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.
Reading: Lecture notes on matchings, §1.1-1.2
Reading: Lecture notes on matchings, §1.3
Reading: Lecture notes on matchings, §1.3
Reading: Lecture notes on matchings, §3.1
Reading: Lecture notes on matchings, §3.2
Reading: Lecture notes on matchings, §4
Reading: Lecture notes on matchings, §4
Reading: Lecture 16 of Dexter Kozen's book "The Design and Analysis of Algorithms"
Reading: Lecture 17 of Kozen's book
Reading: Lecture notes on
combinatorial consequences of the max-flow min-cut theorem.
Reading: Lecture notes on
combinatorial consequences of the max-flow min-cut theorem.
Reading: Supplementary lecture notes on flows; see also Lecture 18 of Kozen's book
Reading:
Lecture notes on linear programming, Section 1.
Reading:
Lecture notes on linear programming, Section 1.
Reading:
Lecture notes on linear programming, Section 2.
Reading: Not yet available.
Reading: Kozen's lecture notes
on NP-completeness, Lectures 21-22
Reading: Kozen's lecture notes
on NP-completeness, Lecture 23
Reading: Kozen's lecture notes
on NP-completeness, Lecture 24
Reading: Lecture notes on convex
optimization, sections 1-3
Reading: Lecture notes on convex
optimization, section 4
Reading: Lecture notes on submodular functions, sections 1-2
Reading: Lecture notes on submodular functions, section 4
Reading: Lecture notes on submodular functions, section 3
Reading: Lecture notes on approximation algorithms, sections 1 and 2.3
Reading: Lecture notes on approximation algorithms, sections 2.1,2.2
Reading: Lecture notes on approximation algorithms, section 3
Reading: Lecture notes on approximation algorithms, section 3
Reading: Lecture notes on approximation algorithms, section 4.1
Reading: Lecture notes on approximation algorithms, section 4.2
Reading: Lecture notes on spectral methods, sections 1-2
Reading: Lecture notes on spectral methods, sections 3-5
Reading: Lecture notes on spectral methods, section 78/30 —
Introduction: course information, start bipartite maximum matching
9/2 —
No class due to Labor Day
9/4 —
Bipartite maximum matching: Hopcroft-Karp algorithm
9/4 —
Bipartite maximum matching: Hopcroft-Karp running time analysis
9/9 —
Minimum-cost bipartite perfect matching: LP relaxation
9/11 —
Minimum-cost bipartite perfect matching: primal-dual algorithm
9/13 —
Online matching: greedy algorithm
9/16 —
Online matching: RANKING algorithm
9/18 —
Network flow: The max-flow min-cut theorem
9/20 —
Network flow: a polynomial-time algorithm
9/23 —
Network flow: max-flow min-cut theorem
9/25 —
Network flow: Combinatorial consequences of max-flow min-cut
9/27 —
Network flow: a strongly polynomial algorithm
9/30 —
NO CLASS DUE TO ROSH HASHANAH.
10/2 —
Linear programming I: Simplex algorithm
10/4 —
Linear programming II: Finishing simplex algorithm
10/7 —
Linear programming III: LP duality
10/9 —
NO CLASS DUE TO YOM KIPPUR.
10/11 —
Linear programming IV: Ellipsoid method
10/14 —
NO CLASS DUE TO FALL BREAK.
10/16 —
NP-Completeness I: Introducing NP-completeness reductions
10/18 —
NP-Completeness II: Independent Set
10/21 —
NP-Completeness III: Max Cut
10/23 —
Convex Optimization I: Unconstrained convex minimization
10/25 —
Convex Optimization II: Constrained convex minimization
10/28 —
Submodularity I: Definitions and Lovász extension
10/30 —
Submodularity II: Constrained monotone submodular maximization
11/1 —
Submodularity III: Packing spanning arborescences
11/4 —
Approximation Algorithms I: Set cover
11/6 —
Approximation Algorithms II: Vertex cover
11/8 —
Approximation Algorithms III: Finish vertex cover, start max cut
11/11 —
Approximation Algorithms IV: Max cut via semidefinite programming
11/13 —
The Chernoff bound
11/15 —
Approximation Algorithms V: Randomized routing and sparsest cut
11/18 —
Spectral methods I: Courant-Fischer and the graph Laplacian
11/20 —
Spectral methods II: Cheeger's Inequality
11/25 —
Spectral methods III: Spectral graph sparsification