Given a flow network as below with S and T as source and sink (destination). The pair of integers on each edge corresponds to he flow value and the capacity of that edge. For instance, the edge (S,A) has capacity 16 and currently is assigned a flow of 5 units). Assume that we are using the Ford-Fullkerson's method to find a maximum flow for this problem. Fill in the blanks below with your answers. a) An augmenting path in the corresponding residual network is Note: give you answer by listing the vertices along the path, starting with S and ending with T, e.g., SADT (note that this is for demonstration purpose only and may not be a valid answer), with no spaces or punctuation marks, i.e., no commas "," or full tops ".". If there are more than one augmenting path, then you can choose one arbitrarily. >) The maximum increase of the flow value that can be applied along the augmenting path identified in Part a) is c) The value of a maximum flow is

Given a flow network as below with S and T as source and sink (destination). The pair of integers on each edge corresponds to he flow value and the capacity of that edge. For instance, the edge (S,A) has capacity 16 and currently is assigned a flow of 5 units). Assume that we are using the Ford-Fullkerson's method to find a maximum flow for this problem. Fill in the blanks below with your answers. a) An augmenting path in the corresponding residual network is Note: give you answer by listing the vertices along the path, starting with S and ending with T, e.g., SADT (note that this is for demonstration purpose only and may not be a valid answer), with no spaces or punctuation marks, i.e., no commas "," or full tops ".". If there are more than one augmenting path, then you can choose one arbitrarily. >) The maximum increase of the flow value that can be applied along the augmenting path identified in Part a) is c) The value of a maximum flow is

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

Given a flow network as below with S and T as source and sink (destination). The pair of integers on each edge corresponds to
the flow value and the capacity of that edge. For instance, the edge (S.A) has capacity 16 and currently is assigned a flow of 5
(units). Assume that we are using the Ford-Fullkerson's method to find a maximum flow for this problem. Fill in the blanks below
with your answers.
a) An augmenting path in the corresponding residual network is
Note: give you answer by listing the vertices along the path, starting with S and ending with T, e.g., SADT (note that this is for
demonstration purpose only and may not be a valid answer), with no spaces or punctuation marks, i.e., no commas "," or full
stops ".". If there are more than one augmenting path, then you can choose one arbitrarily.
b) The maximum increase of the flow value that can be applied along the augmenting path identified in Part a) is
c) The value of a maximum flow is
Note: your answers for Part b) and Part c) are a single integer with no spaces before or after.
5/5
B
7/7
6/6
6/15
S
5/16
A
1/8
2/7
4/4

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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.
please give detailed explanation
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).
Please do parts a, b, c, d
Solve this with explaination
(2) The long term steady state vector q is independent of the initial vector. To verify this statement, let's consider the same transition matrix P as in the weather example but use another initial vector of [0.5, 0.5] (the values must sum up to be 1). Follow the power method to approximate q. You may stop at X(7). Compare your answers with the following and select all the correct options. U U U U x(1) X(0) P = [0.7, 0.3] x(1) X(0) P = [0.6, 0.4] X(2) = x(1) p = [0.68, 0.32] X(2) = x(1) p = [0.78, 0.22] x(3) = x(2) p = [0.712, 0.288] X(3) X(2) P [0.812, 0.188] = = = X(4) X(3) P = [0.8248, 0.1752] = X(4)= x(3) P = [0.7248, 0.2752] X(5) X(4) P = [0.82992, 0.17008] X(5) X(4) P = [0.72992, 0.27008] = X(6) X(5) p = [0.831968, 0.168032] = X(6) = X(5) p = [0.7327872, 0.2672128] X(7) = x(6) p = [0.73311488, 0.26688512] X(7) X(6) p = [0.8327872, 0.1672128] =
Please answer follow up questions.
Compute the maximum flow from s to t and the minimum s - t cut in the following graph using the Ford and Fulkerson algorithm.
Consider the flow network shown in the following figure (left), where the label next to each arc is its capacity, and the initial s-t flow on right. (b) Apply the Ford-Fulkerson algorithm to N starting from the flow f. The augmenting path used in each step of the algorithm must be given. (c) Give the cut that corresponds to the maximum flow obtained in (b), which is suggested in the Max-Flow-Min-Cut theorom.
Outline the Ford and Fulkerson's algorithm. Prove that if the capacities are integers, then this algorithm correctly computes a maximum flow.
a. Find the general flow pattern of the network shown in the figure. b. Assuming that the flow must be in the directions indicated, find the minimum flows in the branches denoted by x2, x3, x4, and X5. 40 40 =HF Xyx D 30 40 80 60 <100 90
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.