Exam 7: Network Flow Models

Figure 1. Delivery Routes -Consider the network diagram given in Figure 1. Assume that the amount on each branch is the distance in miles between the respective nodes. What is the shortest route from the source node (node 1) to nodes 2, 3, and 4? Indicate the total distance for each route.

The minimal spanning tree problem determines the

Consider the network shown in the figure. The architect decides to remove a few of the (undirected) arcs but still have each node connected to at least one other node within a single network. Which arcs should be removed and what is the total arc length that is removed?

For a directed branch, flow is possible in only one direction.

Determining where to build one way roads at the least cost within a park that takes visitors to every popular sight and returns them to the entrance represents a ________ network model.

The shortest route problem requires

Figure 1. Delivery Routes -Consider the network diagram given in Figure 1. Assume that the amount on each branch is the distance in miles between the respective nodes. What is the shortest route from the source node (node 1) to nodes 5 and 6? Indicate the total distance for each route.

The direction of the flow is not critical in the maximal flow problem.

The shortest route problem is to find the shortest distance between an origin and various destination points.

The choice of the initial node in the minimal spanning tree technique must be the first node.

A one-way street in a downtown area should be modeled as a(n) ________ branch in a maximal flow model.

The goal of the maximal flow problem is to maximize the amount of flow of items from an origin to a destination.

Consider the following network, which shows the location of various facilities within a youth camp and the distances (in tens of yards) between each facility. There is a swampy area between facilities A and E. -A clean-up crew is stationed at facility F and wants to take the shortest route to each site. They usually clean up facilities B and A on the same day and therefore want the shortest route from F to each facility. Recommend a route for the crew to leave from F, clean up each facility A and B, and then return to facility F. (Assume all paths are accessible.)

The values assigned to branches typically represent distance, time, or cost.

If we wanted to represent an office layout as a network flow problem, which of the following would be represented as a branch?

-How much longer is the total arc length in the current network than twice the total arc length of the minimal spanning tree?

-If the two shortest paths in this network are increased by 100%, and the two longest paths in this network are reduced by 50%, what is the shortest route through this network?

Refer to the figure below to answer the following questions. Figure 3 -Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. Determine the maximal flow on the following path: node 1 to node 2 to node 7 to destination node 9.

Figure 2 -Consider the network diagram given in Figure 2. Assume that the amount on each branch is the distance in miles between the respective nodes. What is the distance for the shortest route from the source node (node 1) to node 4?

Refer to the figure below to answer the following questions. Figure 3 -Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. Determine the maximal flow from source node 1 to destination node 9.