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 programmingbased exploration of the lecture ideas (60% of grade). Choice of takehome 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.
Homework:
Homework 1 (due Monday, Oct. 8th, Blackboard submission link)
Homework 2 (due Friday, Oct. 26th, Blackboard submission link)
Administrative Information
Lectures: Tuesday & Thursday 3:00pm4:20pm in Friend Center 004.
Teaching Assistants: Sixue Liu (Cliff)  sixuel@cs.princeton.edu, Seyed Sobhan Mir Yoosefi (Sobhan)  syoosefi@cs.princeton.edu.
Office Hours: Pravesh: Immediately after class, 194 Nassau St, Room 219.
Christopher: Immediately after class, Friends 004.
Sixue: Wed. 7:008:00pm, 194 Nassau St, Room 307.
Sobhan: Fri. 2:003:00pm, 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. Submission is managed through Princeton's Blackboard system. A compiled PDF of your
homework should be uploaded by 11:59pm on the due date.
For regular homework problems collaboration is allowed, but solutions must be
writtenup 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.  
2. 9/18  Randomized Minimum Cut  Lecture 2 notes.  
3. 9/20  Concentration Bounds  Lecture 3 notes.  
4. 9/25  Hashing to Reals  Lecture 4 Notes 

Linear Thinking  
5. 9/27  Linear Thinking  Lecture 5 Notes 

6. 10/2  LP Relaxations & Approximation Algorithms  Lecture 6 Notes 

7. 10/4  LP Relaxations Continued 


8. 10/9  Linear Programming Duality  Lecture 8 Notes  
9. 10/11  Learning from Experts: Multiplicative Weights Algorithm  Lecture 9 Notes 

Dimensionality Reduction  
10. 10/16  The JohnsonLindenstrauss Lemma  Lecture 10 Notes  
11. 10/18  Approximate regression, εnets, and Fast JL  
12. 10/23  Nearest Neighbor Search  
13. 10/25  Lowrank Approximation and SVD  
14. 10/30  No Class, Fall Recess  
15. 11/1  No Class, Fall Recess  
16. 11/6  Stochastic Block Model and Spectral Clustering  
Optimization  
17. 11/8  Gradient Descent  
18. 11/13  Ellipsoid Method  
19. 11/15  Interior Point Methods  
20. 11/20  Semidefinite Programming  
11/22  No Class, Thanksgiving  
Select Topics  
21. 11/27  TBA  
22. 11/29  TBA  
23. 12/4  TBA  
24. 12/6  TBA  
25. 12/11  TBA  
26. 12/13  TBA 