6.854/18.415J: Advanced Algorithms (Fall 2021)

Lecture: Monday, Wednesday, and Friday 2:30-4 in 32-123.
Units: 5-0-7 Graduate H-level
Instructors: David Karger karger@mit.edu Office hours: Arrange by email. In Building 32, Room G592
TAs: Angelos Pelecanos apelecan@mit.edu Office hours: Monday and Friday 4-6 in Building 36, Room 36-153 and virtually.
Theia Henderson theia@mit.edu
William Kuszmaul kuszmaul@mit.edu
Course assistant: Rebecca Yadegar ryadegar@csail.mit.edu


  1. If you intend to take this course please fill out this survey. Note that this form does NOT replace official registration via MIT Registrar's office, it's for our own internal bookkeeping.
  2. We will be using NB, a tool that permits students to discuss and ask questions about lecture videos, notes, and problems sets. For feature reasons we will be using one version of the tool to view and discuss videos and another to view and discuss notes and problems sets. You should sign up for NBv1 at this link. You will get a separate invite for NBv2.
  3. We've added this class to psetpartners, which you can use to find collaborators and comply with the collaboration policy which limits the number of psets you can work on with any individual collaborator.
  4. Homework 2 is due on Wednesday 9/22. Don't forget that you can use NB to publicly (or privately to the staff) annotate the problem set with questions and clarifications! Just drag a rectangle around what you want to talk about.
  5. You can now find the course materials for the first half of this course, including all notes and videos, here. These materials should serve to supplement the in-person lectures but not replace them. We've done our best to synchronize everything but there are inevitable inconsistencies between historic lectures and this year's.

Course Overview

The need for efficient algorithms arises in nearly every area of computer science. But the type of problem to be solved, the notion of what algorithms are "efficient," and even the model of computation can vary widely from area to area.
This course is designed to be a capstone course in algorithms that surveys some of the most powerful algorithmic techniques and key computational models. It aims to bring the students up to the level where they can read and understand research papers.
We will cover a broad selection of topics including amortization, hashing, dimensionality reduction, bit scaling, network flow, linear programming, and approximation algorithms. Domains that we will explore include data structures; algorithmic graph theory; streaming algorithms; online algorithms; parallel algorithms; computational geometry; external memory/cache oblivious algorithms; and continuous optimization.

The prerequisites for this class are strong performance in undergraduate courses in algorithms (e.g., 6.046/18.410) and discrete mathematics and probability (6.042 is more than sufficient), in addition to substantial mathematical maturity.

The coursework will involve problem sets and a final project that is research-oriented. For more details, see the handout on course information.

Problem Sets

Problem Set Due Date Solutions Grading Supervisor Gradescope (Mandatory) Time Report Peer Grading Sign-up Late Submission
PS1 Wed, Sep. 15 V8X428 PS1 Survey PS1 Grading PS1 Late
PS2 Wed, Sep. 22 N8N6DB PS2 Survey PS2 Grading PS2 Late


Due Date and Late Submission

Collaboration Policy

Peer Grading


For notes and videos related to each topic, see the course materials.

# Date Topic
1. Wed, Sep. 8: Course introduction. Fibonacci heaps. MST.
2. Fri, Sep. 10: Fibonacci heaps.
3. Mon, Sep. 13: Fibonacci heaps. MST. Persistent Data Structures.
4. Wed, Sep. 15: Splay Trees.
5. Fri, Sep. 17: Splay Trees. Buckets.
Below this point is last year's schedule and subject to change.
All lectures will be done before Thanksgiving
6. Mon, Sep. 20: van Emde Boas Queues and Hashing
7. Wed, Sep. 22: Universal Hashing. Perfect Hashing. Begin Network Flows.
8. Fri, Sep. 24: Network Flows: Charaterization. Augmenting Paths. Max Flow Min Cut Theorem.
9. Mon, Sep. 27: Network Flows: Maximum augmenting path. Capacity Scaling.
10. Wed, Sep. 29: Network Flows: Strongly polynomial algorithms. Blocking Flows.
11. Fri, Oct. 1: Min-Cost Flows: Feasible prices.
12. Mon, Oct. 4: Min-Cost Flows
13. Wed, Oct. 6: Finish Min-Cost Flows and Introduction to Linear Programming.
14. Fri, Oct. 8: Linear Programming: Structure of Optima.
Mon, Oct. 11: Indigenous Peoples Day - No class
15. Wed, Oct. 13: Linear Programming: Strong Duality.
16. Fri, Oct. 15: Linear Programming: Strong Duality and Duality Applications.
17. Mon, Oct. 18: Linear Programming: Duality Applications.
18. Wed, Oct. 20: Linear Programming: Simplex Method.
19. Fri, Oct. 22: Linear Programming: Ellipsoid Method.
20. Mon, Oct. 25: Introduction to Approximation Algorithms.
21. Wed, Oct. 27: Approximation Algorithms: Greedy approaches. Enumeration and FPAS (scheduling)
22. Fri, Oct. 29: Approximation Algorithms: Enumeration, Rounding, Metric TSP.
23. Mon, Nov. 1: Approximation Algorithms: Relaxations
24. Wed, Nov. 3: Approximation Algorithms: Randomized Rounding
25. Fri, Nov. 5: Computational Geometry I.
26. Mon, Nov. 8: Computational Geometry II: Voronoi Diagrams
27. Wed, Nov. 10: Online Algorithms: Ski Rental, Paging.
28. Fri, Nov. 12: Online Algorithms: Paging, Adversaries, Randomization
29. Mon, Nov. 15: Online Algorithms: Adversaries, Randomization, k-server.
30. Wed, Nov. 17: The k-server problem and External Memory Algorithms.
31. Fri, Nov. 19: External Memory Algorithms.
32. Mon, Nov. 22: Parallel Algorithms.
33. Wed, Nov. 24: Parallel Algorithms.
Fri, Nov. 26 Thanksgiving holiday - No class