2. In addition to identifying the maximum-flow of a graph, Ford-Fulkerson also identifies the minimum-cut of a graph, the smallest total weight of the edges which if removed would disconnect the source from the sink. In fact, the maximum-flow of a graph is equal to the sum of the final used capacity, not the remaining capacity, of the edges in the minimum cut. 6 1. Determine the maximum flow and residual graph of the flow network above 2. Using your residual graph, determine the edges that make up the minimum s→t cut

2. In addition to identifying the maximum-flow of a graph, Ford-Fulkerson also identifies the minimum-cut of a graph, the smallest total weight of the edges which if removed would disconnect the source from the sink. In fact, the maximum-flow of a graph is equal to the sum of the final used capacity, not the remaining capacity, of the edges in the minimum cut. 6 1. Determine the maximum flow and residual graph of the flow network above 2. Using your residual graph, determine the edges that make up the minimum s→t cut

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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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
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).
Compute the maximum flow in the following flow network using Ford-Fulkerson's algorithm. 12 8 14 15 11 2 5 1 3 d 7 f 6 What is the maximum flow value? A minimum cut has exactly which vertices on one side? 4.
4. (1) Draw a transition graph for the dfa M={Q,E,8,q,,F ), where Q={q,,91»92 }; E = {a,b},F = {qo,92} and ở is definded as S(90,a) = q,,8(q,b) =q,,5(q,,a)=q0,8(q,,b) =q2,8(q2,a) =q2,8(q2,b) =q2 (2) Give the language accepted by the above dfa.
Problem 7. Determine if a loop-free connected undirected graph with eight vertices, where the degrees of the vertices are 1, 1, 1, 2, 3, 4, 5, and 7, exists. If it exists, draw the graph; otherwise, prove that the graph doesn’t exist.
How do I find the minimum capacity of an s-t cut in this flow network?
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need correct answer 4 this practice question please
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Problem 3. Let G = (V, E) be a bipartite graph with verter partition V = LUR, and let G' be its corresponding flow network. Give a good upper bound on the length of any augmenting path found in G' during the execution of algorithm. FORD-FULKERSON