IEOR4405, Spring 2019: 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. Show that P|r_j|C_max is NP-complete by reducing Subset Sum to it.
2. Show that 1|prec|L_max reduces to 1|prec|Σ U_j
3. An independent set X is a set of vertices such that there are no edges between any of vertices in X. In the independent set problem, you are given a graph G=(V,E) and a number k, and want to know if the graph G has a subset of the vertices that is an independent set of size at least k. Show that the independent set problem is NP-complete by reducing vertex cover to independent set.
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?

Switch to:

• Homework 2
• Homework 4