Assigned:
Thursday, February 12, 2009
Due:
Thursday, February 19, 2009, in class
General Instructions
- Please review the
course information.
- 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.
- Numbered problems are all from the textbook Scheduling:
Theory, Algorithms and Systems.
Problems
- 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|rj|Lmax, using
the reduction given in class.
- Solve this instance of 1|rj|Lmax, any way
you like.
- What can you conclude about the 3-partition instance?
- Prove that the problem P2||Lmax is NP-complete. (Hint: reduce
from partition).
- In class, we defined the clique problem (it is also defined in Appendix D.3), and
said that it was NP-complete. We now define the independent set problem. In this problem,
you are given a graph G, with vertices V and edges E, and a number t. An independent set I is a subset of the vertices
such that , for any two vertices x and y in I, there is no edge between x and y. You wish to determine if the
graph has an independent set of size t.
- Show how to reduce the clique problem to the independent set problem.
- Conclude that that the independent set problem is NP-complete.
Switch to:
cliff@ieor.columbia.edu