601.435/635 Approximation Algorithms - Spring 2026

Instructor: Michael Dinitz
Lecture: T Th 9am - 10:15am, Krieger 308
Office Hours: Tuesday 12pm-1pm and by appointment, Malone 217

Resources:

Syllabus
There is no required textbook, but many lectures will cover topics from the following: The Design of Approximation Algorithms, David P. Williamson and David B. Shmoys, Cambridge University Press, 2011.
Online discussion board: Courselore. Join using this link.

Date	Topic	Reference	Notes
Jan 20	Intro, Vertex Cover	Lecture Notes, Lecture Board, Chapter 1.1
Jan 22	Steiner Tree, TSP	Lecture Notes, Lecture Board, Chapter 2.4, Exercise 2.5
Jan 27	Snow day!
Jan 29	Greedy: Set Cover	Lecture Notes, Lecture Board, Chapter 1.6	HW1 released
Feb 3	Greedy: Max Coverage, k-Center	Lecture Notes, Lecture Board, Chapter 2.2, Exercise 2.11
Feb 5	Local Search: Max Cut and Weighted Max Cut	Lecture Notes, Lecture Board, Chapter 2.6, 9.3
Feb 10	Local Search: Min Degree Spanning Tree	Lecture Notes, Lecture Board, Chapters 2.6, 9.3
Feb 12	Rounding and Dynamic Programming: Knapsack	Lecture Notes, Chapter 3.1	HW1 due, HW2 released
Feb 17	Rounding and Dynamic Programming: Min Makespan Scheduling	Chapter 3.2
Feb 19	Intro to LPs for Approximation Algorithms	Chapters 1.2, 1.3, 4.3, Appendix A
Feb 24	Deterministic Rounding: Metric Uncapacitated Facility Location	Chapter 4.5
Feb 26	Randomized Rounding: Set Cover and UFL	Chapters 1.7, 5.8	HW2 due, HW3 released
Mar 3	Randomized Rounding: Integer Multicommodity Flow	Chapters 5.10, 5.11
Mar 5	Randomized Rounding: Group Steiner Tree	Notes from CMU, GKR paper
Mar 10	Tree Embeddings and Group Steiner Tree
Mar 12	Tree Embeddings: FRT	Chapter 8.5	HW3 due, HW4 released
Mar 24	LPs as Metrics: s-t Mincut and Multiway Cut	Chapters 8.1, 8.2
Mar 26	LPs as Metrics: Multiway Cut and Multicut	Chapter 8.2
Mar 31	LPs as Metrics: Multicut	Chapter 8.3
Apr 2	LP duality and flow/cut gaps	Chapter 1.4, Appendix A	HW4 due, HW5 released
Apr 7	Dual Fitting and Primal-Dual Algorithms	Chapters 1.5, 1.6, 7.1, 7.3
Apr 9	Primal-Dual: Steiner Forest	Chapter 7.4
Apr 14	Strengthening Relaxations: Knapsack-Cover Inequalities	Chapter 7.5
Apr 16	Semidefinite Programming: Max-Cut	Chapters 6.1, 6.2	HW5 due
Apr 21	Semidefinite Programming: Correlation Clustering and Max-2SAT	Chapter 6.4
Apr 23	Hardness of Approximation and the PCP Theorem	Chapters 16.1, 16.2, 16.3
	Hardness of Approximation: Two-Prover Proof Systems and Label Cover	Chapter 16.4

Assignments

Please submit homeworks using Gradescope.

Homework 1: PDF, LaTeX
Homework 2: PDF, LaTeX

Project Information

This course will have a final project. The exact form is flexible and mostly up to you, subject to approval by the instructor. You can work in small groups if you want. Possible ideas include:

Doing new research in approximation algorithms.
Finding a problem in your research area that you can study from an approximation algorithms perspective
Preparing a lecture / presentation / writeup on some aspect of approximation algorithms that we did not cover in class. There has been significant work on approximation algorithms beyond the topics covered in this class, so there is still plenty to learn.

Additional Resources

Some texts that are related to topics we will cover. They are useful for further study in this field.

Iterative Methods in Combinatorial Optimization, Lap Chi Lau, R. Ravi, and Mohit Singh, Cambridge University Press, 2011.
Computational Complexity: A Modern Approach, Sanjeev Arora and Boaz Barak, Cambridge University Press, 2009.
Approximation Algorithms, Vijay V. Vazirani, Springer-Verlag, Berlin, 2001.

Similar courses with nice scribe notes.

Approximation Algorithms by Zachary Friggstad
Approximation Algorithms by Chandra Chekuri
Approximation Algorithms by Anupam Gupta and R. Ravi
Advanced Approximation Algorithms by Anupam Gupta and Ryan O'Donnell

Courses on related material with nice scribe notes.

Topics in Combinatorial Optimization by Chandra Chekuri
The PCP Theorem and Hardness of Approximation by Venkatesan Guruswami and Ryan O'Donnell
Linear and Semidefinite Programming by Anupam Gupta and Ryan O'Donnell