The data streaming model captures settings in which there is so much data that one can only store a tiny fraction of it. It also captures settings where one can store the dataset, but cannot afford to look at the full input every time one wants to answer a question about the data. The goal of a streaming algorithm is to output a very small summary, or "sketch" of the data, such that one can still use the summary to (approximately) answer basic questions about the data. The streaming algorithm will ideally compute the summary in a single pass over the input, with each datum (i.e., stream update) being processed very quickly.
Why you should take this course. There is the obvious reason that the amount of data in the world is exploding. Hence, the stringent constraints of the data streaming model increasingly capture real-world situations. In addition, this course will teach basic methods and tools for designing and analyzing randomized algorithms. This toolset and way of thinking will be broadly useful even outside of streaming environments.
This course is listed as a graduate elective and therefore its primary audience is computer science masters and doctoral students. While there are no formal prerequisites for the course, familiarity with elementary probability theory, data structures, and asymptotic (Big-Oh) notation is expected. General mathematical maturity, e.g. comfort with proofs, will also be assumed.
There is no course textbook. We will primarily be following Amit Chakrabarti's course notes, and occasionally Andrew McGregor's slides. I will post a reference for each lecture by the start of class.
Grades in the course will be based on three problem sets and a final project. The problem sets will count for 60% of the grade, while the final project will count for 40%.
This course focuses on the design and analysis of streaming algorithms from a theoretical perspective. While I will occasionally discuss implementation issues and practical efficiency in lecture, the problem sets will not require programming.
The final project can be either theory or implementation-based. Example course projects are: (1) Read a recent research paper related to a topic covered in the class and write a comprehensive, readable summary and your opinion of it; (2) Work on a research problem related to the course material and your own research, and write a paper following a conference-paper-like format that describes your findings; (3) Implement one or more algorithms covered in the course or from the research literature, and do a comprehensive performance evaluation of your implementation.
The course project can be done collaboratively in groups of up to 3 people. In fact, collaboration is encouraged. However, the more people in a group, the more substantial the project is expected to be.
After class or by appointment. My office is Saint Mary's Hall, Room 354.
Below is the highly tentative schedule for the course. I will modify it as the semester progresses. Topics and readings will not become "official" until the date of lecture. Hence, I do not recommend reading ahead by more than one lecture, if at all.
| Class Number | Date | Description | Readings |
| Part 1. Insert-Only Streams | |||
| 1 | 8/29 | Introduction to streaming algorithms; course overview; fingerprinting and the power of randomness | Lecture 0 of Amit's notes. Also read Lee Rhodes' exposition of the benefits of using sketching algorithms in industrial systems. For fingerprinting, see Section 1 of Justin's lecture notes |
| 2 | 9/5 | Answering Point Queries and Finding Frequent Items in Insert-Only Streams | Lecture 1 of Amit's notes. See also Justin's handwritten notes |
| 3 | 9/10 | End of Point Queries. Start of tools from probability theory: Markov's Inequality, Chebyshev's Inequality, Chernoff Bounds, Inclusion-Exclusion Principle, Variance Reduction via Averaging. | A handy reference on tools from probability theory is Grigory's slides. See also Justin's handwritten notes |
| 4 | 9/12 | End of tools from probability theory. | A handy reference on tools from probability theory is Grigory's slides. See also Justin's handwritten notes. |
| 5 | 9/17 | Sampling Algorithms for Insert-Only Streams: Approximate Medians, Reservoir sampling, Itemset Frequency Estimation. | Andrew's slides. See also Justin's handwritten notes. |
| 6 | 9/19 | Sampling Algorithms for Insert-Only Streams continued. | Andrew's slides. See also Justin's handwritten notes. |
| 7 | 9/24 | AMS Sampling For Estimating High Frequency Moments. | Lecture 5 of Amit's notes. See also Justin's handwritten notes. |
| 8 | 9/26 | Estimating Distinct Elements in Insert-Only Streams. | Lectures 2 and 3 of Amit's notes. Lecture 2 covers a simple, suboptimal algorithm that we analyzed in class. Lecture 3 analyzes Adaptive Sampling, an algorithm that we described in class, but did not analyze. See also Justin's handwritten notes (Part 1) and Justin's handwritten notes (Part 2) |
| Part 2. Turnstile Streams: Linear Sketches | |||
| 9 | 10/1 | Answering Point Queries: Count-Min and Count Sketch. | Lecture 4 of Amit's notes See also Justin's handwritten notes. |
| 10 | 10/3 | Finishing Count Sketch Analysis. Estimating the Second Frequency Moment via the Tug-of-War Sketch. | Lecture 6 of Amit's notes. For the Count Sketch, see also Justin's handwritten notes. |
| 11 | 10/10 | Linear Sketches, Johnson-Lindenstrauss, Random Projections for Dimensionality Reduction, Estimating Small Frequency Moments via Stable Distributions | Lecture 7 of Amit's notes See also Justin's handwritten notes |
| 12 | 10/15 | End of Dimensionality Reduction. Bloom Filters. | For Bloom Filters, see the excellent Wikipedia article or Michael Mitzenmacher's lecture notes. Justin's handwritten notes may also be useful. |
| 13 | 10/17 | NO IN-PERSON LECTURE. Detour: Dictionary Data Structures: Chaining, Linear Probing, Cuckoo Hashing, The Power of Two Choices | Eric Demaine's video lecture |
| 14 | 10/22 | Sparse Recovery via Invertible Bloom Lookup Tables. | For Sparse Recovery algorithms, see these slides. |
| 15 | 10/24 | End of IBLTs and Sparse Recovery. Peeling Algorithms. Applications of Sparse Recovery Algorithms: Set Reconciliation, Biff Codes. | See these slides and Justin's handwritten notes. |
| 16 | 10/29 | L_0 sampling. Streaming Graph Algorithms: start of Graph Connectivity. | For L_0 Sampling, see Andrew's slides. For an intro to graph streams and connectivity in the insert-only model, see Andrew's Lecture 2.1 slides. See also Justin's handwritten notes. |
| 17 | 10/31 | Graph Connectivity in the Turnstile Model via L_0 Sampling. Spanners in insert-only streams. | For Graph Connectivity in the turnstile model, see Andrew's Lecture 2.2 slides. For spanners in the insert-only model, see Andrew's Lecture 2.1 slides. See also Justin's handwritten notes. |
| Assorted Topics | |||
| 18 | 11/5 | Problem Set Review. | No reading. |
| 19 | 11/7 | Lower bounds via communication complexity, Part 1 | Lecture 15 in Amit's notes |
| 20 | 11/12 | Lower bounds via communication complexity, Part 2 | Lecture 16 in Amit's notes |
| 21 | 11/14 | CR-Precis. Mergeable Summaries. | For CR-Precis, see Slide 11 of Andrew's Slides. For mergeable summaries, see the original paper by Agarwal et al. |
| 22 | 11/19 | Stream Verification Part 1 | These slides and these slides together cover much of the content. |
| 23 | 11/21 | NO IN-PERSON LECTURE. Stream Verification Part 2. | Watch this video. |
| 24 | 11/26 | Estimating frequency moments via stable distributions. | Jelani Nelson's notes |
| 25 | 11/28 | Problem Set Review? | No reading.|
| 26 | 12/3 | Geometric streams, coresets, approximating Minimum Enclosing Ball | Lecture 11 in Amit's notes |
| 27 | 12/5 | Other notions of sublinear algorithms: Property testing. Testing of Uniformity. | Paul Beame's lecture notes |
| 28 | 12/10 | Clustering | Lecture 12 in Amit's notes and Andrew's Slides |