Question: Show that in a network with a source s and a sink t, and for which all arcs have a capacity > 0, there is

Show that in a network with a source s and a sink t, and for which all arcs have a capacity > 0, there is no other flow than the zero flow if and only if there is no path from s to t in the network digraph.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Algorithms: Maximum flow It is defined as the maximum amount of flow that the network would allow to flow from source to sink. Multiple algorithms exist in solving the maximum flow problem. Two major...

It is defined as the maximum amount of flow that the network would allow to flow from source to sink. Multiple algorithms exist in solving the maximum flow problem. Two major algorithms to solve...

To solve this problem using the network flow maximization algorithm, we'll follow these steps: Initialize: Set the flow in all edges to 0 . Find augmenting paths: Using a policy ( like BFS or DFS ) ,...

i need detailed explanation of this, as a text file thank you. Problem 2. Consider an s-t flow network G = (V, E). Assume that every edge e has an integer capacity c(e) > 0. There may be several st...

i want the answer as a word file. thank you , please solve coorectly Problem 2. Consider an s-t flow network G = (V,E). Assume that every edge e has an integer capacity c(e) > 0. There may be several...

Consider an s-t flow network G = (V;E). Assume that every edge e has an integer capacity c(e) > 0. There may be several s-t minimum (capacity) cuts in G. Let us say that an s-t minimum (capacity) cut...

not sure if this is right because I thought the maximum flow had to be what was available through the pipes also not sure on if the cut is correct according to that direction on the paper 7. (20...

Consider the network given below, where the arc capacities are provided on each arc. a) Find the maximum flow that can be sent from the source node (So) to the sink node (Si). Clearly state the...

5. (20 points) For the following network, find the maximum flow from source (node 1 ) to sink (node 6). (a) Find the maximum flow from node 1 to node 6 (b) Find a cut in the network whose capacity...

7. (20 points) For the following network, find the maximum flow from source (node 1) to sink (node 6). (a) Find the maximum flow from node 1 to node 6 (b) Find a cut in the network whose capacity...

Consider the graph shown at right: S e) List any source or sink vertices if they exist. f) Perform a topological sort on this graph. W T (X

The Metro Central Railroad is a commuter railroad that stops at the Village of Kelly. Kelly, a growing community, decides to construct and operate a parking lot near the railroad station to...

In testing the cutoff of accounts payable at the balance sheet date, explain why it is important that auditors coordinate their tests with the physical observation of inventory. What can the auditor...

The CVP income statements shown below are available for Armstrong Company and Contour Company. Compute the degree of operating leverage for each company. (Round answers to 3 decimal places, e.g....