随机算法 (Spring 2013): Difference between revisions
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= Announcement = | = Announcement = | ||
* <font color=red size=4> | * <font color=red size=4>所有slides已经上传。</font> | ||
* | * The last [[随机算法 (Spring 2013)/Problem_Set_4|homework assignment]] is out, due on the date of the final exam. | ||
* 前几堂课的讲义已经补上，足够完成第三次作业。 | |||
* The third [[随机算法 (Spring 2013)/Problem_Set_3|homework assignment]] is out, due in two weeks. | |||
* The second [[随机算法 (Spring 2013)/Problem_Set_2|homework assignment]] is out, due in two weeks. | |||
* 第1次作业第3题新增一问。由于是在作业发布之后修改，是否做这一问题不会影响分数，但增加此问会使该题目更有意义。 | |||
* The first [[随机算法 (Spring 2013)/Problem_Set_1|homework assignment]] is out, due in two weeks. | |||
= Course info = | = Course info = | ||
| Line 80: | Line 85: | ||
=== 成绩 Grades === | === 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。 | * 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。 | ||
| Line 94: | Line 99: | ||
= Assignments = | = Assignments = | ||
*[[随机算法 (Spring 2013)/Problem Set 1|Problem Set 1]], due on March 26, Tuesday, in class. | *[[随机算法 (Spring 2013)/Problem Set 1|Problem Set 1]], due on March 26, Tuesday, in class. | ||
*[[随机算法 (Spring 2013)/Problem Set 2|Problem Set 2]], due on April 23, Tuesday, in class. | |||
*[[随机算法 (Spring 2013)/Problem Set 3|Problem Set 3]], due on June 4, Tuesday, in class. | |||
*[[随机算法 (Spring 2013)/Problem Set 4|Problem Set 4]], due on June 24, before final exam. | |||
= Lecture Notes = | = Lecture Notes = | ||
<font color=red size=4>Slides:</font><font size=4> [http://tcs.nju.edu.cn/slides/random2013/random1.pdf 1]| [http://tcs.nju.edu.cn/slides/random2013/random3.pdf 3]| [http://tcs.nju.edu.cn/slides/random2013/random4.pdf 4]| [http://tcs.nju.edu.cn/slides/random2013/random5.pdf 5]| [http://tcs.nju.edu.cn/slides/random2013/random6.pdf 6]| [http://tcs.nju.edu.cn/slides/random2013/random7.pdf 7]| [http://tcs.nju.edu.cn/slides/random2013/random8.pdf 8]| [http://tcs.nju.edu.cn/slides/random2013/random9.pdf 9]| [http://tcs.nju.edu.cn/slides/random2013/random10.pdf 10]| [http://tcs.nju.edu.cn/slides/random2013/random11.pdf 11]| [http://tcs.nju.edu.cn/slides/random2013/random12.pdf 12]| [http://tcs.nju.edu.cn/slides/random2013/random13.pdf 13]| [http://tcs.nju.edu.cn/slides/random2013/random14.pdf 14]| [http://tcs.nju.edu.cn/slides/random2013/random15.pdf 15]| [http://tcs.nju.edu.cn/slides/random2013/random16.pdf 16]| [http://tcs.nju.edu.cn/slides/random2013/random17.pdf 17] </font> | |||
# [[随机算法 (Spring 2013)/Introduction and Probability Space|Introduction and Probability Space]]: checking matrix multiplication, polynomial identity testing | # [[随机算法 (Spring 2013)/Introduction and Probability Space|Introduction and Probability Space]]: checking matrix multiplication, polynomial identity testing | ||
# [[随机算法 (Spring 2013)/Conditional Probability|Conditional Probability]]: polynomial identity testing, min-cut | # [[随机算法 (Spring 2013)/Conditional Probability|Conditional Probability]]: polynomial identity testing, min-cut | ||
# [[随机算法 (Spring 2013)/Random Variables and Expectations|Random Variables and Expectations]]: random quicksort, balls and bins | # [[随机算法 (Spring 2013)/Random Variables and Expectations|Random Variables and Expectations]]: random quicksort, balls and bins | ||
# [[随机算法 (Spring 2013)/Moment and Deviation| Moment and Deviation]]: stable marriage, Markov's inequality, Chebyshev's inequality, median selection | # [[随机算法 (Spring 2013)/Moment and Deviation|Moment and Deviation]]: stable marriage, Markov's inequality, Chebyshev's inequality, median selection | ||
# | # [[随机算法 (Spring 2013)/Threshold and Concentration|Threshold and Concentration]]: random graphs, threshold phenomenon, Chernoff bound | ||
# Chernoff Bound | # [[随机算法 (Spring 2013)/Applications of Chernoff Bound|Applications of Chernoff Bound]]: error reduction, set balancing, packet routing | ||
# Concentration of Measure | # [[随机算法 (Spring 2013)/Concentration of Measure|Concentration of Measure]]: martingales, Azuma's inequality, Doob martingales, chromatic number of random graphs | ||
# The Probabilistic Method | # [[随机算法 (Spring 2013)/Random Projection|Random Projection]]: Johnson-Lindenstrauss Theorem | ||
# Markov Chain and Random Walk | # [[随机算法 (Spring 2013)/Universal Hashing|Universal Hashing]]: <math>k</math>-wise independence, universal hash families, perfect hashing | ||
# Coupling | # [[随机算法 (Spring 2013)/The Probabilistic Method|The Probabilistic Method]]: MAX-SAT, conditional probability method, Lovász Local Lemma | ||
# Expander Graphs | # [[随机算法 (Spring 2013)/Markov Chain and Random Walk|Markov Chain and Random Walk]]: Markov chain, random walk, stationary distribution, convergence of Markov chain, hitting/cover time | ||
# [[随机算法 (Spring 2013)/Mixing Time and Coupling|Mixing Time and Coupling]]: mixing time, coupling lemma, coupling of Markov chain, rapid mixing by coupling | |||
# [[随机算法 (Spring 2013)/Expander Graphs and Mixing|Expander Graphs and Mixing]]: expander graphs, graph spectrum, spectral gap, Cheeger's inequality, rapid mixing of expander walk | |||
# Sampling and Counting | # Sampling and Counting | ||
= The Probability Theory Toolkit = | = The Probability Theory Toolkit = | ||
* [http://en.wikipedia.org/wiki/Probability_space Probability space] and [http://en.wikipedia.org/wiki/Probability_axioms probability axioms] | |||
* [http://en.wikipedia.org/wiki/Independence_(probability_theory)#Independent_events Independent events] | |||
* [http://en.wikipedia.org/wiki/Conditional_probability Conditional probability] | |||
* [http://en.wikipedia.org/wiki/Random_variable Random variable] and [http://en.wikipedia.org/wiki/Expected_value expectation] | |||
* [http://en.wikipedia.org/wiki/Expected_value#Linearity Linearity of expectation] | |||
* The [http://en.wikipedia.org/wiki/Law_of_total_probability law of total probability] and the [http://en.wikipedia.org/wiki/Law_of_total_expectation law of total expectation] | |||
* The [http://en.wikipedia.org/wiki/Boole's_inequality union bound] | |||
* [http://en.wikipedia.org/wiki/Bernoulli_trial Bernoulli trials] | |||
* [http://en.wikipedia.org/wiki/Geometric_distribution Geometric distribution] | |||
* [http://en.wikipedia.org/wiki/Binomial_distribution Binomial distribution] | |||
* [http://en.wikipedia.org/wiki/Markov's_inequality Markov's inequality] | |||
* [http://en.wikipedia.org/wiki/Variance Variance] and [http://en.wikipedia.org/wiki/Covariance covariance] | |||
* [http://en.wikipedia.org/wiki/Chebyshev's_inequality Chebyshev's inequality] | |||
* [http://en.wikipedia.org/wiki/Chernoff_bound Chernoff bound] | |||
* [http://en.wikipedia.org/wiki/Martingale_(probability_theory) Martingale] | |||
* [http://en.wikipedia.org/wiki/Azuma's_inequality Azuma's inequality] and [http://en.wikipedia.org/wiki/Hoeffding's_inequality Hoeffding's inequality] | |||
* [http://en.wikipedia.org/wiki/Doob_martingale Doob martingale] | |||
* [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/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 12:44, 15 September 2017
| Instructor | |
|---|---|
| 尹一通 | |
| yitong.yin@gmail.com yinyt@nju.edu.cn | |
| office | 计算机系 804 |
| Class | |
| Class meetings |
Tuesday, 10am-12pm 仙逸B-207 |
| Office hours |
Wednesday, 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. | |
This is the page for the class Randomized Algorithms for the Spring 2013 semester. Students who take this class should check this page periodically for content updates and new announcements.
Announcement
- 所有slides已经上传。
- The last homework assignment is out, due on the date of the final exam.
- 前几堂课的讲义已经补上，足够完成第三次作业。
- The third homework assignment is out, due in two weeks.
- The second homework assignment is out, due in two weeks.
- 第1次作业第3题新增一问。由于是在作业发布之后修改，是否做这一问题不会影响分数，但增加此问会使该题目更有意义。
- The first homework assignment is out, due in two weeks.
Course info
- Instructor : 尹一通，
- email: yitong.yin@gmail.com, yinyt@nju.edu.cn
- office: 计算机系 804.
- Class meeting: Tuesday 10am-12pm, 仙逸B-207.
- Office hour: Wednesday 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
- Problem Set 1, due on March 26, Tuesday, in class.
- Problem Set 2, due on April 23, Tuesday, in class.
- Problem Set 3, due on June 4, Tuesday, in class.
- Problem Set 4, due on June 24, before final exam.
Lecture Notes
Slides: 1| 3| 4| 5| 6| 7| 8| 9| 10| 11| 12| 13| 14| 15| 16| 17
- Introduction and Probability Space: checking matrix multiplication, polynomial identity testing
- Conditional Probability: polynomial identity testing, min-cut
- Random Variables and Expectations: random quicksort, balls and bins
- Moment and Deviation: stable marriage, Markov's inequality, Chebyshev's inequality, median selection
- Threshold and Concentration: random graphs, threshold phenomenon, Chernoff bound
- Applications of Chernoff Bound: error reduction, set balancing, packet routing
- Concentration of Measure: martingales, Azuma's inequality, Doob martingales, chromatic number of random graphs
- Random Projection: Johnson-Lindenstrauss Theorem
- Universal Hashing: [math]\displaystyle{ k }[/math]-wise independence, universal hash families, perfect hashing
- The Probabilistic Method: MAX-SAT, conditional probability method, Lovász Local Lemma
- Markov Chain and Random Walk: Markov chain, random walk, stationary distribution, convergence of Markov chain, hitting/cover time
- Mixing Time and Coupling: mixing time, coupling lemma, coupling of Markov chain, rapid mixing by coupling
- Expander Graphs and Mixing: expander graphs, graph spectrum, spectral gap, Cheeger's inequality, rapid mixing of expander walk
- Sampling and Counting
The Probability Theory Toolkit
- Probability space and probability axioms
- Independent events
- Conditional probability
- Random variable and expectation
- Linearity of expectation
- The law of total probability and the law of total expectation
- The union bound
- Bernoulli trials
- Geometric distribution
- Binomial distribution
- Markov's inequality
- Variance and covariance
- Chebyshev's inequality
- Chernoff bound
- Martingale
- Azuma's inequality and Hoeffding's inequality
- Doob martingale
- k-wise independence
- The probabilistic method
- The Lovász local lemma and the algorithmic Lovász local lemma
- Markov chain:
- reducibility, Periodicity, stationary distribution, hitting time, cover time;
- mixing time, conductance