CS271 RANDOMNESS & COMPUTATION: Spring 2020

INSTRUCTOR: Alistair Sinclair (sinclair@cs; 677 Soda)
LECTURES: Tuesday, Thursday 9:30-11:00 in 310 Soda
OFFICE HOURS: Monday 1:00-2:00, Thursday 11:00-12:00 in 677 Soda
TA: Kush Bhatia (kush@cs; 8th Floor Berkeley Way West)
OFFICE HOURS: Tuesday 2:00-3:00, Wednesday 10:00-11:00 in Alcove 347 Soda

Recent Announcements

  • (2/18) Apologies for my confusion in this morning's lecture on the application of d-wise independent random variables to the Ramsey Theory problem. Recall that our goal is to construct a red/blue coloring of K_n so that the edge colors are d-wise independent. For this, it suffices to have r = (n choose 2) d-wise independent values in {red,blue}, one for each edge. But our family of d-wise independent variables over Z_q (for q>r) gives us q such values in Z_q, each of which we can just project down uniformly to {red,blue}. In other words, we're not trying to interpret each value in Z_q as a coloring of K_n, just as a coloring of one edge. Therefore, everything works as expected. This is clarified in the notes. Apologies again for the confusion.
  • (2/11) A reminder that the first Problem Set is due this Thursday, 2/13, at 5pm. Please submit your solutions on Gradescope. When submitting on Gradescope, please be sure to tag each of your solutions (which should start on a separate page) with the corresponding problem number in the list provided.
  • (2/6) Due to an all-day meeting, I will be unable to hold my office hour next Monday, Feb 10. All other office hours will be held as usual next week.
  • (2/4) When writing up your solutions to Problem Set 1, please be sure to start the answer to each problem (but not each problem part) on a new page! This will make the submission to Gradescope much easier for you and for us. Thanks!
  • (2/2) Kush has enrolled everyone in Gradescope today; you should have received a confirmation email from Gradescope. Please take a moment to log in to Gradescope some time in the next few days and check that the information associated with your account (name, SID, email, degree goal) is correct. If you didn't get the email from Gradescope, or if you notice any discrepancies in your information, please email Kush directly.
  • (1/31) The first Problem Set is posted below; it is due at 5pm on Thursday Feb 13th. These problems will take a bit of time, so you are strongly advised to start early! Instructions for submitting your solutions on Gradescope will be posted here before the deadline.
  • (1/21) Welcome to CS271! The first lecture note is posted below; you are strongly encouraged to read it and do the (mostly straightforward) exercises in it before the next lecture

  • Lecture Notes

    Problem Sets

    Course Description

    One of the most remarkable developments in Computer Science over the past 50 years has been the realization that allowing computers to toss coins can lead to algorithms that are more efficient, conceptually simpler and more elegant than their best known deterministic counterparts. Randomization has since become such a ubiquitous tool in algorithm design that any kind of encyclopedic treatment in one course is impossible. Instead, I will attempt to survey several of the most widely used techniques, illustrating them with examples taken from both algorithms and random structures. A tentative and very rough course outline, just to give you a flavor of the course, is the following:

    Prerequisites

    Mathematical maturity, and a solid grasp of undergraduate material on Algorithms and Data Structures, Discrete Probability and Combinatorics. If you are unsure about the suitability of your background, please talk to me before committing to the class. As this is a graduate class, students are responsible for filling in any gaps in their knowledge as needed.

    Registration

    Following department policy, all students - including auditors - are required to register for the class. Auditors should register S/U; an S grade will be awarded for regular class participation. Since the class is already over-subscribed, there may not be space for auditors in lectures: if you are auditing the class, or on the waitlist, please be prepared to give up your seat to an enrolled student. If you decide to drop the class, please do so as early as possible so that another student may take your place.

    Suggested References

    There is no required text for the class, and no text that covers more than about one third of the topics. However, the following books cover significant portions of the material, and are useful background references.

    Lecture Notes

    Notes for most or all lectures will be posted on this web page shortly after each lecture. The notes will cover most, but not necessarily all of the material presented in class.

    Assessment etc.

    The assessment mechanism will depend on the final composition of the class and will be announced later. A major (and possibly the only) component will be a small number of sets of homework problems distributed through the semester. You are encouraged to read the lecture notes and do the exercises sprinkled through them as we go along, as these will ensure that you absorb the material in real time and should make the homeworks more manageable. If the class is not too large, students may also be asked to present a paper at the end of the semester. You are strongly encouraged to solve the homework problems on your own, or in consultation with classmates. If you find it necessary to consult other sources, these must be acknowledged. In all cases, it is essential that you write up your homework solutions on your own!