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29 September 2022

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21 September 2022

  • 11:4811:48, 21 September 2022 diff hist +15,811 N 高级算法 (Fall 2022)/Limited independenceCreated page with "= <math>k</math>-wise independence = Recall the definition of independence between events: {{Theorem |Definition (Independent events)| :Events <math>\mathcal{E}_1, \mathcal{E}_2, \ldots, \mathcal{E}_n</math> are '''mutually independent''' if, for any subset <math>I\subseteq\{1,2,\ldots,n\}</math>, ::<math>\begin{align} \Pr\left[\bigwedge_{i\in I}\mathcal{E}_i\right] &= \prod_{i\in I}\Pr[\mathcal{E}_i]. \end{align}</math> }} Similarly, we can define independence between..."
  • 11:4811:48, 21 September 2022 diff hist +75 高级算法 (Fall 2022)→‎Lecture Notes
  • 11:4711:47, 21 September 2022 diff hist +11,376 N 高级算法 (Fall 2022)/Balls into binsCreated page with "=Balls into Bins= Consider throwing <math>m</math> balls into <math>n</math> bins uniformly and independently at random. This is equivalent to a random mapping <math>f:[m]\to[n]</math>. Needless to say, random mapping is an important random model and may have many applications in Computer Science, e.g. hashing. We are concerned with the following three questions regarding the balls into bins model: * birthday problem: the probability that every bin contains at most one..."
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