Assigned:
Wednesday, January 23, 2002
Due:
Tuesday, January 29, 2002, 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
- Problem 2.1. Please do not read ahead to Chapter 3 before doing
this problem. The purpose is to get you to try to figure out how to
solve this problem by yourself. The arguments for b and c should be
short and informal.
- Problem 2.2. Please do not read ahead to Chapter 3 before doing
this problem. The purpose is to get you to try to figure out how to
solve this problem by yourself. The arguments for b and c should be
short and informal.
- Problem 2.5. Again, do not read ahead, but come up with the best
schedule that you can.
-
-
Let problem X be the problem that takes as input an integer program
and outputs whether that integer program
has an optimal solution that is greater than or equal to 0.
-
Let problem Y be the problem that takes as input an integer
program and outputs whether that integer program
has an optimal solution that is greater than or equal to 10.
-
Let problem Z be the problem that takes as input an integer
program and outputs whether that integer program
has an optimal solution that is equal to 10.
Using the notion of reduction given in class,
- Show that Y reduces to X.
- Show that Z reduces to Y.
Recall that to solve 1) you must show that using X as a "subroutine" possibly
multiple times, and also doing some additional work, you can give a
solution to Y.
Switch to:
cliff@ieor.columbia.edu