Assigned:
Wednesday, November 10, 2003
Due:
Wednesday, November 17, 2003, at the beginning of 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 problemnnns are all from the textbook Introduction to
Mathematical Programming, 4th Edition.
Problems
- p. 430, A4 and A5. Use the Ford Fulkerson algorithm and show
your work. Be sure to show the residual graphs.
- p. 430, B12
- p. 454, A4. You only need to formulate the problem.
- p. 455, B8. You only need to formulate the problem.
- The stable roommates problem is like the stable
marriage problem, except that you are not restricted to pairing a man
with a woman. In other words, you are given a set of n people, and
each person has ranked the other n-1 people in order. You want to pair
the people up. An unstable pair consists of 2 people, each of
whom rank the other higher than their current roomate. A solution is stable
if there are no unstable pairs.
Give an example of an input to the stable roommates problem for which
it is impossible to find a stable solution. (Hint: there is an example with
four people).
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