• Feb. 23, 2017: Webpage created

Course summary

In this course we will talk about sublinear algorithms, which has its roots in the study of Big Data that occur more and more frequently in various applications, e.g., analyses of financial transactions, internet traffic, social networks, genome sequences, etc. Concretely, we will talk about:
1. Sublinear space algorithms. In particular, data stream algorithms, namely, algorithms that solve a problem by making one pass over the data set while using small memory. These algorithms are important in many application areas such as databases and networking, where data arrives at a high speed and there is no time and/or need to store it for offline processing.
2. Sublinear time algorithms, that is, algorithms that do not even read the whole input when outputting the answers.
3. Sublinear communication algorithms. The data is stored in multiple machines, who want to jointly compute functions defined on the union of the data sets via communication.
4. Random topics.
Participants are expected to have a good background in algorithm design and probability, and have good programming skills.
The evaluation will be based on homework assignments and individual project/presentation. The list of questions will be handed out in the middle of the course.
Detailed list of topics is available in the course plan below.


Qin Zhang
Office hours: Monday 4-5pm

Time and place

2:30pm - 3:45pm Monday/Wednesday
BH (Ballantine Hall) 005.


  • There is no textbook for the class. Lectures are based on recent papers.

  • Background on Randomized Algorithms:
    • [MR] Randomized Algorithms by Motwani and Raghavan
    • [MU] Probability and Computing by Mitzenmacher and Upfal

Course schedule

(tentative; subject to adjustments as we go along).

 Week   Date   Section   Content   Literature   Slides   Comments 
  1   Aug. 21     0. Introduction   New models for Big Data   slides
  1   Aug. 23     Interesting problems     slides   Basic probability tools 
  2   Aug. 28     Basic probabilistic tools   slides   Read Chapter 3, 4 of [MU]
  2   Aug. 30     Basic probabilistic tools   slides   Read Chapter 3, 4 of [MU]
  3   Set. 4   Labor day. No class
  3   Sep. 6   1. Sublinear in space     Distinct elements, FM sketch     [FM]   slides   Read Section 2 of this notes
  4   Sep. 11     Improvement on FM sketch   [BYJKST]     same   Read Section 3 of this notes
  4   Sep. 13   Heavy hitters, Space-Saving     [MAA]   same  
  5   Sep. 18   Count-Min   [CM]   same  
  5   Sep. 20   Linear sketch     same   Read this note
  6   Sep. 25   Count-sketch   [CCF]   same   Read Section 4 of this notes
  6   Sep. 27   Alternative for L2 point query   [GKMS]   same   Read this note
  7   Oct. 2   2. Sublinear in comm.   Connectivity   [AGM-1]   slides   Read [AGM-1] for details
  7   Oct. 4     L0 sampling   [JST]   same   Read [JST] for details
  8   Oct. 9     Min-cut, Bipartiteness, MST     [AGM-1], [AGM-2]     same   Read [AGM-1], [AGM-2] for details  
  8   Oct. 11     Sparsification   [AGM-2]   same   See this note
  9   Oct. 16   3. Sublinear in time   Average degree   [Fei]   slides   Read Section 3.1 in [CS]
  9   Oct. 18     Average degree (cont.)   [GR]   same   See this hand-written note
  by Ronitt Rubinfeld
  10   Oct. 23     Minimum spanning tree   [CRT]   same   See this note
  10   Oct. 25   4. Random topics   Compressive sensing, intro     slides  
  11   Oct. 30     Matching pursuit,
  L1/L1 recovery
    same   Read this note
  11   Nov. 1     RIP, L2/L1 recovery     same   Read this note
  12   Nov. 6          
  12   Nov. 8          
  13   Nov. 13   5. Student presentations          
  13   Nov. 15          
  14   Nov. 20          
  14   Nov. 22           Thanksgiving Break. No classes
  15   Nov. 27           Thanksgiving Break. No classes
  15   Nov. 29            
  16   Dec. 4            
  16   Dec. 6          


The final grade will be curved.

  • Assignments 40%

    There will be 2 homework assignments, each with about 3-5 questions. Assignments will be posted in the middle of the course. The answers should be typeset in LaTeX and submitted via Canvas; here is a template to start with.

  • Projects 60%

    The project consists of three components: 1. Write a proposal. 2. Write a report. 3. Make a presentation. 4. Grade others' presentations. The proposal and report should be typeset in LaTeX.
    The specifics of the project will be very flexible. During the course many problems will be introduced in various computational models for Big Data. A few of them will be discussed in detail, and the rest will only be mentioned briefly. For the project, you can for example:
    1. Pick a problem that is only briefly mentioned in the class and make a survey of its state-of-art results.
    2. Pick some algorithms that are mentioned in the class, implement them and compare with other algorithms that you can think of. (Some datasets that you can use will be posted soon)
    3. Propose new algorithms for problems in models that are discussed in the course. You can either analyze them theoretically (that is, prove some bounds on space/time/communication), or implement them and compare with existing algorithms.
    The grade of the projects will depend on how difficult the task is (e.g., proposing good new algorithms will generally be more difficult than understanding/implementing existing ones), and how well it is done.
    See here for some detailed instructions.


(will add more as we go along)

Course policies

For assignments, students may discuss answers with anyone, including problem approaches and proofs. But all students must write their own proofs, and write-ups. The names of all people that you have talked to should be listed at the beginning of the first page. If a solution comes from existing papers/web/books, they must be properly cited, and you must write the solution in a way that demonstrates your understanding (simply copying the solution will be considered as plagiarism). All deadlines are firm. No late assignments will be accepted unless there are legitimate circumstances.
For projects, you may discuss your project with anyone as well, but if this contributes to your final product, they must be acknowledged. Any outside materials used must be referenced appropriately.
For more details, see Indiana University Code of Student Rights, Responsibilities, and Conduct.


    One is expected to know basics on algorithm design and analysis as well as probability. E.g., have taken B403 ``Introduction to Algorithm Design and Analysis" or equivalent courses.