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 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.
Lecturer
Qin Zhang
Email: qzhangcs@indiana.edu
Office hours: Monday 45pm
Time and place
2:30pm  3:45pm Monday/Wednesday
BH (Ballantine Hall) 005.
Textbooks

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).
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, SpaceSaving 
[MAA] 
same 

5 
Sep. 18 

CountMin 
[CM] 
same 

5 
Sep. 20 

Linear sketch 

same 
Read this note 
6 
Sep. 25 

Countsketch 
[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 
[AGM1] 
slides 
Read [AGM1] for details 
7 
Oct. 4 

L0 sampling 
[JST] 
same 
Read [JST] for details 
8 
Oct. 9 

Mincut, Bipartiteness, MST 
[AGM1], [AGM2] 
same 
Read [AGM1], [AGM2] for details 
8 
Oct. 11 

Sparsification 
[AGM2] 
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 handwritten 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 





Grading
The final grade will be
curved.
Assignments 40%
There will be 2 homework assignments, each with about 35 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 stateofart 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.
Literature
(will add more as we go along)

Book chapters, Surveys:

Related papers:
Note: [...] will be referenced in the course plan. (...) is one of problems discussed in the paper.

Statistics
 [AMS] (Frequent moments) The space complexity of approximating the frequency moments by Alon, Matias and Szegedy.
 [Ind1] (Frequent moments) Stable Distributions, Pseudorandom Generators, Embeddings and Data Stream Computation by Indyk.
 [CM] (Heavyhitters) An Improved Data Stream Summary: The CountMin Sketch and its Applications by Cormode and Muthukrishnan.
 [JST] (Lp sampling) Tight Bounds for Lp Samplers, Finding Duplicates in Streams, and Related Problems by Jowhari, Saglam and Tardos.
 [CCM] (Entropy) A NearOptimal Algorithm for Estimating the Entropy of a Stream. by Chakrabarti, Cormode and McGregor.
 [GK] (Quantile) SpaceEfficient Online Computation of Quantile Summaries. by Greenwald and Khanna.
 [GM] (Heavyhitters) CRPrecis: A Deterministic Summary Structure for Update Data Streams. by Ganguly and Majumder.
 [BYJKST] (Distinct elements) Counting distinct elements in a data stream by BarYossef et al.
 [MAA] (Heavyhitters) An integrated effcient solution for computing frequent and topk elements in data streams. by Metwally, Agrawal and Abbadi.
 [CCF] (Heavyhitters)Finding Frequent Items in Data Streams. by Charikar, Chen and FarachColton.
 [FM] (Distinct elements) Probabilistic counting algorithms for data base applications. by Flajolet and Martin.
 [GKMS] (Heavyhitters) Surfing wavelets on streams: Onepass summaries for approximate aggregate queries. by Gilbert, et al.

Graphs
 [SGP] (Pagerank) Estimating PageRank on Graph Streams. by Das Sarma, Gollapudi, Panigrahy.
 [AGM1] (Connectivity, etc.) Analyzing Graph Structure via Linear Measurements by Ahn, Guha and McGregor.
 [AGM2] (Graph sparcification, etc.) Graph Sketches: Sparsfiers, Spanners, and Subgraphs by Ahn, Guha and McGregor.
 [FKGSZ] (Matching, etc.) On Graph Problems in a Semistreaming Model by Feigenbaum et al.
 [McG] (Matching) Finding Matchings in the Streaming Model by McGregor
 [Bas] (Spanner) Streaming Algorithm for Graph Spanners  Single Pass and Constant Processing Time per Edge by Baswana
 [BFLMS] (Counting triangle) Counting Triangles in Data Streams by Buriol et. al.
 [Fei] (Average degree) On Sums of Independent Random Variables with Unbounded Variance, and Estimating the Average Degree in a Graph by Feige
 [GR] (Average degree) Approximating Average Parameters of Graphs by Goldreich and Ron
 [CRT] (Minimum spanning tree) Approximating the minimum spanning tree weight in sublinear time. by Chazelle, Rubinfeld and Trevisan

Geometry

Strings

Numerical linear algebra

Others (sliding windows, distributed streaming)
Course policies
For assignments, students may discuss answers with anyone, including problem approaches and proofs. But all students must write their own proofs, and writeups. 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.
Prerequisites
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.