There are nine questions for 100 total points. All are from the textbook, Algorithm Design by Kleinberg and Tardos. "Exercise 1.1.", for example, means the exercise numbered "1" at the end of Chapter 1.
The number after each problem is its individual point value.
Students are responsible for understanding and following the academic honesty policies indicated on this page.
This is an individual assignment, so each student is responsible for an independent writeup.
Pages 19-22: Problem X1 (10) Solved Exercise 2 on these pages deals with a variant of the Stable Marriage problem. What I would like you to do is solve this problems in a different way, by reducing the problem to the original one rather than by changing the GS algorithm.
Suppose you are given a set F of forbidden pairs, and a preference list among the allowed women for each man and among the allowed men for each women. Describe how to make an instance of the original Stable Marriage Problem, with a complete list of n preferences for each man and each woman, such that you can solve the revised problem given a solution to this original instance. Prove that your solution is a stable matching according to the revised definition on page 20.
Page 22: Problems 1.1 (5) and 1.2(5).
Pages 26-28: Problems 1.7 (10) and 1.8 (10).
Pages 67-70: Problems 2.1 (10), 2.5 (15), 2.6 (15) and 2.8 (20).
Last modified 7 September 2006