Syllabus

- The Design of Approximation Algorithms, David P. Williamson and David B. Shmoys, Cambridge University Press, 2011.

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

Jan 31 | Intro, Vertex Cover | Chapter 1.1 | |

Feb 2 | Steiner Tree, TSP | Chapter 2.4, Exercise 2.5 | |

Feb 7 | Greedy: Set Cover and Maximum Coverage | Chapter 1.6, Exercise 2.11 | |

Feb 9 | Greedy: k-Center and Makespan Scheduling | Chapters 2.2, 2.3 | |

Feb 14 | Local Search: Max-Cut and Weighted Max-Cut | ||

Feb 16 | Local Search: Min Degree Spanning Tree | Chapters 2.6, 9.3 | HW1 released |

Feb 21 | Rounding and Dynamic Programming: Knapsack and Min-Makespan Scheduling | Chapters 3.1, 3.2 | |

Feb 23 | Rounding and Dynamic Programming: Min-Makespan Scheduling and Bin Packing | Chapters 3.2, 3.3 | HW1 due |

Feb 28 | Intro to LPs for Approximation Algorithms | Chapters 1.2, 1.3, 4.3, Appendix A | |

Mar 2 | Deterministic Rounding: Metric Uncapacitated Facility Location | Chapter 4.5 | HW2 out |

Mar 7 | Randomized Rounding: Set Cover and UFL | Chapters 1.7, 5.4, 5.8 | |

Mar 2 | Randomized Rounding: Max Dicut and Integer Routing | Chapters 5.10, 5.11 | HW2 due |

Mar 14 | Snow day! | ||

Mar 16 | Randomized Rounding: Group Steiner Tree | Notes from CMU, GKR paper | HW3 released |

Mar 28 | GST and Tree Embeddings | ||

Mar 30 | No class: Mike away |
HW3 due | |

Apr 4 | Tree Embeddings | Chapter 8.5 | |

Apr 6 | Tree embeddings, Steiner Point Removal, LPs as Metrics | Chapter 8.5, Theorem 8.19 (Chapter 8.6) | HW4 released |

Apr 11 | LPs as Metrics: Multiway Cut | Chapters 8.1, 8.2 | |

Apr 13 | LP Duality | Chapter 1.4, Appendix A | HW4 due |

Apr 18 | Dual Fitting and Primal-Dual | Chapters 1.5, 1.6, 7.1, 7.3 | |

Apr 20 | Primal-Dual: Steiner Forest | Chapter 7.4 | HW5 released |

Apr 25 | Semidefinite Programming: Max-Cut | Chapters 6.1, 6.2 | |

Apr 27 | SDP II: Correlation Clustering and Max-2SAT | Chapter 6.4 | HW5 due |

May 2 | No class: Mike Away |

- Homework 1: PDF, LaTeX. Due February 23.
- Homework 2: PDF, LaTeX. Due March 9.
- Homework 3: PDF, LaTeX. Due March 30.
- Homework 4: PDF, LaTeX. Due April 13.
- Homework 5: PDF, LaTeX. Due April 27.

**Jan 31:**Welcome to the class!

- 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