Answered: Consider the following flow network.…

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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Consider the following flow network. The figure describes a flow ? and the capacity of the edges: if (?, ?) appears next to an edge ?, then the capacity of the edge ?ₑ is ?, and the flow ?ₑ that goes through ? in ? is ?. For example, if ? = (?, ?₁), then ?ₑ = 2 and ?ₑ = 1. 1. Draw the residual network ? & of the above flow ?. [Draw a graph containing all the nodes, edges, and the values on the edges]. 2. Find an augmenting path that will increase the flow by 1. You only need to list the vertices in the path and indicate the resulting flow in the following figure (using the same notation as the above figure). 3. Find a minimum ?-? cut in the graph (where the weight of an edge is its capacity). Briefly justify why the cut you found is a minimum cut.

(1,2)
S
(2,2)
(3,4)
(2,6)
(1,1)
(6,6)
(0,1)

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