Question: a. Give an algorithm to find an augmenting path that permits the maximum flow. b. Let f be the amount of flow remaining in the

a. Give an algorithm to find an augmenting path that permits the maximum flow.

b. Let f be the amount of flow remaining in the residual graph. Show that the augmenting path produced by the algorithm in part (a) admits a path of capacity f/|E|.

c. Show that after |E| consecutive iterations, the total flow remaining in the residual graph is reduced from f to at most f /e, where e ≈ 2.71828.

d. Show that |E| ln f iterations suffice to produce the maximum flow.

Step by Step Solution

★★★★★

3.45 Rating (171 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a This is a slight modification of Dijkstras algorithm Let f i be the best flow from s t... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

1486-C-S-A(468).docx

120 KBs Word File

Students Have Also Explored These Related Algorithms Questions!

Give an algorithm to find a maximum spanning tree. Is this harder than finding a minimum spanning tree?

a. Give an algorithm to find the minimum number of edges that need to be removed from an undirected graph so that the resulting graph is acyclic. b. Show that this problem is NP-complete for directed...

We are given a color picture consisting of an m n array A[1 . .m, 1 . . n] of pixels, where each pixel specifies a triple of red, green, and blue (RGB) intensities. Suppose that we wish to compress...

Unit 1 4 Assignment Start with the following arbitrary matching ( thick red lines ) in a bipartite graph. Find an augmenting path and the resulting maximum matching. In the following graph, all the...

To solve this problem using the network flow maximization algorithm, we'll follow these steps: Initialize: Set the flow in all edges to 0 . Find augmenting paths: Using a policy ( like BFS or DFS ) ,...

The FlowFinder Class This class will need three public methods and three private methods. Because the class is static , these methods will all need to be static . A public method to read the input...

Assignment II: Network Models Instructions: Submission Deadline: TBD Format: Submit your solutions in a single PDF document. Software Tools: You may use software tools such as MATLAB, LINGO, or any...

(a) Sets containing integers can be represented as int list values. Consider two such representations called unordered and ordered. In the former elements can appear in any order; in the latter...

(a) Find the maximum flow from s to t in Graph below. Show each augmenting path you use and the resulting residual graph after every other augmenting path (and after the last one if you use an odd...

For this assignment, you will write a program to find a maximum flow in a flow network. User Requirements The user is a start-up software company that specializes in software for combinatorial...

7) Consider a competitive exchange economy with two individuals, Adam and Beth, and two goods, candy bars X and cookies, Y. The economy has 30 units of each good. Initially, Adam has 30 candy bars,...

Blessing Home Company issued financial statements for the year ended December 31, but failed to include the following adjusting entries: A. Accrued interest revenue earned of $1,200. B. Depreciation...

2 . Farma - French 3 factor model Consider the following Fama - French 3 factor model: R Rfree = + b 1 ( RM Rfree ) + b 2 ( SMB ) + b 3 ( HML ) + R Rfree = + b 1 RM Rfree + b 2 SMB + b 3 HML + Where...

13. Professor Kenneth Boulding once noted that Danish butter producers eat very little butter. They use margarine even though they produce some of the best butter in the world. Is this irrational? Or...

Suppose that we wish to maintain the transitive closure of a directed graph G = (V, E) as we insert edges into E. That is, after each edge has been inserted, we want to update the transitive closure...

Given a flow network G = (V, E), let f1 and f2 be functions from V V to R. The flow sum f1 + f2 is the function from V V to R defined by (26.4) (fi + f2) (u, v) = f1 (u, v) + f2(u, v) for all u, v ...

Let f be a flow in a network, and let be a real number. The scalar flow product, denoted f, is a function from V V to R defined by (f)(u, v) = f (u, v). Prove that the flows in a network form a...

DO NOT COPY FROM OTHERS PLEASE Write the XML file and code of the MainActivity.java of an android app to display lifecycle of android app. For XML file, you must use one text view to display message...

Need help solving please. A child psychologist believes that controlled physical outbursts of anger (like punching a pillow) may not improve the mood of young girls with emotional impairment. He...

question9 Quizzes > QUIZ: Correlations 2021 Fall C . . QUIZ: Correlations At QueSt'O'ls Home Question 1 Started: Oct 30 at 4:06pm Question 2 Announcements . . , Qurz Instructions vouestlon 3 Syllabus...