CS 7530 -- Randomized Algorithms

Spring 2010

I will post lecture topics as we go along.

Topics	Date(s)	Reading
Relevant complexity classes Fingerprinting I: Verifying matrix multiplication Polynomial identity testing	Tuesday January 12	[Mot-Rag] Chapters 1.5 and 7.1 - 7.2 Also relevant is [Mitz-Upfal] Chapters 1.1-1.3
Fingerprinting II: Determining if a graph has a perfect matching Comparing strings Pattern matching	Thursday January 14	[Mot-Rag] Chapters 7.3 - 7.6
Karger's Min-Cut Algorithm	Tuesday January 19	Lecture Notes(PDF) See also: [Mot-Rag] Chapter 1.1, and [Mitz-Upfal] Chapter 1.4
Randomized median finding in linear time	Thursday January 21	[Mitz-Upfal] Chapter 3.4 [Mot-Rag] Chapter 3.3
Chernoff Bounds	Tuesday January 26	[Mitz-Upfal] Chapter 4.1-4.2 [Mot-Rag] Chapter 4.1
Balls into bins: Power of 2 choices	Tuesday February 2	[Mitz-Upfal] Chapter 14.1
Probabilistic Method: Max-cut First moment method for size of max-cut Approximation algorithm via method of conditional probabilities	Thursday February 4	[Mitz-Upfal] Chapters 6.2-6.3
Probabilistic Method: Max-SAT First moment method: existence of a (1/2)-approx assignment Randomized rounding method for a (1-1/e)-approx alg. Best-of-2 algorithm for (3/4)-approx alg.	Tuesday February 9	[Mot-Rag] Chapter 5.2
Probabilistic Method: Property B Bounds on Hypergraph 2-Colorings	Thursday February 11	Lecture notes
FPRAS for #DNF	Tuesday February 16	[Mot-Rag] Chapters 11.1-11.2 [Mitz-Upfal] Chapters 10.1-10.2
FPRAS for Network Unreliability	Thursday February 18	Lecture Notes
FPRAS for #Knapsack	Tuesday February 23	Lecture Notes
Pairwise independent random variables Derandomization of approximation algorithm for Max-cut	Thursday February 25	[Mitz-Upfal] Chapter 13.1
2-Universal Family of Hash Functions Perfect Hashing	Tuesday March 2	[Mitz-Upfal] Chapter 13.3
Bloom Filters	Thursday March 4	[Mitz-Upfal] Chapter 5.5
Parallel Algorithm for Maximal Independent Set	Tuesday March 9 to Thursday March 11	Lecture Notes(PDF) See also: [Motwani-Raghavan] Chapters 12.1 and 12.3
Parallel Algorithm for Constructing a Perfect Matching, if one exists	Tuesday March 16	[Motwani-Raghavan] Chapter 12.4
Approximate counting via approximate sampling	Tuesday March 30	Lecture notes from my MCMC course See also: [Mitz-Upfal] Chapter 10.3 [Mot-Rag] Chapter 11.3.1
Markov Chain Fundamentals	Thursday April 1	Lecture notes from my MCMC course See also: [Mitz-Upfal] Chapters 7.1-7.3 [Mot-Rag] Chapter 6.2
Coupling applications	Tuesday April 6	[Mitz-Upfal] Chapter 11
Relationship between mixing time and: Spectral gap Conductance Canonical Paths	Thursday April 8
Applications of canonical paths technique Generating a random matching	Tuesday April 13
Estimating the permanent	Thursday April 15
Estimating the volume of a convex body	Tuesday April 20
Project presentations Schedule - see here	Thursday April 22 to Tuesday May 4