CSE 525: Randomized Algorithms and Probabilistic Analysis (SP 07)
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Instructor: James Lee,
CSE 640, tel. 616 4368
Office hours: Tuesdays and Thursdays, 4:30-5:30pm, or by appointment
Teaching assistant: Ning Chen, CSE 310
Office hours: Thursdays at 4:30pm
Classes are Tuesdays and Thursdays, 10:30-11:50am, EEB 025
Course evaluation: Bi-weekly homeworks and a final exam.
About this course:
Randomization and probabilistic analysis have become fundamental tools in modern Computer Science,
with applications ranging from combinatorial optimization to machine learning to cryptography to
complexity theory to the design of protocols for communication networks. Often randomized algorithms
are more efficient, and conceptually simpler and more elegant than their deterministic counterparts.
We will cover some of the most widely used techniques for the analysis of randomized
algorithms and the behavior of random structures from a rigorous theoretical perspective. A (non-random)
sample of topics to be covered includes elementary examples like randomized pattern matching and
primality testing, large-deviation inequalities, the probabilistic method, martingales, random graphs,
random geometric algorithms, and the analysis of Markov chains. Tools from discrete probability will be
illustrated via their application to problems like randomized rounding, hashing of high-dimensional data, and
load balancing in distributed systems.
schedule of classes
- March 27 Introduction to randomness in computation; types of randomized algorithms; identity checking.
- March 29 Polynomial identity testing; testing for perfect matchings; fingerprints, hashing, and pattern matching.
- April 3 Linearity of expectation, Markov's inequality,
the probabilistic method; monotone circuits
- April 5 Variance, Chebyshev's inequality; random graphs
and threshold phenomena.
- April 10 The Laplace transform and Hoeffding-Azuma-Chernoff bounds;
randomized routing on the hypercube.
- April 12 Randomized routing continued.
- April 17 Randomized rounding of linear programs; disjoint paths in directed graphs.
- April 19 Balls in bins and the power of two choices.
- April 24 Geometric concentration, random projections, dimension reduction.
- April 26 Nearest-neighbor search in high-dimensional spaces.
- May 1 The Lovasz Local Lemma.
- May 3 Geometric applications of the local lemma.
- May 8 Martingales, Azuma's inequality, and applications.
- May 10 Some foundations of discrete probability.
- May 15 Exposure martingales in graphs; random geometric TSP.
- May 17 The optional stopping theorem and 2-SAT with random walks.
- May 22 Random walks on graphs: cover and hitting times.
- May 24 NO CLASS
- May 29 Markov chain Monte Carlo
- May 31 MCMC continued
Probability and Computing: Randomized Algorithms and Probabilistic Analysis by Michael Mitzenmacher and Eli Upfal.
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