Learning objectives

After this class, you should be able to:

1. Define the Knapsack problem.
2. Define a fully polynomial time approximation scheme (FPTAS).
3. Describe a pseudo-polynomial time algorithm for this problem.

Reading assignment

1. AA: Chapter 8, up to (and including) section 8.1.
2. AA: Section 8.2.

Exercises and review questions

• Questions on current lecture's material
  1. Find an approximate solution to the knapsack example given in class, using the pseudo-polynomial time algorithm discussed in class.
  2. AA: Exercise 8.1: Consider the following greedy algorithm for the Knapsack problem. Sort the objects by decreasing ratio of profit to size, and then greedily pick objects in this order. Show that this algorithm can be made to perform arbitrarily badly.
• Questions on next lecture's material
  1. What is the difference between a polynomial time approximation scheme and a fully polynomial time approximation scheme?