- Syllabus
- There is no required textbook, but many lectures will cover topics from the following: The Design of Approximation Algorithms, David P. Williamson and David B. Shmoys, Cambridge University Press, 2011.
- Online discussion board: Piazza

Date | Topic | Reference | Notes |
---|---|---|---|

Jan 26 | Intro, Vertex Cover | Lecture Notes, Lecture Board, Video, Chapter 1.1 | |

Jan 31 | Steiner Tree, TSP | Lecture Notes, Lecture Board, Video, Chapter 2.4, Exercise 2.5 | |

Feb 2 | Greedy: Set Cover | Lecture Notes, Lecture Board, Video, Chapter 1.6 | |

Feb 4 | Greedy: Max Coverage, k-Center | Lecture Notes, Lecture Board, Video, Chapter 2.2, Exercise 2.11 | |

Feb 9 | Local Search: Max Cut and Weighted Max Cut | Lecture Notes, Lecture Board, Video | HW1 released |

Feb 11 | Local Search: Min Degree Spanning Tree | Lecture Notes, Lecture Board, Video, Chapters 2.6, 9.3 | |

Feb 16 | Rounding and Dynamic Programming: Knapsack | Lecture Notes, Lecture Board, Video, Chapter 3.1 | |

Feb 18 | Rounding and Dynamic Programming: Min Makespan Scheduling | Lecture Notes, Lecture Board, Video, Chapter 3.2 | HW1 due, HW2 released |

Feb 23 | Intro to LPs for Approximation Algorithms | Lecture Notes, Lecture Board, Video, Chapters 1.2, 1.3, 4.3, Appendix A | |

Feb 25 | Deterministic Rounding: Metric Uncapacitated Facility Location | Lecture Notes, Lecture Board, Video, Chapter 4.5 | |

Mar 2 | Randomized Rounding: Set Cover and UFL | Lecture Notes, Lecture Board, Video, Chapters 1.7, 5.8 | |

Mar 4 | Randomized Rounding: Integer Multicommodity Flow | Lecture Notes, Lecture Board, Video, Chapters 5.10, 5.11 | HW2 due, HW3 released |

Mar 12 | Randomized Rounding: Group Steiner Tree | Lecture Notes, Lecture Board, Video, Notes from CMU, GKR paper | |

Mar 14 | Tree Embeddings and Group Steiner Tree | Lecture Notes, Lecture Board, Video | |

Mar 16 | Tree Embeddings: FRT | Lecture Notes, Lecture Board, Video, Chapter 8.5 | |

Mar 18 | LPs as Metrics: s-t Mincut and Multiway Cut | Lecture Notes, Lecture Board, Video, Chapters 8.1, 8.2 | HW3 due, HW4 released |

Mar 23 | LPs as Metrics: Multiway Cut and Multicut | Lecture Notes, Lecture Board, Video, Chapter 8.2 | |

Mar 25 | LPs as Metrics: Multicut | Lecture Notes, Lecture Board, Video, Chapter 8.3 | |

Apr 1 | LP duality and flow/cut gaps | Lecture Notes, Lecture Board, Video, Chapter 1.4, Appendix A | HW4 due, HW5 released |

Apr 6 | Dual Fitting and Primal-Dual Algorithms | Lecture Notes, Lecture Board, Video, Chapters 1.5, 1.6, 7.1, 7.3 | |

Apr 8 | Primal-Dual: Steiner Forest | Lecture Notes, Lecture Board, Video, Chapter 7.4 | |

Apr 13 | Strengthening Relaxations: Knapsack-Cover Inequalities | Lecture Notes, Lecture Board, Video, Chapter 7.5 | |

Apr 15 | Semidefinite Programming: Max-Cut | Lecture Notes, Lecture Board, Video, Chapters 6.1, 6.2 | HW5 due |

Apr 20 | Semidefinite Programming: Correlation Clustering and Max-2SAT | Lecture Notes, Lecture Board, Video, Chapter 6.4 | |

Apr 27 | Hardness of Approximation and the PCP Theorem | Lecture Board, Video, Chapters 16.1, 16.2, 16.3 | |

Apr 29 | Hardness of Approximation: Two-Prover Proof Systems and Label Cover | Lecture Notes, Lecture Board, Video, Chapter 16.4 |

- Homework 1: PDF, LaTeX. Due February 18.
- Homework 2: PDF, LaTeX. Due March 4.
- Homework 3: PDF, LaTeX. Due March 18.
- Homework 4: PDF, LaTeX. Due April 1.
- Homework 5: PDF, LaTeX. Due April 15.

- Iterative Methods in Combinatorial Optimization, Lap Chi Lau, R. Ravi, and Mohit Singh, Cambridge University Press, 2011.
- Computational Complexity: A Modern Approach, Sanjeev Arora and Boaz Barak, Cambridge University Press, 2009.
- Approximation Algorithms, Vijay V. Vazirani, Springer-Verlag, Berlin, 2001.

- Approximation Algorithms by Zachary Friggstad
- Approximation Algorithms by Chandra Chekuri
- Approximation Algorithms by Anupam Gupta and R. Ravi
- Advanced Approximation Algorithms by Anupam Gupta and Ryan O'Donnell

- Topics in Combinatorial Optimization by Chandra Chekuri
- The PCP Theorem and Hardness of Approximation by Venkatesan Guruswami and Ryan O'Donnell
- Linear and Semidefinite Programming by Anupam Gupta and Ryan O'Donnell