6.854/18.415J: Advanced Algorithms (Fall 2020)

Lecture: Monday, Wednesday, and Friday 2:30-4 (Online lectures)
Units: 5-0-7 Graduate H-level
Instructors: David Karger karger@mit.edu Office hours: Arrange by email. In Building 32, Room G592
TAs: Josh Brunner brunnerj@mit.edu
 Christian Altamirano bdiehs@mit.edu
 Thiago Bergamaschi thiagob@mit.edu
Office hours: Monday 5:30-6:30pm and Friday 4-5pm online
Course assistant: Rebecca Yadegar ryadegar@csail.mit.edu

Course Announcements

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


Due Date and Late Submission


Peer Grading

Problem Set Due Date Solutions Grading Supervisor Gradescope code (Mandatory) Time Report Peer Grading Sign-up Late Submission
PS1 Wed, Sep. 9 Josh MY4B55 PS1 Time Survey PS1 Peer Grading PS1 Late Form
PS2 Wed, Sep. 16 Thiago MPV7N7 PS2 Time Survey PS2 Peer Grading PS2 Late Form
PS3 Wed, Sep. 23 Christian 95YNW7 PS3 Time Survey PS3 Peer Grading PS3 Late Form


Warning: This is last year's schedule, and will be changing. But we will finish lectures before Thanksgiving.

Be aware that some of the scribe notes might be very old, and do not necessarily reflect exactly what happened in this year's class.
# Date Topic Raw Notes Scribe Video
1. Wed, Sep. 2: Course introduction. Fibonacci heaps. MST. nb and nb nb video
2. Fri, Sep. 4: Fibonacci heaps. MST. Persistent Data Structures Intro. nb nb video
3. Wed, Sep. 9: Persistent Data Structures. Splay trees intro. nb nb video
4. Fri, Sep. 11: Splay trees. nb nb video
4. Mon, Sep. 14: Dial's Algorithm. Tries. Multi-level buckets. nb nb video
5. Wed, Sep. 16: Hashing. Universal Hashing. Perfect Hashing nb nb video
6. Mon, Sep. 14: Network Flows: Characterization. Decomposition. Augmenting Paths. nb nb video
7. Wed, Sep. 16: Network Flows: Maximum augmenting path. Capacity Scaling. nb nb
Network Flows: Strongly polynomial algorithms. nb
Fri, Sep. 18: (No class, student holiday)
8. Mon, Sep. 21: Min-Cost Flows: Feasible prices. nb nb
9. Wed, Sep. 23: Finish Min-Cost Flows. nb
10. Fri, Sep. 25: Introduction to Linear Programming. nb nb
11. Mon, Sep. 28: Linear Programming: Structure of Optima. Strong Duality. nb nb
12. Wed, Sep. 30: Linear Programming: Duality Applications. nb nb
13. Fri, Oct. 2: Linear Programming: Simplex Method. nb
14. Mon, Oct. 5: Linear Programming: Ellipsoid Method. nb
20. Wed, Oct. 21:
21. Fri, Oct. 23: Introduction to Approximation Algorithms. nb nb
22. Mon, Oct. 26: Approximation Algorithms: Greedy approaches. Enumeration and FPRAS (scheduling) nb
23. Wed, Oct. 28: Approximation Algorithms: Rounding LP solutions (Vertex Cover, Facility Location).
24. Fri, Oct. 30: Approximation Algorithms: MAX-SAT, parameterized complexity nb
24. Mon, Nov. 2: Computational Geometry I. nb nb
25. Wed, Nov. 4: Computational Geometry II. nb
26. Fri, Nov. 6: Online Algorithms: Ski Rental, Paging. nb nb
24. Wed, Nov. 9: Online Algorithms: Ski Rental, Paging. nb nb
25. Fri, Nov. 17: Online Algorithms: Adversaries, Randomization, k-server.
26. Mon, Nov. 20: Computational Geometry I. nb nb
Wed, Nov. 22: (No class)
Fri, Nov. 24: (No class)
27. Mon, Nov. 27: Computational Geometry II. nb