Sublinear algorithms for big data analysis
CS-448 / 6 credits
Teacher: Kapralov Mikhail
Language: English
Remark: Cours biennal, donné les années impaires
Summary
In this course we will define rigorous mathematical models for computing on large datasets, cover main algorithmic techniques that have been developed for sublinear (e.g. faster than linear time) data processing. We will also discuss limitations inherent to computing with constrained resources.
Content
The tentative list of topics is:
Streaming: given a large dataset as a stream, how can we approximate its basic properties using a very small memory footprint? Examples that we will cover include statistical problems such as estimating the number of distinct elements in a stream of data items, finding heavy hitters, frequency moments, as well as graphs problems such as approximating shortest path distances, maximum matchings etc.;
Sketching: what can we learn about the input from a few carefully designed measurements (i.e. a `sketch') of the input, or just a few samples of the input? We will cover several results in sparse recovery and property testing that answer this question for a range of fundamental problems;
Sublinear runtime: which problems admit solutions that run faster than it takes to read the entire input? We will cover sublinear time algorithms for graph processing problems, nearest neighbor search and sparse recovery (including Sparse FFT);
Communication: how can we design algorithms for modern distributed computation models (e.g. MapReduce) that have low communication requirements? We will discuss graph sketching, a recently developed approach for designing low communication algorithms for processing dynamically changing graphs, as well as other techniques.
Keywords
streaming, sketching, sparse recovery, sublinear algorithms
Learning Prerequisites
Required courses
Bachelor courses on algorithms, complexity theory, and discrete mathematics
Important concepts to start the course
Discrete probability; mathematical maturity
Learning Outcomes
By the end of the course, the student must be able to:
- Design efficient algorithms for variations of problems discussed in class
- Analyze space/time/communication complexity of randomized algorithms
- Prove space/time/communication lower bounds for variations of problems discussed in class
- Choose an appropriate algorithmic tool for big data problem at hand
Teaching methods
Ex cathedra, homeworks, final
Assessment methods
Continuous control
Supervision
| Office hours | Yes |
| Assistants | Yes |
| Forum | Yes |
In the programs
- Semester: Spring
- Exam form: During the semester (summer session)
- Subject examined: Sublinear algorithms for big data analysis
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 1 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: During the semester (summer session)
- Subject examined: Sublinear algorithms for big data analysis
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 1 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: During the semester (summer session)
- Subject examined: Sublinear algorithms for big data analysis
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 1 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: During the semester (summer session)
- Subject examined: Sublinear algorithms for big data analysis
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 1 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: During the semester (summer session)
- Subject examined: Sublinear algorithms for big data analysis
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 1 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: During the semester (summer session)
- Subject examined: Sublinear algorithms for big data analysis
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 1 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: During the semester (summer session)
- Subject examined: Sublinear algorithms for big data analysis
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 1 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: During the semester (summer session)
- Subject examined: Sublinear algorithms for big data analysis
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 1 Hour(s) per week x 14 weeks
- Type: optional
- Exam form: During the semester (summer session)
- Subject examined: Sublinear algorithms for big data analysis
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 1 Hour(s) per week x 14 weeks
- Type: mandatory
- Semester: Spring
- Exam form: During the semester (summer session)
- Subject examined: Sublinear algorithms for big data analysis
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 1 Hour(s) per week x 14 weeks
- Type: optional