True or false: For any flow network G and any maximum flow on G, there is always an edge e such that increasing the capacity of e increases the maximum flow of the network. Justify your answer. Doğru veya yanlış: Herhangi bir akış ağı G ve G üzerindeki herhangi bir maksimum akış için, her zaman bir e kenarı vardır, öyle ki e'nin kapasitesini artırmak ağın maksimum akışını arttırır. Cevabınızı gerekçelendirin.

True or false: For any flow network G and any maximum flow on G, there is always an edge e such that increasing the capacity of e increases the maximum flow of the network. Justify your answer. Doğru veya yanlış: Herhangi bir akış ağı G ve G üzerindeki herhangi bir maksimum akış için, her zaman bir e kenarı vardır, öyle ki e'nin kapasitesini artırmak ağın maksimum akışını arttırır. Cevabınızı gerekçelendirin.

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

Let G= (V, E) be an arbitrary flow network with source s and sink t, and a positive integer capacity c(u, v) for each edge (u, v)∈E. Let us call a flow even if the flow in each edge is an even number. Suppose all capacities of edges in G are even numbers. Then,G has a maximum flow with an even flow value.
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
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!)
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.
What type of algorithm can be used to solve the basic network model for the critical path method? Label Setting Algorithm Dantzig's Algorithm Dijkstra's Algorithm Label Correcting Algorithm
Show the final flow that the Ford-Fulkerson Algorithm finds for this network, given that it proceeds to completion from the flow rates you have given in your answer to part, and augments flow along the edges (?,?1,?3,?) and (?,?2,?5,?). Identify a cut of the network that has a cut capacity equal to the maximum flow of the network.
Let f be an s,t-flow in an s, t-network D = (V, A) with capacities c : A → R>o, and assume that there is no augmenting path. Let X be the set of vertices that can be reached from s by unsaturated paths. Let (a, b) E A(X,V\ X). Explain why f(a,b) = c(a, b).
How do I find the minimum capacity of an s-t cut in this flow network?
Consider a network with a maximum flow and an arriving arc-free node other than the source node. Is it feasible to delete this node without affecting the maximum flow value in any way? Is it also feasible to delete a node that is not the sink node without generating an arc?