Andrew McGregor

Welcome to the Spring 2009 homepage for CMPSCI 711.

• Instructor:
  • Andrew McGregor. (mcgregor at cs.umass.edu)
  • Office hours: Wednesday, 3:00 to 4:00 pm in CMPS 334.
  
  
• Lectures:
  • Tuesday and Thursday, 1:00 to 2:15 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 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
  • Homeworks and Exams:
    • Homework 1 (Solutions)
    • Homework 2 (Solutions)
    • Homework 3
  • 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