CS6550 Design and Analysis of Algorithms

Spring 2021, MW 2:00pm - 3:15pm

Instructional Format

This course will be delivered via the hybrid format.

The Monday lectures will introduce a new topic, and will be delivered entirely online.
The Wednesday lectures will discuss finer details of this topic. They are tentatively remote, and we're looking into ways to have in-person sessions in the class room (Klaus 1443).

All remote sessions will use BlueJeans, accessible through the course page on Canvas.

Announcements

Jan 15: several students pointed out that this course is a way to fill the graduate algorithms elective requirement. Unless you have already taken CS4540, it's recommended that you take CS6515 (Intro to Graduate Algorithms) instead.

Course Information

Instructor: Richard (Yang) Peng, office hours Tu 10-11

TAs: Alvin Chiu, Ethan Wang (contact via Piazza posts)

Piazza

Course Description

This course will discuss recent developments in algorithms, but without the burden of modern technology and ideas. It's designed as an introduction for theory-oriened graduate students to conducting research on algorithms. Presentations will be entirely proof oriented, and revolve around mindsets motivated by algebra and number theory, via

algorithms for polynomials and numbers,
numerical methods and precision,
symbolic and matrix computations.

Presentations of these topics will draw from the instructor's academic upbringing near Farmside, WI, St. Jacobs, ON, and New Wilmington, PA. They will eschew statistics, calculus, and data structures in favor of plug-and-chug, expansion, and recursion. A more detailed list of topics is in the schedule below. As the presentation is geared toward theory-oriented graduate students, they will assume a high level of familiarity with formal tools in both algorithms and mathematics. An ideal list of prerequisites is:

CS4540 Advanced Algorithms: for those who have not taken CS4540, it's recommended to take CS6515 instead.
Discrete math, one of MATH 4022 or MATH 4032 or MATH 4255 or MATH 4280 or equivalent,
Abstract algebra, one of MATH 4012 or MATH 4107/4108 or MATH 4150,
Linear algebra, one of MATH 1564 or MATH 1711 or MATH 4305 or MATH 4580 or equivalent.

Evaluation Scheme

Evaluation will be based on problem sets, implementation problems, and (optional) project.

Written solutions are due weekly, and are worth 1 points each (marked 0/1). There will be at least 150 problems released.
Coding solutions are cumulative, worth up to 5 points, but subject to availability as they are created by projects,
The project is worth up to 20 points. A list of possible topics is below the schedule.

Note that the grading is additive, and not scaled to the total number possible points. For example, 42 points from the problem sets, plus 6 coding problems, and 18 points from the project, would result in a final grade of 90 (that's sufficient for an A).

Both written and coded solutions will be submitted through Canvas. As this is very much a problem solving course, collaboration is strongly discouraged. For coding submission, which will be listed separately, you should also include a screenshot of your results on the auto grader.

Schedule

		Problem Set 0 (solutions)
W Jan 20	Modular arithmetic	notes slides Problem Set 1 (solutions)
M Jan 25	Bit complexity of arithmetic	notes slides Problem Set 2 (solutions)
W Jan 27	Generators of Multiplicative Groups Mod p	notes slides
M Feb 1	Fast Convolution	notes slides Problem Set 3 (solutions)
W Feb 3	Generating Functions	notes slides
M Feb 8	Primality Testing	notes slides Problem Set 4 (solutions)
W Feb 10	Factoring	notes slides
M Feb 15	Quadratic Sieve	notes Problem Set 5 (solutions)
W Feb 17	Number Fields	notes

M Feb 22	Inequalities	notes slides Problem Set 6 (solutions)
W Feb 24	No Ideas	notes slides
M Mar 1	Iterative Methods	notes slides Problem Set 7 (solutions)
W Mar 3	Iterative Methods 2	notes slides
M Mar 8	Multiplicative Weight Update	notes slides
W Mar 10		notes slides
M Mar 15	Concentration Bounds	notes slides Problem Set 8 (solutions)
W Mar 17		slides
M Mar 22	Interior Point Method	slides Problem Set 9 (solutions)
W Mar 24	Mid-Semester Break

M Mar 29	Divide-and-Conquer	notes slides Problem Set 10
W Mar 31	PartitionTrees	notes slides
M Apr 5	Kinetic Tournament Trees	notes slides Problem Set 11
W Apr 7	B-Trees and Lazy Propagation	notes slides
M Apr 12	Applications of Range Search	notes slides Problem Set 12
W Apr 14	Partially Recursive Lazy Updates	notes slides
M Apr 19	Matrix Multiplication 1	notes slides Problem Set 13
W Apr 21	Matrix Multiplication 2	slides
M Apr 26	Shifted Number Systems

Projects

Projects will revolve around creating and maintaining coding-based problems on an auto grader. They can be done in groups of size up to three, for which each can receive up to 20 points. An example of such an autogradable problem is Fast Factorial Calculator 3. Topics relevant to this course that I suggest are:

fast multiplication,
primitive roots / number theory,
generating functions,
polynomial factorization,
integer factorization,
primality testing,
iterative methods,
regression,
isotonic regression,
interior point method,
sparse / separable matrix algorithms and data structures,
Hankel/Toeplitz matrix algorithms,
fast multipole method,
exact/rational matrix inverses,

For those opting in for the project, there will be two meetings to discuss its status. Any accommodation requests for also making the presentations and meetings remote will be given full consideration without any negative impact on your grade.

Statement of Intent for Classroom Inclusivity

As a member of the Georgia Tech community, I am committed to creating a learning environment in which all of my students feel safe and included. Because we are individuals with varying needs, I am reliant on your feedback to achieve this goal. To that end, I invite you to enter into dialogue with me about the things I can stop, start, and continue doing to make my classroom an environment in which every student feels valued and can engage actively in our learning community.

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