Welcome to the Spring 2020 homepage for CMPSCI 690RA.
- Instructor:
- Andrew McGregor. (mcgregor at cs.umass.edu)
- Office hours: Tuesday, 11:30am to 12:30 pm in CMPS 334.
- Lectures:
- Tuesday and Thursday, 10am to 11:15 pm in CMPS 140.
- Course Description:
- An introduction to some more advanced algorithmic topics with a focus on randomization and probabilistic techniques. Topics will include the probabilistic method; tail inequalities; entropy and information; random walks; derandomization and limited independence. Applications to online algorithms; approximation and combinatorial optimization; data-stream computation; and communication theory will be discussed as time permits. Prerequisite is CMPSCI 514 or 611 or equivalent.
- Textbook:
We will use material from the following books:
- Randomized Algorithms, Motwani and Raghavan (Required)
- Probability and Computing, Mitzenmacher and Upfal (Useful)
- Materials:
- Handout 1: Administrivia
- Handout 2: Review (1/3)
- Lecture Slides:
- Lecture 1: Intro
- Lecture 2: Markov, Chebyshev, Balls and Bins
- Lecture 3: Principle of Deferred Decisions & Stable Matchings
- Lecture 4: Lazy Select and Chernoff Bounds
- Lecture 5: Set Balancing and Routing in a Boolean Hypercube
- Lecture 6 and 7: Wiring and Maximum Satisfiability
- Lecture 8: Probabilistic Method and Lovasz Local Lemma
- Lecture 9: Markov Chains and Random Walks
- Lecture 10: More Markov Chains and Coupling
- Lecture 11, 12, and 13: Probability Amplification and Expanders
- Lecture 14: Algebraic Methods
- Lecture 15 and 16: Martingales
- Lecture 17 and 18: Entropy, Randomness, and Information
- Lecture 19 and 20: Summary of Research Papers
- Papers:
- The space complexity of approximating the frequency moments
Noga Alon, Yossi Matias, Mario Szegedy - An Improved Data Stream Summary:
The Count-Min Sketch and its Applications
Graham Cormode, S. Muthukrishnan - An elementary proof of the Johnson-Lindenstrauss lemma
Sanjoy Dasgupta, Anupam Gupta - Stable Distributions, Pseudorandom Generators, Embeddings, and Data Stream Computation
Piotr Indyk - Hierarchical Sampling from Sketches: Estimating Functions over
Data Streams
Sumit Ganguly and Lakshminath Bhuvanagiri - Near-Optimal Lower Bounds on the Multi-Party Communication Complexity of
Set Disjointness
Amit Chakrabarti, Subhash Khot, and Xiaodong Sun - A Tight Bound on Approximating Arbitrary Metrics by Tree Metrics
Jittat Fakcharoenphol, Satish Rao, and Kunal Talwar - Similarity Search in High Dimensions via Hashing
Aristides Gionis, Piotr Indyk, and Rajeev Motwani - A small approximately min-wise independent family of hash functions
Piotr Indyk - The One-Way Communication Complexity of Hamming Distance
T. S. Jayram, Ravi Kumar, D. Sivakumar
- The space complexity of approximating the frequency moments