Network Flows, K&T; Ch.7 Ex.12. You are given a flow network with unit-capacity
ID: 3709252 • Letter: N
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