随机算法 (Fall 2015): Difference between revisions

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= Lecture Notes =
= Lecture Notes =
# [[随机算法 (Fall 2015)/Identity Testing|Identity Testing]]: checking matrix multiplication, polynomial identity testing, communication complexity    | ([ftp://tcs.nju.edu.cn/slides/random2015/IdentityTesting.pdf slides])
# [[随机算法 (Fall 2015)/Identity Testing|Identity Testing]]: checking matrix multiplication, polynomial identity testing, communication complexity    | ([http://tcs.nju.edu.cn/slides/random2015/IdentityTesting.pdf slides])
# [[随机算法 (Fall 2015)/Fingerprinting|Fingerprinting]]: fingerprinting, the Karp-Rabin algorithm for pattern matching, primality testing    | ([ftp://tcs.nju.edu.cn/slides/random2015/Fingerprinting.pdf slides])
# [[随机算法 (Fall 2015)/Fingerprinting|Fingerprinting]]: fingerprinting, the Karp-Rabin algorithm for pattern matching, primality testing    | ([http://tcs.nju.edu.cn/slides/random2015/Fingerprinting.pdf slides])
# [[随机算法 (Fall 2015)/Balls and Bins|Balls and Bins]]: balls into bins model, birthday problem, perfect hashing, coupon collector problem, stable matching, occupancy problem  | ([ftp://tcs.nju.edu.cn/slides/random2015/BallsNBins.pdf slides])
# [[随机算法 (Fall 2015)/Balls and Bins|Balls and Bins]]: balls into bins model, birthday problem, perfect hashing, coupon collector problem, stable matching, occupancy problem  | ([http://tcs.nju.edu.cn/slides/random2015/BallsNBins.pdf slides])
# [[随机算法 (Fall 2015)/Min-cut|Min-cut]]: Karger's Min-cut algorithm    | ([ftp://tcs.nju.edu.cn/slides/random2015/Min-Cut.pdf slides])
# [[随机算法 (Fall 2015)/Min-cut|Min-cut]]: Karger's Min-cut algorithm    | ([http://tcs.nju.edu.cn/slides/random2015/Min-Cut.pdf slides])
# [[随机算法 (Fall 2015)/Moment and Deviation|Moment and Deviation]]: Markov's inequality, Chebyshev's inequality, median selection, random graphs, threshold phenomenon    | ([ftp://tcs.nju.edu.cn/slides/random2015/Moments.pdf slides])
# [[随机算法 (Fall 2015)/Moment and Deviation|Moment and Deviation]]: Markov's inequality, Chebyshev's inequality, median selection, random graphs, threshold phenomenon    | ([http://tcs.nju.edu.cn/slides/random2015/Moments.pdf slides])
# [[随机算法 (Fall 2015)/Universal Hashing|Universal Hashing]]: <math>k</math>-wise independence, universal hash families, perfect hashing    | ([ftp://tcs.nju.edu.cn/slides/random2015/UniversalHashing.pdf slides])
# [[随机算法 (Fall 2015)/Universal Hashing|Universal Hashing]]: <math>k</math>-wise independence, universal hash families, perfect hashing    | ([http://tcs.nju.edu.cn/slides/random2015/UniversalHashing.pdf slides])
# [[随机算法 (Fall 2015)/Randomized rounding|Randomized rounding]]: max-SAT, LP relaxation, randomized rounding    | ([ftp://tcs.nju.edu.cn/slides/random2015/RandomRounding.pdf slides])
# [[随机算法 (Fall 2015)/Randomized rounding|Randomized rounding]]: max-SAT, LP relaxation, randomized rounding    | ([http://tcs.nju.edu.cn/slides/random2015/RandomRounding.pdf slides])
# [[随机算法 (Fall 2015)/Lovász Local Lemma|Lovász Local Lemma]]:
# [[随机算法 (Fall 2015)/Lovász Local Lemma|Lovász Local Lemma]]:     | ([http://tcs.nju.edu.cn/slides/random2015/LLL.pdf slides])
# [[随机算法 (Fall 2015)/Chernoff Bound|Chernoff Bound]]: moment generating function, Chernoff bound, balls into bins, set balancing
# [[随机算法 (Fall 2015)/Chernoff Bound|Chernoff Bound]]: moment generating function, Chernoff bound, balls into bins, set balancing     | ([http://tcs.nju.edu.cn/slides/random2015/Chernoff.pdf slides])
# [[随机算法 (Fall 2015)/Concentration of Measure|Concentration of Measure]]: bounded difference method, Johnson-Lindenstrauss Theorem
# [[随机算法 (Fall 2015)/Concentration of Measure|Concentration of Measure]]: martingales, Azuma's inequality, Doob sequence, bounded difference method, Johnson-Lindenstrauss Theorem     | ([http://tcs.nju.edu.cn/slides/random2015/Concentration.pdf slides])
# [[随机算法 (Fall 2015)/Markov Chain and Random Walk|Markov Chain and Random Walk]]: Markov chain, random walk, stationary distribution, convergence of Markov chain, hitting/cover time    | ([http://tcs.nju.edu.cn/slides/random2015/MarkovChain.pdf slides])
# [[随机算法 (Fall 2015)/Mixing Time and Coupling|Mixing Time and Coupling]]: mixing time, coupling lemma, coupling of Markov chain, rapid mixing by coupling    | ([http://tcs.nju.edu.cn/slides/random2015/Coupling.pdf slides])
# [[随机算法 (Fall 2015)/Expander Graphs and Mixing|Expander Graphs and Mixing]]: expander graphs, graph spectrum, spectral gap, Cheeger's inequality, rapid mixing of expander walk    | ([http://tcs.nju.edu.cn/slides/random2015/Mixing.pdf slides])


= The Probability Theory Toolkit =
= The Probability Theory Toolkit =
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* [http://en.wikipedia.org/wiki/Pairwise_independence k-wise independence]
* [http://en.wikipedia.org/wiki/Pairwise_independence k-wise independence]
* The [http://en.wikipedia.org/wiki/Probabilistic_method  probabilistic method]
* The [http://en.wikipedia.org/wiki/Probabilistic_method  probabilistic method]
* The [http://en.wikipedia.org/wiki/Lov%C3%A1sz_local_lemma  Lovász local lemma]  and the [http://en.wikipedia.org/wiki/Algorithmic_Lov%C3%A1sz_local_lemma algorithmic Lovász local lemma]
* [http://en.wikipedia.org/wiki/Markov_chain Markov chain]:
::[http://en.wikipedia.org/wiki/Markov_chain#Reducibility reducibility], [http://en.wikipedia.org/wiki/Markov_chain#Periodicity Periodicity], [http://en.wikipedia.org/wiki/Markov_chain#Steady-state_analysis_and_limiting_distributions stationary distribution], [http://en.wikipedia.org/wiki/Hitting_time hitting time], cover time;
::[http://en.wikipedia.org/wiki/Markov_chain_mixing_time mixing time], [http://en.wikipedia.org/wiki/Conductance_(probability) conductance]

Latest revision as of 12:43, 15 September 2017

随机算法
Randomized Algorithms
Instructor
尹一通
Email yitong.yin@gmail.com yinyt@nju.edu.cn
office 计算机系 804
Class
Class meetings Friday, 4pm-6pm
仙I-206
Office hours Tuesday, 2-4pm
计算机系 804
Textbooks
Motwani and Raghavan.
Randomized Algorithms.
Cambridge Univ Press, 1995.
Mitzenmacher and Upfal.
Probability and Computing: Randomized Algorithms and Probabilistic Analysis.
Cambridge Univ Press, 2005.
v · d · e

This is the page for the class Randomized Algorithms for the Fall 2015 semester. Students who take this class should check this page periodically for content updates and new announcements.

Announcement

  • (2015/9/6) 第一次课程slides已上传。
  • (2015/9/22) Balls into bins 部分的slides已上传。
  • (2015/9/25) 第一次作业已发布，10月9日上课收。
  • (2015/10/29) 在蔡沛程同学的神勇帮助下，我们的课程网站服务器终于重新上线了！
  • (2015/10/29) 10月30日周五的课，由于校运动会本科生和研究生课程都要停课，故再停课一次 -_-|||
  • (2015/11/13) 讲义中关于随机图阈值现象的部分已经补齐。
  • (2015/11/13) 第二次作业已发布，11月27日上课收。
  • (2015/11/29) Lovasz local lemma 部分的讲义目前正在大幅度的改写，以反应algorithmic LLL的最新内容。写好之后会通知。

Course info

  • Instructor : 尹一通，
  • email: yitong.yin@gmail.com, yinyt@nju.edu.cn
  • office: 计算机系 804.
  • Class meeting: Friday 4pm-6pm, 仙I-206.
  • Office hour: Tuesday 2-4pm, 计算机系 804.

Syllabus

先修课程 Prerequisites

  • 必须：离散数学，概率论，线性代数。
  • 推荐：算法设计与分析。

Course materials

成绩 Grades

  • 课程成绩：本课程将会有若干次作业和一次期末考试。最终成绩将由平时作业成绩和期末考试成绩综合得出。
  • 迟交：如果有特殊的理由，无法按时完成作业，请提前联系授课老师，给出正当理由。否则迟交的作业将不被接受。

学术诚信 Academic Integrity

学术诚信是所有从事学术活动的学生和学者最基本的职业道德底线，本课程将不遗余力的维护学术诚信规范，违反这一底线的行为将不会被容忍。

作业完成的原则：署你名字的工作必须由你完成。允许讨论，但作业必须独立完成，并在作业中列出所有参与讨论的人。不允许其他任何形式的合作——尤其是与已经完成作业的同学“讨论”。

本课程将对剽窃行为采取零容忍的态度。在完成作业过程中，对他人工作（出版物、互联网资料、其他人的作业等）直接的文本抄袭和对关键思想、关键元素的抄袭，按照 ACM Policy on Plagiarism的解释，都将视为剽窃。剽窃者成绩将被取消。如果发现互相抄袭行为， 抄袭和被抄袭双方的成绩都将被取消。因此请主动防止自己的作业被他人抄袭。

学术诚信影响学生个人的品行，也关乎整个教育系统的正常运转。为了一点分数而做出学术不端的行为，不仅使自己沦为一个欺骗者，也使他人的诚实努力失去意义。让我们一起努力维护一个诚信的环境。

Assignments

Lecture Notes

  1. Identity Testing: checking matrix multiplication, polynomial identity testing, communication complexity | (slides)
  2. Fingerprinting: fingerprinting, the Karp-Rabin algorithm for pattern matching, primality testing | (slides)
  3. Balls and Bins: balls into bins model, birthday problem, perfect hashing, coupon collector problem, stable matching, occupancy problem | (slides)
  4. Min-cut: Karger's Min-cut algorithm | (slides)
  5. Moment and Deviation: Markov's inequality, Chebyshev's inequality, median selection, random graphs, threshold phenomenon | (slides)
  6. Universal Hashing: [math]\displaystyle{ k }[/math]-wise independence, universal hash families, perfect hashing | (slides)
  7. Randomized rounding: max-SAT, LP relaxation, randomized rounding | (slides)
  8. Lovász Local Lemma: | (slides)
  9. Chernoff Bound: moment generating function, Chernoff bound, balls into bins, set balancing | (slides)
  10. Concentration of Measure: martingales, Azuma's inequality, Doob sequence, bounded difference method, Johnson-Lindenstrauss Theorem | (slides)
  11. Markov Chain and Random Walk: Markov chain, random walk, stationary distribution, convergence of Markov chain, hitting/cover time | (slides)
  12. Mixing Time and Coupling: mixing time, coupling lemma, coupling of Markov chain, rapid mixing by coupling | (slides)
  13. Expander Graphs and Mixing: expander graphs, graph spectrum, spectral gap, Cheeger's inequality, rapid mixing of expander walk | (slides)

The Probability Theory Toolkit

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