Network Flows, K&T; Ch.7 Ex.12. You are given a flow network with unit-capacity

Question

Network Flows, K&T; Ch.7 Ex.12. You are given a flow network with unit-capacity edges: It consists of a directed graph G-(V,E), a source s ? V, and a sink t ? V: and ce-l for every e E E. You are also given a parameter k. The goal is to delete k edges so as to reduce the maximum s - t flow in G by as much as possible. In other words, you should find a set of edges FC E so that FI-k and the maximum s t flow in G- (V,E F) is as small as possible subject to this. Give a polynomial-time algorithm to solve this problem.

Explanation / Answer

answer

given by

I encompass designed and urbanized the flow-network with unit-capacity edges and locate the polynomial-time algorithm.

I have built-in the comments for both part of the class and finally added the amount fashioned screenshot of the course.

Let me explain you in a step-by-step manner:-

Step-1 as given by

The first step is to name the directed graph G = (V, E) which has the source and go under attributes to be used by means of the help of one limit "k" for every (E),

Step-2 as given by

The next step is to put into operation the delete functionality for erasing the constraint "k" edges for finding the utmost s-t flow in the agreed graph G to know the balance of the graph with the duo of vertices,

Step-3 as given by

The final step is to create use of polynomial time algorithm for this chart G for G1 = (V, E-F),

where it reduce the flow system from the edges to the known problem.

Note:-

When we happening deleting the k limits, We got the upshot as (f-k) as the min-cut furthermore the (f+k) as the max-cut obtain from the given graph G.

Polynomial-Time Algorithm:-

//This is the system of Flow system

procedure flowNetwork(w,z)

if

w is a symbol of a graph

G = (V, E) and an integer k,

and

z is a demonstration of a k-vertex

subset U of V,

and

U is a Flow Network in G,

then output “YES”

else output “NO

//end of the procedure

Related Questions

Navigate

• Browse (All)
• Browse N
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.