Tentative List of Topics for the Semester

Lecture Schedule

Links to video recordings of the lectures will be posted here for asynchronous viewing.

8/26— Matchings I: Bipartite maximum matching (Video; Notes)

Reading: Lecture notes on matchings, §1.1-1.3

8/28— Matchings II: Hopcroft-Karp algorithm (Video; Notes)

Reading: Lecture notes on matchings, §1.4

8/30— Matchings III: Min-cost bipartite perfect matching — Éva Tardos, guest lecturer (Video; Notes)

Reading: Lecture notes on matchings, §3.1

9/2— NO CLASS DUE TO LABOR DAY

9/4— Matchings IV: Analysis of Hopcroft-Karp (Video; Notes)

Reading: Lecture notes on matchings, §1.4

9/6— Matchings V: LP relaxation of min-cost matching (Video; Notes)

Reading: Lecture notes on matchings, §3.2-3.3

9/9— Matchings V: Online matching (Video; Notes)

Reading: Lecture notes on matchings, §4

9/11— Digression: The ski rental problem (Video; Notes)

9/13— Digression II: Online primal-dual analysis (Video; Notes)

9/16— Matchings VI: Analysis of RANKING (Video; Notes)

Reading: Lecture notes on matchings, §4

9/18— Matchings VII: Finishing analysis of RANKING; starting algebraic algorithms for matching (Video; Notes)

Reading: Lecture notes on matchings, §5.1-5.2

9/20— Matchings VIII: Algebraic Algorithms (continued) (Video; Notes)

Reading: Lecture notes on matchings, §5.1-5.2

9/23— Linear Programming I: Problem definition and observations (Video; Notes)

Reading: Lecture notes on linear programming, §1-2

9/25— Linear Programming II: Duality (Video; Notes)

Reading: Lecture notes on linear programming, §2

9/27— Linear Programming III: Simplex method (Video; Notes)

Reading: Lecture notes on linear programming, §1

9/30— Linear Programming IV: Proof of strong duality (Video; Notes)

Reading: Lecture notes on linear programming, §2

10/2— Linear Programming V: Separation Oracles (Video; Notes)

10/4— Linear Programming VI: Ellipsoid Algorithm (Video; Notes)

10/7— Network Flow I: Minimum cut problems (Video; Notes)

Reading: Lecture notes on network flow, §1-2

10/9— Network Flow II: Max-flow min-cut (Video; Notes)

Reading: Lecture notes on network flow, §1-2

10/11— Network Flow III: Ford-Fulkerson (Video; Notes)

Reading: Lecture notes on network flow, §3

10/16— Network Flow IV: Dinitz's Algorithm (Video; Notes)

Reading: Lecture notes on network flow, §4

10/18— Network Flow V: Applications (Video; Notes)

Reading: Lecture notes on network flow, §6

10/21— Multicommodity Flow I: Sparsest Cut and Multicommodity Flow Problems (Video; Notes)

Reading: Lecture notes on multicommodity flows, §3.1, 4.1

10/23— Multicommodity Flow II: Approximate Max-Flow Min-Cut (Video; Notes)

Reading: Lecture notes on multicommodity flows, §4.2-4.3

10/25— The Chernoff Bound (Video; Notes)

Reading: Lecture notes on multicommodity flows, §5.1

10/28— Multicommodity Flow III: Randomized Rounding for Approximate Congestion Minimization (Video; Notes)

Reading: Lecture notes on multicommodity flows, §5.2

10/30— Multicommodity Flow IV: Approximate Max-Flow Min-Cut Recap (Video; Notes)

Reading: Lecture notes on multicommodity flows, §4.2-4.3

11/1— Multicommodity Flow V: Finishing Approximate Max-Flow Min-Cut (Video; Notes)

Reading: Lecture notes on multicommodity flows, §4.2-4.3

11/4— Multiplicative Weights I: Halving and Weighted Majority (Video; Notes)

Reading: Lecture notes on multicommodity flows, §1

11/6— Multiplicative Weights II: Hedge (Video; Notes)

Reading: Lecture notes on multicommodity flows, §1 and §6

11/8— Multiplicative Weights III: Minimax Theorem (Video; Notes)

Reading: Lecture notes on multicommodity flows, §6

11/11— Lecture Not Recorded

11/13— Multiplicative Weights IV: Solving Multicommodity Flow (Video; Notes)

Reading: Lecture notes on multicommodity flows, §3

11/15— Spectral Methods I: The Graph Laplacian (Video; Notes)

Reading: Lecture notes on spectral methods, §2-3

11/18— Spectral Methods II: Degree-weighting and normalization (Video; Notes)

Reading: Lecture notes on spectral methods, §1, §4

11/20— Spectral Methods III: Cheeger's Inequality, part 1 (Video; Notes)

Reading: Lecture notes on spectral methods, §4

11/22— Spectral Methods IV: Cheeger's Inequality, part 2 (Video; Notes)

Reading: Lecture notes on spectral methods, §5

11/25— Spectral Methods V: Max-Cut and the Goemans-Williamson Algorithm (Video; Notes)

Reading: Lecture notes on approximation algorithms, §3

11/27-29— Thanksgiving Break

12/2— Markov Chains I: Sampling Problems (Video; Notes)

Reading: Lecture notes on Markov Chains, Sections 1-2

12/4— Markov Chains II: Metropolis Algorithm (Video; Notes)

Reading: Lecture notes on Markov Chains, Sections 3-4

12/6— Markov Chains III: Mixing Times and Couplings (Video; Notes)

Reading: Lecture notes on Markov Chains, Section 5

12/9— Markov Chains IV: Sampling Matchings (Video; Notes)

Reading: Lecture notes on Markov Chains, Section 6
See also Jerrum and Sinclair's paper on sampling matchings.