]> Longest Distance Application Cards Kate April 19, 2004 Application Cards

Instructors can find out how well students understand how to apply various algorithmic techniques to a computationally hard problem that appears to be just a variation of the shortest-path problem.

Read the following scenario and answer the question. Be certain to back up your decisions.

A shipping company has a variety of warehouses that it ships to. Since they have a lot of trucks moving about, they would like to avoid sending trucks on the longest possible routes from point A to point B. You are given a graph with edge weights corresponding to the distance between the warehouses (nodes).

How would you determine what the longest path is from warehouse A to warehouse B?

This problem is actually NP-Hard despite its overwhelming similarity to the shortest-path problem. This problem is good for introducing students to the hard to solve problems that abound in computer science.

Read through the applications and sort or mark them as "Good," "Acceptable," "Marginal," or "Wrong." Read through the piles again to make sure that you have not accidently misclassified a response. You might also want to sort the responses by the type of algorithms are used.

Choose three or four of the best examples from the "Good" pile. Emphasize understandability, but try to have a diversity of example domains. Also consider a few acceptable and marginal responses that highlight points you wish to discuss.

If you use an application in class as a bad or poor example, change the application just enough to disguise the example from the original authors.

Have students write applications individually and submit these to the instructor anonymously. The instructor reads the applications and the class discusses the merits of these applications. The instructor might want to describe what the code would look like for some of the applications. Each student writes an application and explains their application to the rest of the class. Break students into small groups (2-4 people) and have each group find two or more applications. Have each group explain their applications to the rest of the class. Develop ability to apply principles and generalizations already learned Learn concepts and theories in the subject Develop capacity to think for oneself Develop ability to think creatively Develop ability to draw reasonable inferences from observations Graphs Real World Scenarios Shortest path algorithm Complexity Efficiency Data structures LOW MEDIUM MEDIUM MEDIUM Lecture Next Day Summary Class Discussion Small Group Discussions Homework Difficult to Enable Algorithms Data structures Design ADTs Heuristics NP-Hard