Lecture Topics (tentative)

Video recordings of the lectures up until September 20, 2019, can be found on Mediasite . The video recordings of lectures from CS 6820 in Fall 2018 are also archived.

8/30 — Introduction: course information, start bipartite maximum matching

Reading: Lecture notes on matchings, §1.1-1.2

9/2 — No class due to Labor Day

9/4 — Bipartite maximum matching: Hopcroft-Karp algorithm

Reading: Lecture notes on matchings, §1.3

9/4 — Bipartite maximum matching: Hopcroft-Karp running time analysis

Reading: Lecture notes on matchings, §1.3

9/9 — Minimum-cost bipartite perfect matching: LP relaxation

Reading: Lecture notes on matchings, §3.1

9/11 — Minimum-cost bipartite perfect matching: primal-dual algorithm

Reading: Lecture notes on matchings, §3.2

9/13 — Online matching: greedy algorithm

Reading: Lecture notes on matchings, §4

9/16 — Online matching: RANKING algorithm

Reading: Lecture notes on matchings, §4

9/18 — Network flow: The max-flow min-cut theorem

Reading: Lecture 16 of Dexter Kozen's book "The Design and Analysis of Algorithms"

9/20 — Network flow: a polynomial-time algorithm

Reading: Lecture 17 of Kozen's book

9/23 — Network flow: max-flow min-cut theorem

Reading: Lecture notes on combinatorial consequences of the max-flow min-cut theorem.

9/25 — Network flow: Combinatorial consequences of max-flow min-cut

Reading: Lecture notes on combinatorial consequences of the max-flow min-cut theorem.

9/27 — Network flow: a strongly polynomial algorithm

Reading: Supplementary lecture notes on flows; see also Lecture 18 of Kozen's book

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9/30 — NO CLASS DUE TO ROSH HASHANAH.

10/2 — Linear programming I: Simplex algorithm

Reading: Lecture notes on linear programming, Section 1.

10/4 — Linear programming II: Finishing simplex algorithm

Reading: Lecture notes on linear programming, Section 1.

10/7 — Linear programming III: LP duality

Reading: Lecture notes on linear programming, Section 2.

10/9 — NO CLASS DUE TO YOM KIPPUR.

10/11 — Linear programming IV: Ellipsoid method

Reading: Not yet available.

10/14 — NO CLASS DUE TO FALL BREAK.

10/16 — NP-Completeness I: Introducing NP-completeness reductions

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

10/18 — NP-Completeness II: Independent Set

Reading: Kozen's lecture notes on NP-completeness, Lecture 23

10/21 — NP-Completeness III: Max Cut

Reading: Kozen's lecture notes on NP-completeness, Lecture 24

10/23 — Convex Optimization I: Unconstrained convex minimization

Reading: Lecture notes on convex optimization, sections 1-3

10/25 — Convex Optimization II: Constrained convex minimization

Reading: Lecture notes on convex optimization, section 4

10/28 — Submodularity I: Definitions and Lovász extension

Reading: Lecture notes on submodular functions, sections 1-2

10/30 — Submodularity II: Constrained monotone submodular maximization

Reading: Lecture notes on submodular functions, section 4

11/1 — Submodularity III: Packing spanning arborescences

Reading: Lecture notes on submodular functions, section 3

11/4 — Approximation Algorithms I: Set cover

Reading: Lecture notes on approximation algorithms, sections 1 and 2.3

11/6 — Approximation Algorithms II: Vertex cover

Reading: Lecture notes on approximation algorithms, sections 2.1,2.2

11/8 — Approximation Algorithms III: Finish vertex cover, start max cut

Reading: Lecture notes on approximation algorithms, section 3

11/11 — Approximation Algorithms IV: Max cut via semidefinite programming

Reading: Lecture notes on approximation algorithms, section 3

11/13 — The Chernoff bound

Reading: Lecture notes on approximation algorithms, section 4.1

11/15 — Approximation Algorithms V: Randomized routing and sparsest cut

Reading: Lecture notes on approximation algorithms, section 4.2

and notes on sparsest cut in Section 4 of the lecture notes on the multiplicative weights method (from CS 6820, Fall 2016).

11/18 — Spectral methods I: Courant-Fischer and the graph Laplacian

Reading: Lecture notes on spectral methods, sections 1-2

11/20 — Spectral methods II: Cheeger's Inequality

Reading: Lecture notes on spectral methods, sections 3-5

11/25 — Spectral methods III: Spectral graph sparsification

Reading: Lecture notes on spectral methods, section 7