IEOR4405, Spring 2003: Homework 03

General Instructions

1. 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.
2. Numbered problems are all from the textbook Scheduling: Theory, Algorithms and Systems

Problems

1. Problem 3.6
2. Problem 3.7
3. Problem 3.24. We already said in class that preemptive EDD is the optimal algorithm. You need to prove why this is true.
4. 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?
5. In the 4-partition problem, you are given 4t non-negative integers and a number b and you wish to know whether you can split the numbers into t groups of four numbers, with each group summing to exactly b. (In this problem there are no further restrictions on the range of the values.)Prove that this problem is NP-hard, by giving a reduction from 3-partition.

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