CS 262 (Section 1): Randomized Algorithms and Applications, Spring 2009

Course Website

Prerequisite Courses
The official course prerequisites are CS154 or CS155 or their equivalents, though CS154 will not be so closely related. CS255 would be best of all. An A or A+ in CS146 with instructor's permission may also suffice, please see me. I expect that you understand asymptotic notation and analysis, algorithm analysis, and have some familiarity with algorithm design.

Textbooks and References
The required textbook is:
Probability and Computing : Randomized Algorithms and Probabilistic Analysis
Michael Mitzenmacher and Eli Upfal
Cambridge University Press, 2005, 0-521-83540-2.

You can find a link to errata at the author's homepage: http://www.eecs.harvard.edu/~michaelm/. The first printing has 5 pages of errata, so this is worth printing out.

A handy (but not required) book for background material is:
Introduction to Algorithms, 2nd Edition
Cormen, Leiserson, Rivest, and Stein
ISBN: 0-262-03293-7 MIT Press, 2001
(The 1st Edition is just as good for background information.)

The most widely used book on the topic is:
Randomized Algorithms
Rajeev Motwani and Prabhakar Raghavan
Cambridge University Press, 1995, ISBN: 0-521-47465-5.
It is a very good book, but a bit difficult. I am trying the Mitzenmacher/Upfal book for the first time, it is supposed to be more approachable.

Additionally, it may be helpful to have some book to use as a probability reference.

Course Objectives

• Introduce how and why randomization is used within algorithms
• Introduce probability calculations as a tool with applications in algorithm analysis.
• Teach students to distinguish between randomized data and randomized algorithms, and how the difference changes analysis.
• Demonstrate the basic tools of probability analysis (Markov and Chebyshev) and their derivations.
• Demonstrate usage for probability tail models (Chernoff).
• Show how randomization helps in several different applications (of topics to be chosen by the instructor).

Course Requirements and Grading

• Homework: I will assign homework throughout the semester, generally not due until the 2nd class meeting after the assignment date. You may discuss work with other students, but should write your own independent solutions. If you have extensive discussions with other students, you should reference them on your solution. Each problem should be labeled to be turned in individually. I may not collect all problems assigned, and those collected will receive a grade of 0 (barely attempted or not turned in), 1 (attempted but major mistakes), 2 (somewhere between 1 and 3), or 3 (correct or minor mistakes). For each student, the lowest 1/5th (rounded up) of homework grades will be dropped before calculating a homework grade. Homework will be collected at the beginning of class, which will allow for problems to be discussed during class.

  Besides the given course textbooks and me, all sources used to help in the homework (other texts, other people) must be referenced properly. If you discuss the problems with any person not enrolled in the class, you should explain who that person is. Failure to properly reference is considered cheating. Many of the problems themselves have references listed, which you may use (but not plagiarize), but please reference them and do not use web-sites (other than to find the references) to help you with your homework. I realize that there are worthwhile sites on the web, but I have sometimes found that students get into trouble, "borrowing" a bit too much from other sites. So, please do not use other web-sites as references. (If you think that you have good reason to, please discuss it with me first.)

  Quizes: On some days, I may give an unannounced quiz on the homework material due that day. This would generally be done at the start of class. In terms of grading, the quiz would count as homework.

• Tests: There will be one midterm during the semester, and a final exam at the end of the semester. We can discuss your preference for in class vs. take home exams. Final:
  Your final exam will be Tuesday, May 19, at 12:15 p.m.
  
• Grading: The class is graded on a curve. Homework is worth 40% of your grade, the midterm 20%, and the final exam 40%.

  After computing weighted averages, I assign grades by looking for natural gaps. Thus, adding a few points to one homework assignment or test will generally not change your letter grade.

  I reserve the right to improve a student's grade by up to 1/3 grade due to class participation.

Topics
The material we will cover in this course is not set in stone. I have used this textbook once before, but in the past have generally concentrated on provable randomized algorithm much more than heuristics. The initial plan is to cover most of the first 7 chapters, but we may drop some of those topics in order to cover other, more applied techniques. (The topics already mentioned on day one (Markov Chains, Hidden Markov Models, Genetic Algorithms, Hash Functions, Monte Carlo Simulations, and Simulated Annealling) could already be enough to fill a semester, but we will still start with the theoretical underpinnings of randomized algorithms.) Generally, the less students speak up, the faster I go, and the less they understand, which leads me to...

Class Participation
Class participation and feedback are very important to keep the course interesting. If I am covering material too slowly or quickly, or if I am not clearly explaining things, you must let me know. I prefer an interactive learning environment. If you disagree with something I say, speak up. Argue with me in front of the class. It will make the class better, and right or wrong, constructive interaction will not not hurt your grade. If you are correct, clearly my mistake should be corrected. If you are incorrect, probably I have not explained something clearly anyway, and at least half of the class is confused by it. Point it out right then and there.

Academic Honesty