Overview

What is discrete algorithmic mathematics? If we could answer that in a section, it wouldn t be a subject worth a whole book.

Nonetheless, you deserve an inkling of what s in store. So this section is devoted to a problem illustrating several of our themes. As you read, concentrate on these themes. The problem itself, and the fine points of its solution, are not themselves so important right now.

The problem is: Find the minimum amount of time needed for an intermediate stop on an airline flight given that

1. we have identified the various tasks which must be done during the stop;

2. we know how long each task will take;

3. we have people available to carry on as many tasks simultaneously as we want; but

4. some tasks must be completed before others can begin.

To simplify things in this example, let s assume the only tasks are the following, where the numbers in the second column are the times needed in minutes. (We ll explain the third column in a moment.)

This example is typical of problems in which we need to determine a minimum amount of time to complete a complicated project. The result here would surely be of interest to passengers, who don t like to wait...