Fall 2019 — 40391 Topics in computer science and optimization

This course is an introduction to algorithms for combinatorial optimization problems and for convex optimization problems. Topics will include greedy and dynamic programming approaches to network optimization problems, cut, flow and matching algorithms, linear programming, gradient descent, mirror descent, and Follow-the-Regularized-Leader algorithm for online convex optimization.

General information

Instructor: Luca Trevisan


Office hours: Thursdays 11-noon in 3-E1-14 Roentgen (from Sept 12 to Dec 5)

Exam: the take-home final exam was out on October 21 and is due on November 1


Past lectures

  1. 9/11. Overview of the course. Greedy methodology. Minimum spanning tree. (Reference: Dasgupta section 5.1)
  2. 9/17. Dynamic programming methodology. O(nm) time algorithm to compute edit distance. (Reference: Dasgupta 6.3 - it is a good idea to read sections 6.1 and 6.2 as well)
  3. 9/18. Dynamic programming algorithms for shortest paths in the presence of negative weights: single source in time O(|V|*|E|), all pairs in time O(|V|^3), in DAGs in time O(|V| +|E|). (References: Dasgupta sections 4.6, 4.7 and 6.6)
  4. 9/24. Dijsktra's algorithm. (Reference: Dasgupta section 4.4)
  5. 9/25. Ford-Fulkerson algorithm for maximum flow. (Reference: lecture 9 of my CS261 notes and Section 7.2 of Dasgupta)
  6. 10/1. Analysis of Ford-Fulkerson algorithm, max flow - min cut theorem, analysis of Edmonds-Karp algorithm. (Reference: references of last lecture and section 11.2 of my CS261 notes)
  7. 10/2. Reduction of matching in bipartite graphs to max flow. (Reference: Dasgupta section 7.3 and sections 14.1 and 14.2 of my CS261 notes)
  8. 10/8. Proof of Hall's theorem using reduction of matching to flow. Beginning of discussion of linear programming. (Reference: Dasgupta 7.1, lecture 5 of my CS261 notes)
  9. 10/9. Linear programming: geometric interpretation, simplex algorithm, phase 1 and phase 2 of simplex algorithm. (Reference: Dasgupta 7.6)
  10. 10/15. Linear programming: informal overview of ellipsoid and interior-point algorithms. Duality. Introduction to 2-player 0-sum games. (Reference: Dasgupta 7.4 and 7.5, Sections 5.2.4 and Lecture 6 of my CS261 notes)
  11. 10/16. Online optimization, multiplicative weight updates. Reference: Notes for lecture 11
  12. 10/23. The "Follow-the-Regularized-Leader" algorithm. Reference: Notes for lecture 12

Plan for the course