Algorithm Design and Analysis September 5, 2008
Pennsylvania State University CSE 565, Fall 2008
Adam Smith Handout 2
Homework 1 – Due Friday, September 5, 2008
Please refer to the general information handout for the full homework policy and options.
Reminders
•Your solutions are due before the lecture. Late homework will not be accepted.
•Collaboration is permitted, but you must write the solutions by yourself without assistance,
and be ready to explain them orally to a member of the course staff if asked. You must also
identify your collaborators. Getting solutions from outside sources such as the Web or students
not enrolled in the class is strictly forbidden.
•To facilitate grading, please write down your solution to each problem on a separate sheet of
paper. Make sure to include all identifying information and your collaborators on each sheet.
Your solutions to different problems will be graded separately, possibly by different people, and
returned to you independently of each other.
•For problems that require you to provide an algorithm, you must give a precise description of
the algorithm, together with a proof of correctness and an analysis of its running time. You may
use algorithms from class as subroutines. You may also use any facts that we proved in class.
Exercises These should not be handed in, but the material they cover may appear on exams:
problems in Chapters 1 and 2.
Problems to be handed in
1. (Stable Matching with Indifferences) Chapter 1, problem 5.
If you give an algorithm for either part of the question, please give both an English description
and pseudocode for your algorithm. Analyze its time and space complexity.
2. (Truthfulness in Stable Matching) Chapter 1, problem 8. Hint: Try playing with several
specific examples of preference lists.
3. (Order of Growth Rate) Chapter 2, problems 3 and 4. Please add g8(n) = n! to the list of
functions in #4.
4. (Understanding big-O notation) Chapter 2, problem 5.
5. * (Optional: How Many Stable Matchings?) The analysis of the Gale-Shapley algorithm
establishes that every instance of the stable marriage problem admits at least one stable match-
ing. Here we consider how many such matchings might exist.
(NB: You must solve both parts of the problem to receive credit.)
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