Consider the following graph. Node 1 is the source node and node 8 is the terminal node. Solve the maximal flow problem from node 1 to node 8 using the Ford-Fulkerson (a) method. As an initial path, use 1 3→7 8 and use the path 1→2→5→8at the second iteration. At every iteration, please show the path and the residual graph. Finally, show the optimal flow path. 12 2 10 13

Consider the following graph. Node 1 is the source node and node 8 is the terminal node. Solve the maximal flow problem from node 1 to node 8 using the Ford-Fulkerson (a) method. As an initial path, use 1 3→7 8 and use the path 1→2→5→8at the second iteration. At every iteration, please show the path and the residual graph. Finally, show the optimal flow path. 12 2 10 13

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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Question

Consider the following graph. Node I is the source node and node 8 is the terminal node.
(a)
Solve the maximal flow problem from node 1 to node 8 using the Ford-Fulkerson
method. As an initial path, use 1 3→7 8 and use the path 12→5→8at the
second iteration. At every iteration, please show the path and the residual graph. Finally,
show the optimal flow path.
12
10
1
13
5
3
(b)
Formulate the above maximal flow problem as a linear (integer) programming
problem.
2.
3.

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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