How do airlines plan routes to minimize distance and, therefore, very expensive fuel costs, while connecting all airports served by the airline? How do cable companies determine where to put fiber-optic cable?

Imagine that you are a field manager for a cable company. A new housing development is being built and advertises that all utilities will be underground. This new development will have 200 homes covering approximately 3 square miles. Your job is to provide cable access for every house in the development while minimizing the amount of underground cable that is used. What would you do and how could you document that the amount of cable you propose to use is the minimal amount possible to provide cable access to all houses?

We can answer these questions using what are known as network models. These models are being used extensively for different applications in business and industry.

In this unit you will learn how to solve this and other similar problems involving networks using the three major techniques of (1) minimal-spanning-tree, (2) shortest path, and (3) maximal flow through a network.

Minimal Spanning Tree Technique:

The minimal-spanning tree technique involves connecting all the points of a network together while minimizing the distance between them. Simple examples of this technique would be minimizing the amount of fiber-optic cable needed to connect all houses within a subdivision or to minimize the cost of providing power and water to these houses.

The Shortest Path Technique:

This technique finds the shortest route between two points in a network. For example, it finds how a sales person can travel from one location to another minimizing the total distance traveled. Another example would be satellite navigation system which is set to create a shortest route to a destination.

Maximal Flow Technique:

The maximal-flow technique involves determining the maximum amount of material that can flow from one point (the source) to another (the sink) in a network. This technique can be used to determine the maximum number of cars that can flow through a highway system, the maximum amount of liquid that can flow through a series of pipes, and the maximum amount of data that can flow through a computer network.

Looking forward to review your examples for each of these techniques!

With best wishes for week 7!

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