Spring'26: Complexity of Computation and Hardness of Approximation (CS 538)

Wednesday: 12:30-15:30
Busch Campus

Instructor: Karthik C. S.

This is a graduate course in computational complexity theory. The course will place special emphasis on providing context and intuition for the material covered. For the first half of the course, we will follow Goldreich's textbook; for the second half, we will use various surveys, research articles, and lecture notes.

Prerequisites: It will be helpful to have some background in algorithms and/or discrete mathematics, but no formal prerequisite will be enforced. If you do not satisfy the official prerequisites but are still interested in registering for the course and are concerned about being sufficiently prepared, please send me an email.
The only real prerequisite is some mathematical maturity.

Grading: To pass the course, you must satisfy both of the following requirements:
(1) You must get at least 7 questions completely correct in Homework 1. The homework is due on February 1.
(2) You must attend at least 9 out of the first 12 lectures.

Each student must either present a 1-hour lecture or submit a detailed report at the end of the course.
Your entire grade will be based on this component (conditional on meeting the two passing criteria above).
You will work with the instructor throughout the course to make progress on your lecture/report.

Topics and schedule


Lecture # When Topic
Lecture 1 01/21 Models of Computation (Chapter 1), P and NP (Chapter 2; Section 2.1), NP-Completeness (Chapter 2; Sections 2.2, 2.3, and 2.4)
Lecture 2 01/28 Polynomial Time Hierarchy (Chapter 3), Hierarchy theorems (Chapter 4),
and Time vs. Space (Chapter 5; Section 5.1)
Lecture 3 02/04 Space bounded complexity (Chapter 5; Sections 5.2, 5.3, and 5.4)
Lecture 4 02/11 Randomized and Counting computation (Chapter 6)
Lecture 5 02/18 Interactive proofs, AM, MA, Zero Knowledge Proofs (Chapter 9)
Lecture 6 02/25 IP = PSPACE Theorem
Lecture 7 03/04 Hardness Amplification
Lecture 8 03/11 PCP Theorem (Algebraic Proof Part I)
03/18 NO LECTURE
Lecture 9 03/25 PCP Theorem (Algebraic Proof Part II)
Lecture 10 04/01 PCP Theorem (Combinatorial Proof)
Lecture 11 04/08 Hardness of Approximation of Clique and Set Cover
Lecture 12 04/15 Unique Games Conjecture
Lecture 13 04/22 Presentations (virtual)
Lecture 14 04/29 Presentations (virtual)