6.854/18.415J: Advanced Algorithms (Fall 2016)

Lecture: Monday, Wednesday, and Friday 2:30-4 in 32-141.
Units: 5-0-7 Graduate H-level
Instructors: David Karger karger at mit edu Office hours: Arrange by email. In Building 32, Room G592
Aleksander Mądry madry at mit edu Office hours: Arrange by email. In Building 32, Room G666
TAs: John Peebles jpeebles at mit.edu
  Tal Wagner talw at mit.edu
Office hours: Mondays, 4:30pm-5:30pm, Room 36-112
Fridays, 4:00pm-5:00pm, Room 36-144
Course assistant: Rebecca Yadegar ryadegar at 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 programing, 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 Grading Supervisor Graders (Mandatory) Time Report (Optional) Difficulty/Usefulness Survey
PS 1 Fri, Sep. 16 John sahasag@mit.edu 3(c); bristy@mit.edu 2; baxelrod@mit.edu 1; hongzi@mit.edu 5(c,d); ececca@mit.edu 5(a,b); yilundu@mit.edu 4; epayne@mit.edu 3(a,b) Link Link
PS 2 Wed, Sep. 21 Tal P1 nkb@mit.edu ;
P2 zanger@mit.edu ;
P3 umaroy@mit.edu ;
P4 timngo@mit.edu ;
P5 weiqiaoh@mit.edu ;
P6 ztzhang@mit.edu
Link Link
PS 3 Wed, Sep. 28 John P1 sshader@mit.edu;
P2 ycy@mit.edu;
P3 jimmy42@mit.edu;
P4 kaxiotis@mit.edu;
P5 tianxiao@mit.edu;
P6 ctunoku+6854@mit.edu
Link Link
PS 4 Wed, Oct. 5 Tal P1 dzaefn@mit.edu ;
P2 keyulu@mit.edu ;
P3 pahrens@mit.edu ;
P4 luh@mit.edu ;
P5 ronuchit@mit.edu
Link Link
PS 5 Fri, Oct. 14 John P1 hayks@mit.edu;
P2 arsen@mit.edu;
P3 alet+6854@mit.edu;
P4 hujh@mit.edu;
P5 bpchen@mit.edu
Link Link
PS 6 Wed, Oct. 19 Tal P1 abhijitm@mit.edu ;
P2 kocabey@mit.edu ;
P3 diomidov@mit.edu ;
P4 akkas@mit.edu ;
P5 jbpatel@mit.edu
Link Link
PS 7 Wed, Oct. 26 John Sign up here to grade pset7 Link Link


Note: The schedule is subject to change, 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 Notes
1. Wed, Sep. 7: Course introduction. Persistent data structures. nb
2. Fri, Sep. 9: Splay trees. nb
3. Mon, Sep. 12: Integer Queues: Dial's Algorithm. Tries. nb
4. Wed, Sep. 14: Integer Queues: Denardo and Fox, Van Emde Boas nb
5. Fri, Sep. 16:
Universal Hashing. Perfect Hashing.
Streaming Model I: Distinct Elements Problem.
6. Mon, Sep. 19:
Streaming Model II: Heavy Hitters Problem
Dimensionality Reduction: Johnson-Lindenstrauss Lemma.
7. Wed, Sep. 21: Network Flows I: Flow Decomposition and Augmenting Paths. nb
Fri, Sep. 23: NO CLASS (Student Holiday).
8. Mon, Sep. 26: Network Flows II: Basic Flow Algorithms and Capacity Scaling. nb
9. Wed, Sep. 28: Network Flows III: Strongly Polynomial Time Max Flow Algorithms. nb
10. Fri, Sep. 30: Network Flows IV: Blocking Flows.
Mon, Oct 3: (OPTIONAL LECTURE) Spectral Graph Theory I: The Graph Laplacian and its Eigenvalues. nb
11. Wed, Oct 5: Network Flows V: Min-Cost Flow and Cycle Cancelling Algorithm.
12. Fri, Oct 7: Network Flows VI: Min-Cost Flow and Feasible Prices.
Mon, Oct 10: NO CLASS (Columbus Day).
Wed, Oct 12: (OPTIONAL LECTURE) Spectral Graph Theory II: Random Walks and Laplacian Spectrum. nb
13. Fri, Oct 14: Introduction to Linear Programming, Structure of Optima. nb
14. Mon, Oct 17: Strong Duality, and Complementary Slackness. nb
15. Wed, Oct 19: Simplex and Ellipsoid Method.
16. Fri, Oct 21: Gradient Descent Method and its Applications. nb
17. Mon, Oct 24: Interior-Point Methods.


Wed, Sep. 7
Fri, Sep. 9