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.
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
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
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
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 LP11.4 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);PCP lecture at UW 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
Williamson-Shmoys.