Homework

• Homework 1 (Background)
• Homework 2
• Homework 3

Lecture slides.

• Lecture 1. Matching. Draft Slides.
  Draft Handout/slides.
  
  Readings: matching.
  Reading: duality.
• Lecture 2. Strong Duality. Draft Slides.
  Draft Handout/slides.
  
  Reading: Goemans notes.
  
  Reading: Lagrange and Hyperplane.
  
• Lecture 3. Strong Duality (continued.) Lagrangian Dual. Draft Slides.
  Draft Handout/slides.
  
  Reading: Lagrange and Hyperplane.
  
  Reading: Boyd Book. Chapter 5.1 and 11.
  
• Lecture 4. Central Path. Interior Point.
  Draft Slides.
  Draft Handout/slides.
  
  Reading: Boyd Book. Chapter 5.1 and 11.
• Lecture 5. Central Path. Interior Point.(continued)
  Draft Slides.
  Draft Handout/slides.
  
• Lecture 6. Perceptron. Multiplicative Weights.
  Draft Slides.
  Draft Handout/slides.
  
  Reading: Perceptron
  Reading: Experts
  Reading: Experts Applications
• Lecture 7. Multiplicative Weights.
  Draft Slides.
  Draft Handout/slides.
• Lecture 8. Multiplicative Weights. Games. Congestion.
  Draft Slides.
  Draft Handout/slides.
• Lecture 9. Boosting.
  Draft Slides.
  Draft Handout/slides.
  Reading: Raghavendra notes.
  
  
• Lecture 10. Gradient, Mirror Descent. Coupling. Draft Slides.
  Draft Handout/slides.
  Allen-Zhu,Orecchia Linear Coupling paper.
  
• Lecture 11. Coupling. Begin Iterative Methods.
  Draft Slides.
  Draft Handout/slides.
• Lecture 12. Eigenvalues. Linear System Solvers.
  Draft Slides.
  Draft Handout/slides.
• Lecture 13. Eigenvalues. Linear System Solvers.
  Draft Slides.
  Draft Handout/slides.
  Eigenvalues and cuts Notes.
• Lecture 14. Linear System Solvers.
  Draft Slides.
  Draft Handout/slides.
  Williamson Notes.
• Lecture 14. Linear System Solvers.
  Draft Slides.
  Draft Handout/slides.
  Williamson Notes.
• Lecture 15. Linear System Solvers.
  Draft Slides.
  Draft Handout/slides.
  
• Lecture 16. Cheeger.
  Draft Slides.
  Draft Handout/slides.
  Cheeger Notes.
  Cheeger Notes (Hard part).
  
• Lecture 17. Cheeger
  Draft Slides.
  Draft Handout/slides.
  
• Lecture 18. HST
  Draft Slides.
  Draft Handout/slides.
  Paper.
  
• Lecture 19. Minimum Cut. Concentration.
  Draft Slides.
  Draft Handout/slides.
  
• Lecture 20. Johnson-Lindenstrass
  Draft Slides.
  Draft Handout/slides.
  Notes.
  
• Lecture 21. PCA applications
  Draft Slides.
  Draft Handout/slides.
  PCA Notes.
  
• Lecture 22. Streaming
  Draft Slides.
  Draft Handout/slides.
  Streaming.
  Streaming Two.
  
• Lecture 23. Power of two choices. Cuckoo hashing.
  Draft Slides.
  Draft Handout/slides.
  Power of Two choices notes.
  
• Lecture 24. Monte Carlo Markov Chains. Expanders for Randomness.
  Draft Slides.
  Draft Handout/slides.
  
• Lecture 25. Approximation Algorithm for Facility Location.
  Draft Slides.
  Draft Handout/slides.
  CMU(A. Gupta) notes 1
  CMU(A. Gupta) notes 2
  
• Lecture 26. Nash's Theorem. And Sparsest cut.
  Draft Slides.
  Draft Handout/slides.
  
• Lecture 27. Negative weight Shortest Paths. Near Linear Time!!!!
  Draft Slides.
  Draft Handout/slides.
  
• Lecture 28. Negative weight Shortest Paths with Reals: Breakthrough!
  Draft Slides.
  Draft Handout/slides.
  

Notes. References.

• Matching Draft Notes.
• LP Notes.
  Goemans notes.
  Draft note: duality/complementary slackness.
• More LP notes.
  Lagrange and Convex Separation.

Course Outline

This course will focus on algorithms and the mathematics behind them. It will touch upon combinatorial algorithms, optimization, statistical algorithms, and a variety of other things. Beauty is key. Trying to get to what is really happening is key, and beauty. Perhaps they are the same thing.

Course Staff

Scheduling

Assessment