6.5210J/18.415J: Advanced Algorithms (Fall 2022, Previously 6.854)

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: Theia Henderson theia@mit.edu Office hours: TBD
Course assistant: Rebecca Yadegar ryadegar@csail.mit.edu

Announcements

  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.

Past 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., 6.1220J/18.410J, previously 6.046) and discrete mathematics and probability (6.1200J, previously 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

Submission

Due Date and Late Submission

Collaboration Policy

Peer Grading

Lectures

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

All lectures will be done before Thanksgiving
# Date Topic
Schedule below subject to change.
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: Persistent Data Structures. Splay Trees.
5. Fri, Sep. 17: Splay Trees.
6. Mon, Sep. 20: Buckets.
7. Wed, Sep. 22: Van Emde Boas Queues. Universal Hashing.
8. Fri, Sep. 24: Perfect Hashing. Max Flow: Flow Decomposition. S-T Cuts.
9. Mon, Sep. 27: Max Flow: Max-Flow Min-Cut. Augmenting Path Algorithms.
10. Wed, Sep. 29: Max Flow: Scaling. Strongly polynomial algorithms. Blocking Flows.
11. Fri, Oct. 1: Blocking Flows. State-of-the-Art Max Flow Results.
12. Mon, Oct. 4: Min Cost Flows
13. Wed, Oct. 6: Min Cost Flow Algorithms
14. Fri, Oct. 8: Linear Programming: Introduction. Size of Solutions.
Mon, Oct. 11: Indigenous Peoples Day - No class
15. Wed, Oct. 13: Linear Programming: Geometry. Structure of Optima. Duality Introduction.
16. Fri, Oct. 15: Linear Programming: Strong Duality.
17. Mon, Oct. 18: Linear Programming: Rules for Taking Duals. Duality Examples. Complementary Slackness.
18. Wed, Oct. 20: Linear Programming: Min-Cost Circulation Dual. Simplex Method.
19. Fri, Oct. 22: Linear Programming: Simplex Method. Ellipsoid Method.
20. Mon, Oct. 25: Linear Programming: Interior Point Method. Approximation Algorithms: Introduction.
21. Wed, Oct. 27: Approximation Algorithms: Greedy approaches. Scheduling. Approximation Schemes (PAS).
22. Fri, Oct. 29: Approximation Algorithms: Fully Polynomial Time Approximation Schemes (FPAS). Rounding. Enumeration.
23. Mon, Nov. 1: Approximation Algorithms: Relaxations. TSP. LP Relaxations.
24. Wed, Nov. 3: Approximation Algorithms: LP Relaxations. Facility Location. Approximation-Preserving Reductions.
25. Fri, Nov. 5: Approximation Algorithms: Randomized Rounding. Fixed Parameter Tractability.
26. Mon, Nov. 8: Treewidth. Computational Geometry: Range Trees. Sweep Algorithms.
27. Wed, Nov. 10: Computational Geometry: Voronoi Diagrams.
28. Fri, Nov. 12: Online Algorithms: Ski Rental. Finance.
29. Mon, Nov. 15: Online Algorithms: Load Balancing. Paging. Randomization.
30. Wed, Nov. 17: Online Algorithms: Paging. Randomization. K-Server Problem.
31. Fri, Nov. 19: Online Algorithms: K-Server Problem. External Memory Algorithms: Matrices. Linked Lists. Search Trees.
32. Mon, Nov. 22: External Memory Algorithms: Sorting. Buffer Trees. Cache Oblivious Algorithms.
Wed, Nov. 24: Thanksgiving holiday - No class
Fri, Nov. 26 Thanksgiving holiday - No class
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