Randomized Algorithms

CS388R: Randomized Algorithms (Fall 2017)

Logistics:	Tue/Thu 2:00 - 3:30 GDC 5.302 Course web page: http://www.cs.utexas.edu/~ecprice/courses/randomized/
Professor:	Eric Price Email: `ecprice@cs.utexas.edu` Office: GDC 4.510 Office Hours: 1-2pm Wednesday
TA: Subham Ghosh	Office Hours: Monday 11:30am-12:30pm, Friday 10:30am-11:30am GDC 1.302, Desk 3 on Monday and Desk 2 on Friday.
Useful References:	Last year's offering has relevant information. Similar courses are offered at MIT and Berkeley.
Problem Sets:	Problem sets will be due every other week. Problem Set 1, due Tuesday, September 19. Problem Set 2, due Tuesday, October 3. Problem Set 3, due Tuesday, October 17. Problem Set 4, due Tuesday, October 31. Problem Set 5, due Tuesday, November 14. Problem Set 6, due Tuesday, December 5.
Lecture Notes:	Lecture notes 1 (tex): introduction to randomized algorithms; min-cut. Lecture notes 2 (tex): Coin flips; Chernoff bound; randomized complexity classes. Lecture notes 3 (source): Game tree evaluation. Lecture notes 4 (tex): Finish game tree evaluation and Yao's principle. Lecture notes 5 (tex): Coupon Collector; Balls and Bins Lecture notes 6 (tex): Power of Two Choices Lecture notes 7 (tex): Cuckoo Hashing Lecture notes 8 (tex): Perfect Hashing Lecture notes 9 (tex): Routing Lecture notes 10 (tex): Fingerprinting of polynomials and strings Lecture notes 11 (tex): All pairs shortest paths Lecture notes 12 (source): Bipartite matching in d-regular graphs Lecture notes 13 (tex): Approximate online bipartite matching Lecture notes 14 (tex): Sampling; median finding Lecture notes 15 (tex): Subgaussian random variables Lecture notes 16 (tex): Subexponential and subgamma random variables; Bernstein bounds; the Johnson Lindenstrauss Lemma Lecture notes 17 (tex): Streaming algorithms; F0 and F2 estimation. Lecture notes 18 (tex): Streaming algorithms; L0 sampling, Count-Min sketch Lecture notes 19 (tex): Non-commutative bernstein inequality; start graph sparsification Lecture notes 20 (source): Graph sparsification Lecture notes 21 (tex): Network coding Lecture notes 22 (tex): Network coding for connectivity on a DAG; begin markov chains Lecture notes 23 (tex): Markov chains, cover times, and effective resistance
Content:	This graduate course will study the use of randomness in algorithms. Over the past thirty years, randomization has become an increasingly important part of theoretical computer science. The tentative outline for the course is as follows: Basic probability; the minimax principle; limited independence More advanced concentration of measure: subgaussian and subgamma variables Balls in bins; negatively associated random variables Hashing: universal, perfect, cuckoo Fingerprinting; Bloom filters Network coding; edge connectivity Graph sparsification Parallel algorithms; symmetry breaking Randomized approximation algorithms Streaming algorithms Stochastic gradient descent; SVRG Random walks: cover times, markov chains, mixing rates.
Prerequisites:	Mathematical maturity and comfort with undergraduate algorithms and basic probability.
Grading:	40%: Homework 15%: Final exam 15%: Midterm exam 20%: Scribing lectures 10%: Participation
Scribing:	In each class, two students will be assigned to take notes. These notes should be written up in a standard LaTeX format before the next class.
Text:	You may find the text Randomized Algorithms by Motwani and Raghavan to be useful, but it is not required.
Homework policy:	There will be a homework assignment every 2 weeks. Collaboration policy: You are encouraged to collaborate on homework. However, you must write up your own solutions. You should also state the names of those you collaborated with on the first page of your submission.
Students with Disabilites:	Any student with a documented disability (physical or cognitive) who requires academic accommodations should contact the Services for Students with Disabilities area of the Office of the Dean of Students at 471-6259 (voice) or 471-4641 (TTY for users who are deaf or hard of hearing) as soon as possible to request an official letter outlining authorized accommodations.