Princeton COS 521
Advanced Algorithm Design

Capstone graduate algorithms course covering advanced topics such as randomness, optimization, and high dimensional geometry. We also explore diverse applications of algorithmic tools and thinking.

Instructors: Pravesh Kothari, Christopher Musco

Course Summary

Material: COS 521 gives a broad yet deep exposure to algorithmic advances of the past few decades, preparing students to read and understand research papers in algorithms. Course is suitable for graduate students (including those not in CS) and advanced undergrads.

Prerequisites: One undergraduate course in algorithms (e.g., COS 423), or equivalent mathematical maturity. Listeners and auditors are welcome with prior permission.

Coursework: Two lectures per week. 5 homeworks, including some simple programming-based exploration of the lecture ideas (60% of grade). Choice of take-home final in January, or a term project in groups of two (40% of grade). For specific policy on grading, late assignments, etc. please see the grading policy sheet.

Resources: There is no official text -- we will use our own lecture notes and assorted online resources. Please see course webpages from previous years for additional material.

Administrative Information

Lectures: Tuesday & Thursday 3:00pm-4:20pm in Friend Center 004.

Teaching Assistants: Sixue Liu (Cliff) -, Seyed Sobhan Mir Yoosefi (Sobhan) -

Office Hours: Pravesh: Immediately after class, 194 Nassau St, Room 219.
Christopher: Immediately after class, Friends 004.
Sixue: Wed. 7:00-8:00pm, 194 Nassau St, Room 307.
Sobhan: Fri. 2:00-3:00pm, 35 Olden St, Room 431.

Piazza: Course discussion and questions will be managed through Piazza. Please sign up here.

Homework: We require students to prepare problem sets in LaTeX. You can use this template. A compiled PDF of your homework should be emailed with the subject "CS521 HW #" to by 11:59pm on the due date.

For regular homework problems collaboration is allowed, but solutions must be written-up individually. Students must list collaborators for each problem separately, or write "No Collaborators" if you worked alone. Collaboration is not allowed on bonus problems (see grading policy).

Lecture # Topic Required Reading Optional Reading
Randomness and Hashing
1. 9/13 Hashing Lecture 1 notes.
  • Interesting paper and lecture on the practical importance of choosing a hash function with the right independence properties.
  • Blog post on attacks against hash-based data structures.
2. 9/18 Randomized Minimum Cut
3. 9/20 Concentration Bounds
4. 9/25 Hashing to Reals
Linear Thinking
5. 9/27 Multiplicative Weights
6. 10/2 Linear Programming
7. 10/4 LP Relaxation & Approximation Algorithms
8. 10/9 LP Duality & Game Theory
Dimensionality Reduction
9. 10/11 Johnson-Lindenstrauss Lemma
10. 10/16 Nearest Neighbor Search
11. 10/18 Low-rank Approximation and SVD
12. 10/23 Stochastic Block Model and Spectral Clustering
13. 10/25 Random Walks and Markov Chains
10/30 No Class, Fall Recess
11/1 No Class, Fall Recess
14.11/6 Gradient Descent
15. 11/8 Ellipsoid Method
16. 11/13 Interior Point Methods
17. 11/15 Semidefinite Programming
18. 11/20 TBA
11/22 No Class, Thanksgiving
Select Topics
19. 11/27 TBA
20. 11/29 TBA
21. 12/4 TBA
22. 12/6 TBA
23. 12/11 TBA
24. 12/13 TBA