随机算法 (Fall 2011)

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随机算法 Randomized Algorithms

Randomized Algorithms by Motwani and Raghavan
Instructor
尹一通
Email yitong.yin@gmail.com yinyt@nju.edu.cn
office 蒙民伟楼 406
Class
Class meetings TBA
TBA
Office hours TBA
Textbook
Motwani and Raghavan, Randomized Algorithms. Cambridge Univ Press, 1995.
v · d · e

This is the page for the class Randomized Algorithms for the Fall 2011 semester. Students who take this class should check this page periodically for content updates and new announcements.

Announcement

There is no announcement yet.

Course info

  • Instructor : 尹一通,
  • email: yitong.yin@gmail.com, yinyt@nju.edu.cn
  • office: MMW 406.
  • Class meeting: TBA.
  • Office hour: TBA.

Syllabus

随机化(randomization)是现代计算机科学最重要的方法之一,近二十年来被广泛的应用于计算机科学的各个领域。在这些应用的背后,是一些共通的随机化原理。在随机算法这门课程中,我们将用数学的语言描述这些原理,将会介绍以下内容:

  • 一些重要的随机算法的设计思想和理论分析;
  • 概率论工具及其在算法分析中的应用,包括常用的概率不等式,以及数学证明的概率方法 (the probabilistic method);
  • 随机算法的概率模型,包括典型的随机算法模型,以及概率复杂度模型。

作为一门理论课程,这门课的内容偏重数学上的分析和证明。这么做的目的不单纯是为了追求严格性,而是因为用更聪明的方法去解决问题往往需要具备有一定深度的数学思维和数学洞察力。

先修课程 Prerequisites

  • 必须:离散数学,概率论。
  • 推荐:算法设计与分析。

Course materials

Policies

Assignments

There is no assignments yet.

Lecture Notes

  1. Introduction
  2. Probability Basics
  3. Balls and Bins
  4. Moment and Deviation
  5. Hashing and Fingerprinting
  6. Chernoff Bound
  7. Concentration of Measure
  8. Dimension Reduction
  9. The Probabilistic Method
  10. Approximation Algorithms, On-line Algorithms
  11. Markov Chain and Random Walk
  12. Random Walk Algorithms
  13. Coupling and Mixing Time
  14. Expander Graphs I
  15. Expander Graphs II
  16. Sampling and Counting
  17. Markov Chain Monte Carlo (MCMC)
  18. Complexity

The Probability Theory Toolkit

reducibility, Periodicity, stationary distribution, hitting time, cover time;
mixing time, conductance