近似算法讨论班 (Fall 2011)

Syllabus

• Time: every Thursday, 6:30pm.
• Place: CS building, 228.

• Organizer: 尹一通

• office: CS building, 804
• email: yitong.yin@gmail.com

Reference materials

• Vijay Vazirani. Approximation Algorithms. Springer, 2004.
• David Williamson and David Shmoys. The Design of Approximation Algorithms. Cambridge Univ Press, 2011.
• Michel Goemans. Linear Programming. Lecture notes of Advanced Algorithms class at MIT.
• Venkatesan Guruswami and Ryan O'Donnell. The PCP Theorem and Hardness of Approximation.

Schedule

Dates	Speakers	Topics	Readings
9.26	张驰豪 （上海交通大学）	Introduction to approximation algorithms. Approximation ratio; set cover; rounding an LP; LP duality; greedy algorithms.	Chap. 1 of Williamson-Shmoys.
10.8	张驰豪 （上海交通大学）	Greedy algorithms and local search. Scheduling with deadlines; [math]\displaystyle{ k }[/math]-center; minimize makespan; metric TSP; min-degree spanning tree.	Chap. 2.1-2.4 of Williamson-Shmoys.
10.13	詹宇森 蒋炎岩 尹一通	Local search (cont.). Scale and round. Min-degree spanning tree; local search; potential analysis; Knapsack; dynamic programming; pseudo-polynomial time; scale and round; FPTAS.	Chap. 2.6, 3.1 of Williamson-Shmoys.
10.20	老师出差，暂停一次。
10.27	陈嘉	Linear Programming. Linear Programming; the simplex method; duality; strong duality theorem; von Neumann's minmax theorem.	[slides] Geomans' notes on LP
11.4	周源 (Carnegie Mellon University)	Approximation (and inapproximability) of MAX-CUT. MAX-CUT; the probabilistic method; semi-definite programming (SDP); rounding SDP; inapproximability; gap-reduction; probabilistically checkable proofs (PCP); the PCP theorem; label cover game; parallel repetition theorem; unique label cover game; the unique games conjecture (UGC); Boolean function; Fourier transformation; Parseval's identity; influence; noise operator; stability; long code reduction; majority is the stablest (MIS);	Chap. 6.1, 6.2 of Williamson-Shmoys. PCP lecture at UW by Guruswami and O'Donnell
11.10	张驰豪 （上海交通大学） 尹一通	Scale and round (cont.). Deterministic rounding of LP. Bin packing; first-fit; exhaustive search; polynomial-time approximation scheme (PTAS). Scheduling on a single machine; completion time; preemptive; shortest remaining processing time (SRPT); the ellipsoid algorithm; separation oracle.	Chap. 3.3, 4.1-4.3 of Williamson-Shmoys.
11.17	张驰豪 （上海交通大学）	The primal-dual method.	Chap. 7.1-7.4 of Williamson-Shmoys.
11.24	朱小虎 张驰豪 （上海交通大学）	The Steiner tree problem.
12.1	詹宇森 张驰豪 （上海交通大学）	Prize-collection Steiner tree; rounding; derandomization.
12.8	陈嘉	Algorithmic Game Theory. Strategic games; mechanism design; combinatorial auction; Vickrey auction; VCG auction.
12.15	尹一通	Approximate counting; correlation decay; spin systems.