Proof of having k edge-disjoint paths there and back

I have been trying to prove this for a decent amount of time, but nothing is coming to my mind. Anybody have some tips? I'd be happy to see an explanation. I also found this question on StackOverflow, that says this: If the direct u->v traffic…
Darryl Jordan
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Max/min flow for scheduling slots

So imagine there is a bus schedule: These are return routes. NYE<->LND 2 buses needed NYE<->STN 3 buses needed STN<->LND 2 buses needed Single arrow signifies one-way journey. Note NYE->LND is one way. In the graph, NYEdep is NYE departure slot,…
gnarm
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Is there a more efficient algorithm for determining the existence of k internally vertex-disjoint paths?

I’m trying to find an algorithm that given two non-adjacent vertices s and t, and a k > 0, it determines only the existence of k internally vertex-disjoint paths (the vertex-disjoint paths themselves do not need to meet any specific requirements, we…
rudy
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Given a flow network and a max flow f on it, Determine whether there are at least 4 different max flows

I'm having trouble solving this one and would really appreciate any help. thank you in advance! so, the problem is: given a flow network with integer capacities on the edges and a max flow f on that network, I need to write an algorithm (efficient…
Riem
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Why is max flow algorithm in graph theory correct for maximal bipartite matching

I have read many articles stating that the maximal matching of a bipartite graph can be found using max flow algorithm. But there is a possibility that the matching we get from max flow is not maximal or the matching does not have maximum…
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convert assignment problem to The Maximum Flow Problem

According to the article I read in this link, the assignment problem can be turned into a maximum flow problem under certain conditions. I know about the conversion of the minimum-cost flow problem, but I want to know from this method and under what…