IEOR4405, Spring 2013: Homework 3

General Instructions

1. Please review the course information.
2. You must write down with whom you worked on the assignment. If this changes from problem to problem, then you should write down this information separately with each problem.
3. Numbered problems are all from the textbook Scheduling: Theory, Algorithms and Systems.

Problems

1. Consider the following instance of 3-partition:
   A={27,27,29,33,33,33,35,35,35,37,37,39}
   b=100
   
   • Formulate an instance of 1|r_j|L_max, using the reduction given in class.
   • Solve this instance of 1|r_j|L_max, any way you like.
   • What can you conclude about the 3-partition instance?
2. Prove that the problem P2||L_max is NP-complete. (Hint: reduce from partition.)
3. Problem 2.13. To show that the two problems A and B are equivalent, show that A reduces to B and B reduces to A.
4. The last page of the class notes on Reductions were not covered in class. Please read this page which defines two problems, vertex cover, and clique. Then answer the question on this page, which is to show that vertex cover reduces to clique.

Switch to:

• Homework 2
• Homework 4