CS270

Combinatorial Algorithms and Data Structures

Fall 2025

Assessment

Homeworks

Notes and Handouts

Ed Stem

Homework

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. Review first order methods. Begin Iterative Methods. Eigenvalues.
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 15. Linear System Solvers. Cheeger.
Draft Slides.
Draft Handout/slides.
Lecture 16. Cheeger.
Draft Slides.
Draft Handout/slides.
Cheeger Notes.
Cheeger Notes (Hard part).
Original Cheeger Paper.
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/PCA Applications
Draft Slides.
Draft Handout/slides.
Notes.
PCA Notes.
Lecture 21. PCA applications/Streaming
Draft Slides.
Draft Handout/slides.
PCA Notes.
Streaming.
Streaming Two.
Lecture 22. Streaming. Power of two choices.
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.

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

Satish Rao (satishr@cs.berkeley.edu)

Scheduling

The class meets on Monday 5:00-6:30 PM and Wednesday 5:30-7:00 PM in 306 Soda.

Assessment

There will be some homeworks that will be sample graded, and perhaps other assignments (e.g., simple online assignments), and a final exam. This could change a bit over the semester as we may try to incorporate AI to help your learning, e.g., perhaps you will be asked to do scribe notes.