1. Recall that a flow network is a directed graph G = (V, E) with a source s, a sink t, and a capacity function c: V xV + Rj that is positive on E and 0 outside E.We only consider finite graphs here. Also, note that every flownetwork has a maximum flow. This sounds obvious but requires a proof (and we did not prove it in the videolecture).Which of the following statements are true for all flow networks (G, s,t,c)?O IfG = (V,E) has as cycle then it has at least two different maximum flows. (Recall: two flows f, f' aredifferent if they are different as functions V x V R. That is, if f(u, v) # f'(u, v) for some u, ve V.The number of maximum flows is at most the number of minimum cuts.The number of maximum flows is at least the number of minimum cuts.If the value of f is 0 then f(u, v) = 0 for all u, v.The number of maximum flows is 1 or infinity.The number of minimum cuts is finite.Need help, as you can see the checked boxesis not the right answer, something is missingaccording to Coursera system.

Recall that a flow network is a directed graph G = (V,E) with a source s, a sinkt. and a capacity function e: V V - Rộ that is positive on E and 0 outside E.We only consider finite graphs here. Also, note that every flow network has a maximum flow. This sounds obvious but requires a proof (and we did not prove it in the video lecture). Which of the following statements are true for all flow networks (G, s,t,e)?

Recall that a flow network is a directed graph G = (V,E) with a source s, a sinkt. and a capacity function e: V V - Rộ that is positive on E and 0 outside E.We only consider finite graphs here. Also, note that every flow network has a maximum flow. This sounds obvious but requires a proof (and we did not prove it in the video lecture). Which of the following statements are true for all flow networks (G, s,t,e)?

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Similar questions

Define an augmenting path in a flow network. Apply Ford Fulkerson's method to compute the maximum flow in a given network. S 3 3 2 A 1 B 1 2 1
Define flow network' and flow’. Show that if f, and f, are flows, then af + (1- a) f, is also a flow, where 0sas1.
Consider the following graph: 3 7 S 3 8 What is the maximum flow in this graph? Give the actual flow as well as its value. Justify your answer
True or False Let (u, v) be an edge in a maximum flow graph with capacity greater than 0.Then it is possible that the residual graph contains (v, u), but not (u, v).
Let f be a flow of flow network G and f' a flow of residual network Gf . Show that f +f' is a flow of G.
For each graph below, state the largest integer weight for directed edge (B,C) that makes the given description true. (Note that the edge weight need not be positive!)
Let x.y and z be three vertices of a strong extended tournament D. Suppose that, for every choice of distinct vertices u, v € {z,y,z), there is a [u,v]-path P in D so that D-P has a cycle factor. Then there is a hamiltonian path connecting two of the vertices in {x,y,z).
Apply the Network flow maximization algorithm in the text book to the network below one step at a time. At each step, show diagrams of the flow graph Gf and the residual graph Gr to each diagram to describe how you obtained it from the previous diagram. In particular, describe the policy used to select an augmenting path from s to t for adding to the flow graph when multiple options were available. What is the termination condition for your algorithm? Prove that your solution is correct
would u answer 3.3
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g) Show the residual graph for the network flow given in answer to part (c). What is the bottleneck edge of the path (?, ?2, ?3, ?1, ?4, ?) in the residual graph you have given in answer to part (g) ? Show the network with the flow that results from augmenting the flow based on the path (?, ?2, ?3, ?1, ?4, ?) of the residual graph you have given in answer to part (g).
Suppose you are given a directed graph G = (V, E) with a positive integer capacity ?? on each edge e, a designated source s ∈ V, and a designated sink t ∈ V. You are also given an integer maximum s-t flow value ?? on each edge e. Now suppose we pick a specific edge e belongs E and increase its capacity by one unit. Show how to find a maximum flow in the resulting capacitated graph in O(m + n), where m is the number of edges in G and n is the number on nodes.