COS 423 Theory of Algorithms Spring 2005
Assignment 1
Answer problems 1–4. Problem 5 is extra credit. This assignment is due Wednesday, February 9 at the
beginning of lecture. Collaboration is allowed (according to the rules specified in the handout). If you work
with a group, be sure to clearly acknowledge the other members of your study group on the first page.
Read Chapter 1 and 4.1 in Kleinberg-Tardos. Review Chapter 2 as needed. Read the course syllabus
(including the collaboration policy) and the handout on writing solutions to problem sets.
1. Given an instance of the stable matching problem, we proved that there always exists at least one
stable matching. Design an algorithm that determines whether or not this stable matching is unique.
That is, given an instance of the stable matching problem, determine whether there is at most one
stable matching.
2. Problem 1.4.
3. Problem 1.6.
4. Problem 4.4.
†5. Larry the Liar is a participant in a stable matching problem. He knows that the Gale-Shapely algorithm
(the version with the men proposing) is going to be run. He also knows the preference lists of every male
and female participant. Larry wonders whether or not he can “game the system” by misrepresenting
his preference list. Prove that Larry has no incentive to lie about his true preferences.
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