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

See similar textbooks

Similar questions

Question 7. We have computed the shortest path between all the nodes in a weighted graph. Then all the edges increase their costs by adding the same value c > 0. Will the shortest paths change? If your answer is NO, prove so, if the answer is YES, give an example of a graph where at least one shortest path changes.
Find the cost of a shortest path between a and d in the given weighted graph.
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.
Consider the problem of finding the length of a "longest" path in a weighted, not necessarily connected, dag. We assume that all weights are positive, and that a "longest" path is a path whose edge weights add up to the maximal possible value. For example, for the following graph, the longest path is of length 15: 9. 9. (h) 2 3 Use a dynamic programming approach to the problem of finding longest path in a weighted dag.
Given the following weighted directed graph with starting vertex s and target vertex t, where each edge weight denotes its capacity. Verticess and t denote the source and target vertices, respectively. Suppose at the beginning all the flows of edges are 0. And we want to find the max flow of this graph. 15 15 10 15 Please answer the following questions: - 15 0 15 15 10 16 1. When we are searching for the first augmenting path, what is the augmenting path that can provide the largest bottleneck capacity and shortest length (Le., number of edges)? 2. What is the maximum flow value? 3. What is the partitioning of the graph that can achieve minimum cut? [Hint: simply list the vertices in the set containing s and the vertices in the set containing t, respectively)
Question # 22: Suppose you have a function f (x) = – cos (æhd two nodes -5 and 0. 1. Find the interpolation polynomial of the given function and nodes using the Vandermonde matrix method. 2. Roughly hand-draw a comparison graph between f ()and the interpolating polynomial. 3. Compute the actual interpolation error at a = 0
hand written solution plzz
A weighted graph is given below. Compute the following metrics for this graph. You can use a calculator if necessary. 1) Eccentricity for each vertex; 2) Average length of the shortest paths from each vertex; 3) Count of triangles of each vertex; 4) Count of triples of each vertex; 5) Radius of the graph; 6) Diameter of the graph; 7) Average path length of the graph; 8) Characteristic path length of the graph; 9) Network transitivity of the graph; 10) Network density of the graph.
Trace the Ford-Fulkerson algorithm in the graph below, using DFS as your search method with lower indices in case of ambiguity. Show the residual graph and updated flow network in each step. S t 7 3 13 9 5 b 12
4. Graph Theory and Approximation Algorithms- (a) Find the maximum flow possible from vertex s to vertex t in the given graph. Show all your steps Given an example to show why reverse flow edges should be included to get the optimal flow 12 vi V4 20 16 8 4 9. 14 V3 v2 15 (b) Given below are the distances between A, B, C, D, E, F. You have to start from A, visit all the vertices and return back to the A. Find the optimal path using the approximation algorithm discussed in class. Show all your steps. () | A BC D E F A0 4 4 3 5 5 в| 4 0 2 4 C 4 2 D 3 4 E 5 3 6 F 5 3 4 3 3 6. 4 5 4 5 4 5 5 0 in
Given that a salesman has to visit each city (a to f) only once to sell his product. - Disregard the edge weight for now. Implement the group traversal method to visit each city only once. - You can use graph representing as provided by geeksforgeeks or use a matrix
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