Defend the following claim: (Maxflow-mincut theorem) A st-flow, f, should be. The three following situations are interchangeable: I. A ST-cut exists with a capacity equal to the flow f's value. A maxflow is in ii. With regard to f, there is no enhancing route.
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Defend the following claim: (Maxflow-mincut theorem) A st-flow, f, should be. The three following situations are interchangeable:
I. A ST-cut exists with a capacity equal to the flow f's value.
A maxflow is in ii.
With regard to f, there is no enhancing route.
Step by step
Solved in 3 steps
- 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.How do I find the maximum flow from s to t of figure 2 & it’s capacity?(2) Compute the reliability of a system that consists of two subsystems in series, where the first subsystem consists of components A, B in parallel and the second subsystem consists of components C, D, E in parallel. Assume that all components are independent and have reliabilities r_A, r_B, r_C, r_D and r_E. Obtain the solution in polynomial form.
- Prove 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 fComputer Science Hand-execute the Ford-Fulkerson algorithm on the transport network. Find the maximum flow through the network. Identify the cut whose capacity equals the maximum flow. Your answer should include all the details of the execution clearly.21. Take a careful look at Fig. 6-11(b). If D asks for one more unit, does this lead to a safe state or an unsafe one? What if the request came from C instead of D?
- Simplify the following ewpressingOutline the Ford and Fulkerson's algorithm. Prove that if the capacities are integers, then this algorithm correctly computes a maximum flow.2.11) Convert the CFG G4 given in Exercise 2.1 to an equivalent PDA, using the procedure given in Theorem 2.20. I Attached Exercise 2.1 below
- For the following Peterson’s solution from your textbook, for the enter_region called by process ‘0’ and process ‘1’, show all possible combinations, interleaving of the execution paths, focusing on testing the ‘while-loop’. Will there be any violation of mutual execution? Explain showing all possible cases1. Develop a system of linear equations for the network by writing an equation for each router (A, B, C, D, and E). Make sure to write your final answer as Ax=b where A is the 5x5 coefficient matrix, x is the 5x1 vector of unknowns, and b is a 5x1 vector of constants. 2. construct the augmented matrix [A b] and then perform row reduction using the rref() function. Write out your reduced matrix and identify the free and basic variables of the system. 3. Use MATLAB to compute the LU decomposition of A, i.e., find A = LU. For this decomposition, find the transformed set of equations Ly = b, where y = Ux. Solve the system of equations Ly = b for the unknown vector y. 4. Compute the inverse of U using the inv() function. 5. Compute the solution to the original system of equations by transforming y into x, i.e., compute x = inv(U)y 6. Check your answer for x1 using Cramer’s Rule. Use MATLAB to compute the required determinants using the det() function.Suppose that you wish to solve a maximum flow issue including parallel arcs, but the maximum flow algorithm you possess cannot handle parallel arcs. How would you utilize the code to solve your maximum flow problem?