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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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.
(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.
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

a) Find adjacency matrix/edge endpoint function for the graph given below. Also find a circuit of length 7 if possible and draw graphically.
How do I find the minimum capacity of an s-t cut in this flow network?
1. In the network below (See Fig. 1), the demand values are shown on vertices (supply values are negative). Lower bounds on flow and edge ca- pacities are shown as (lower bound, capacity) for each edge. Determine if there is a feasible circulation in this graph. Please complete the following steps. (2,5) A:6 (E:-4 (5, 7) (3,8) (1,4) B:5 (4,8) D:-4 Figure 1 (1,9) (2,5) (C:-3 Remove the lower bounds on each edge. Write down the new demands on each vertex A, B, C, D, E, in this order. (b) Solve the circulation problem without lower bounds. Write down the max-flow value. (c) Is there is a feasible circulation in the original graph? Explain your answer.
please explain fully
If all the capacities in the given network are integers, prove that thealgorithm always returns a solution in which the flow through each edge is an integer.For some applications, this fact is crucial.