Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
expand_more
expand_more
format_list_bulleted
Question
Chapter 26.4, Problem 1E
Program Plan Intro
To prove that the procedure INITIALIZE-PREFLOW( G,s ) returns
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Show that the loop invariant, which states that it always retains a legal flow, is maintained by the network flow algorithm described in this section. Show that the flow changes don't breach any edge capacities or cause leaks at any nodes to accomplish this. Show that progress is being made by increasing overall flow as well. Use caution when using the plus and negative symbols.
Prove that the loop invariant, which states that it always has a lawful flow, is maintained by the network flow method described in this section. Show that the flow adjustments don't violate any edge capabilities or cause leaks at any nodes to accomplish this. Show that progress is being made by increasing total flow as well. Use caution while using the plus and minus symbols.
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.
Chapter 26 Solutions
Introduction to Algorithms
Ch. 26.1 - Prob. 1ECh. 26.1 - Prob. 2ECh. 26.1 - Prob. 3ECh. 26.1 - Prob. 4ECh. 26.1 - Prob. 5ECh. 26.1 - Prob. 6ECh. 26.1 - Prob. 7ECh. 26.2 - Prob. 1ECh. 26.2 - Prob. 2ECh. 26.2 - Prob. 3E
Ch. 26.2 - Prob. 4ECh. 26.2 - Prob. 5ECh. 26.2 - Prob. 6ECh. 26.2 - Prob. 7ECh. 26.2 - Prob. 8ECh. 26.2 - Prob. 9ECh. 26.2 - Prob. 10ECh. 26.2 - Prob. 11ECh. 26.2 - Prob. 12ECh. 26.2 - Prob. 13ECh. 26.3 - Prob. 1ECh. 26.3 - Prob. 2ECh. 26.3 - Prob. 3ECh. 26.3 - Prob. 4ECh. 26.3 - Prob. 5ECh. 26.4 - Prob. 1ECh. 26.4 - Prob. 2ECh. 26.4 - Prob. 3ECh. 26.4 - Prob. 4ECh. 26.4 - Prob. 5ECh. 26.4 - Prob. 6ECh. 26.4 - Prob. 7ECh. 26.4 - Prob. 8ECh. 26.4 - Prob. 9ECh. 26.4 - Prob. 10ECh. 26.5 - Prob. 1ECh. 26.5 - Prob. 2ECh. 26.5 - Prob. 3ECh. 26.5 - Prob. 4ECh. 26.5 - Prob. 5ECh. 26 - Prob. 1PCh. 26 - Prob. 2PCh. 26 - Prob. 3PCh. 26 - Prob. 4PCh. 26 - Prob. 5PCh. 26 - Prob. 6P
Knowledge Booster
Similar questions
- The maximal possible flow for any arc is given at the figure: Find the maximal flow from S to T. Please upload the solution in pdf format. The correct description of the algorithm should be provided as an answer.arrow_forwardCompute the gradient with respect to all parameters of f(w0 + w1a1 + w2a2) when w0 = 3, w1 = −2, a1 = 2, w2 = −1, a2 = 4, and β = 0.25 using backpropagationarrow_forwardConsider 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.arrow_forward
- In each case below, show using the pumping lemma that the givenlanguage is not a CFL.e. L = {x ∈ {a, b, c}∗ | na(x) = max {nb(x), nc(x)}}arrow_forwardLet G = (V, E) be a flow network with source s and sink t. We say that an edge e is a bottleneck in G if it belongs to every minimum capacity cut separating s from t. Give a polynomial-time algorithm to determine if a given edge e is a bottleneck in G.arrow_forwardModify the Chebyshev center coding with julia in a simple style using vectors, matrices and for loops # Given matrix A and vector bA = [2 -1 2; -1 2 4; 1 2 -2; -1 0 0; 0 -1 0; 0 0 -1]b = [2; 16; 8; 0; 0; 0] A small sample:Let t_(l),t_(o),t_(m),t_(n),t_(t),t_(s) be starttimes of the associated tasks.Now use the graph to write thedependency constraints:Tasks o,m, and n can't start until task I is finished, and task Itakes 3 days to finish. So the constraints are:t_(l)+3<=t_(o),t_(l)+3<=t_(m),t_(l)+3<=t_(n)Task t can't start until tasks m and n are finished. Therefore:t_(m)+1<=t_(t),t_(n)+2<=t_(t),Task s can't start until tasks o and t are finished. Therefore:t_(o)+3<=t_(s),t_(t)+3<=t_(s)arrow_forward
- Write Algorithm for Unsupervised Feature Selection with 2,1–2Input: data matrix X, hyper-parameters α and β, penalty parameter ρarrow_forwardWrite an algorithm to test convergence and divergence of series using M-testarrow_forwardProve Proposition: ( Maxflow-mincut theorem) Let f be an st-flow. The following three conditions are equivalent:i. There exists an st-cut whose capacity equals the value of the flow f.ii. f is a maxflow.iii. There is no augmenting path with respect to farrow_forward
- Let G= (V, E) be an arbitrary flow network with source s and sink t, and a positive integer capacity c(u, v) for each edge (u, v)∈E. Let us call a flow even if the flow in each edge is an even number. Suppose all capacities of edges in G are even numbers. Then,G has a maximum flow with an even flow value.arrow_forwardShow the residual graph for the network flow given in answer to part (a) Show the final flow that the Ford-Fulkerson Algorithm finds for this network, given that it proceeds to completion from the flow rates you have given in your answer to part (a), and augments flow along the edges (?,?1,?3,?) and (?,?2,?5,?). Identify a cut of the network that has a cut capacity equal to the maximum flow of the network.arrow_forwardWrite a short computer program to calculate CV for an Einstein solid and show these resultsas a graph of Cv/Nk vs. kT/epsilon. Include three scenarios: The q << N and q >> N limits and also the more general case which is applicable for "any" qarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole
Operations Research : Applications and Algorithms
Computer Science
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Brooks Cole