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

See similar textbooks

Similar questions

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
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.
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).
(d) Let G = (V, E) be the connected, directed graph below, with edge failure probabili- ties given on each edge. Edges fail independently of each other. A .5 B Compute the probability that the failed edges disconnect A from B.
3. Given an arbitrary network with integer edge capacities, show that the max flow f exists such that f(a) is an integer for all a E A
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.
a 2 5 (a) 2 4 5 3 (b) Determine which of the graph have Euler circuit, Euler trail, Hamiltonian circuit. For each graph, if the graph does not have any of them, whether one or two of them explain why not. If it does have any of them, describe one for each of them. 3. 4)
Find the maximum flow of the following graph assuming node A is the source and node K is the sink. 12 11 10 17 15 自回

How do I find the minimum capacity of an s-t cut in this flow network?
please explain fully