Lecture Topics (tentative)

Video recordings of all the lectures can be found on Mediasite .

8/24 — Introduction

Reading: Lecture notes on matchings, §1.1-1.2

8/27 — Bipartite maximum matching: naïve algorithm

Reading: Lecture notes on matchings, §1.3

8/29 — Bipartite maximum matching: Hopcroft-Karp algorithm

Reading: Lecture notes on matchings, §1.4

8/31 — Minimum-cost bipartite perfect matching: LP relaxation

Reading: Lecture notes on matchings, §3.1

9/3 — No class due to Labor Day

9/5 — Minimum-cost bipartite perfect matching: primal-dual algorithm

Reading: Lecture notes on matchings, §3.2

9/7 — Minimum-cost bipartite perfect matching: primal-dual algorithm, part 2

Reading: Lecture notes on matchings, §3.2

9/10 — No class due to Rosh Hashanah

9/12 — Online matching, part 1

Reading: Lecture notes on matchings, §4

9/14 — Online matching, part 1

Reading: Lecture notes on matchings, §4

9/17 — Network flow I: The Max-Flow Min-Cut Theorem

Reading: Kozen's book, Lecture 16

9/19 — Network flow II: Combinatorial applications of max-flow min-cut

(Guest lecture by Matvey Soloviev.)

Reading: Lecture notes on flows, §3

9/21 — Network flow III: The Ford-Fulkerson and Edmonds-Karp algorithms

Reading: Lecture notes on flows, §4-5.1

9/24 — Network flow IV: Dinitz's algorithms

Reading: Lecture notes on flows, §4-5.1

9/26 — Linear Programming I: Basic definitions and examples

Reading: Linear programming notes by Eva Tardos (Fall 2014), Sections 1 and 2.

9/28 — Linear Programming II: The simplex method

Reading: Lecture notes on the simplex method, through end of Section 1.1.

9/28 — Linear Programming II: The simplex method

Reading: Lecture notes on the simplex method, through end of Section 1.1.

10/1 — Linear Programming III: LP duality

Reading: Lecture notes on the simplex method.

10/3 — Linear Programming IV: Ellipsoid method

Reading: Linear programming notes by Eva Tardos (Fall 2014), Section 6. See also the notes by Santosh Vempala.

10/5 — Linear Programming V: Ellipsoid method, continued

Reading: Linear programming notes by Eva Tardos (Fall 2014), Section 6. See also the notes by Santosh Vempala.

10/10 — Semidefinite Programming

(Guest lecture by Jonathan Shi.)

Reading: Lecture notes on semidefinite programming.

10/12 — Convex Optimization

Reading: Lecture notes on convex optimization.

10/15 — NP-Completeness I: Independent Set and Related Problems

Reading: Kozen's lecture notes on NP-Completeness, Lectures 21-22

10/17 — NP-Completeness II: Hamiltonian Circuit and Related Problems

Reading: Kozen's lecture notes on NP-Completeness, Lecture 24 (second half)

10/19 — NP-Completeness III: Subset Sum and Related Problems

Reading: Kozen's lcture notes on NP-completeness, Lecture 24 (first half)