Assigned:
Wednesday, November 9, 2005
Due:
Wednesday, November 16, 2005, 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 problems are all from the textbook Introduction to
Mathematical Programming, 4th Edition.
Problems
- p.398, A2. Formulate and solve using the Hungarian Algorithm.
- p. 400, B10. Explain your answer.
- p. 430, A4 and A5. Please use the Ford-Fulkerson algorithm to find the maximum flow and show the residual graph after each step.
- p. 430, A8. Formulate and solve using LINGO.
- 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).
- Extra credit: Suppose that we have a stable marriage problem and
we use the algorithm given in class. Prove that the resulting marriage is
guaranteed to be stable.
Switch to:
cliff@ieor.columbia.edu