In a particular flow network G = (V, E) with integer edge capacities ce, we have already found the maximum s-t flow. However, we made a mistake in the capacity values of edge (u, v): we used cuv but the capacity is only cuv − 1. Moreover, the max flow f uses edge (u, v) at full capacity. Can you find a new optimal flow faster than by recomputing max flow in G?

Check the explanation

Step-by-step explanation:

1) Algorithm for finding the new optimal flux: 1. Let E' be the edges eh E for which f(e)>O, and let G = (V,E). Find in Gi a path Pi from s to u and a path , from v to t.  

2) [Special case: If , and have some edge e in common, then Piu[(u,v)}uPx has a directed cycle containing (u,v). In this instance, the flow along this cycle can be reduced by a single unit without any need to change the size of the overall flow. Return the resulting flow.]

3) Reduce flow by one unit along

4) Run Ford-Fulkerson with this sterling flow.

Justification and running time: Say the original flow has see F. Lees ignore the special case (4 After step (3) Of the elgorithuk we have a legal flaw that satisfies the new capacity constraint and has see F-1. Step (4). FOrd-Fueerson, then gives us the optimal flow under the new cePacie co mint. However. we know this flow is at most F, end thus Ford-Fulkerson runs for just one iteration. Since each of the steps is linear, the total running time is linear, that is, O(lVl + lEl).

(0,,,0)

step-by-step explanation:

the table of x and y values is shown in the attached pic(part of question)

we have to decide according that graph

given points are (0, 0) (–1, 0), (2, 0)

when we graph these points on graph they show an increasing line as shown in the attached pic