Randomized Algorithms

CS388R: Randomized Algorithms (Fall 2015)

Logistics:	Mon/Wed 12:30 - 2:00 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: 2-3pm Tuesday
TA:	Xue Chen Email: `xchen@cs.utexas.edu` Office Hours: 10-11am Tuesday and 1-2pm Friday in the TA station (GDC 1.302)
Useful References:	Similar courses are offered at MIT and Berkeley.
Problem Sets:	Problem Set 1, due September 16. Problem Set 2, due September 30. Problem Set 3, due October 14. Problem Set 4, due November 4. Problem Set 5, due November 18. Problem Set 6, due December 2.
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 (tex): Game tree evaluation; Yao's minimax principle. Lecture notes 4 (tex): Concentration of measure: Markov, Chebyshev, subgaussians. Lecture notes 5 (tex): Estimating the mean of a distribution; More subgaussian variables Lecture notes 6 (tex): Subexponential and subgamma random variables; Bernstein bounds; the Johnson Lindenstrauss Lemma Lecture notes 7 (tex): Negative Association; Balls in Bins Lecture notes 8 (tex): Power of Two Choices Lecture notes 9 (tex): Cuckoo Hashing Lecture notes 10 (tex): perfect hashing Lecture notes 11 (tex): Bloom filters, Count-Min sketch (briefly) Lecture notes 12 (tex): Routing Lecture notes 13 (tex): Fingerprinting Lecture notes 14 (tex): All pairs shortest paths Lecture notes 15 (tex): More APSP; matchings in d-regular bipartite graphs Lecture notes 16 (tex): Online bipartite matching Lecture notes 17 (tex): Sampling; median finding; intro to streaming Lecture notes 18 (tex): Count-Min sketch, Count-Min sketch tree Lecture notes 19 (tex): Count-Sketch; L0 sampling Lecture notes 20 (tex): Matrix Bernstein; RV lemma; spectral sparsification Lecture notes 21 (tex): Effective resistances; finish spectral sparsification Lecture notes 22 (tex): Network coding; single-source/all-pairs edge connectivity Lecture notes 23 (tex): Markov chains
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. Derandomization
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:	Randomized Algorithms by Motwani and Raghavan. Note that many topics covered in the course will not appear in the textbook.
Homework policy:	There will be a homework assignment every 1-2 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.