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Update CSE347_L9.md

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Zheyuan Wu
2024-12-03 17:27:14 -06:00
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@@ -85,7 +85,7 @@ Claim: If we choose $h$ randomly from a universal family of hash functions, $H$,
Question: What are some good properties and what does it mean by with high probability?
Claim: Given a universal family of hash functions, $H$, $S=\{a_1,a_2,\cdots,a_n\}\subset \mathbb{N}$. For any probability $0\leq \delta\leq 1$, if $n\leq \sqrt{4m\delta}$, the chance that no two keys hash to the same slot is $\geq1-\delta$.
Claim: Given a universal family of hash functions, $H$, $S=\{a_1,a_2,\cdots,a_n\}\subset \mathbb{N}$. For any probability $0\leq \delta\leq 1$, if $n\leq \sqrt{2m\delta}$, the chance that no two keys hash to the same slot is $\geq1-\delta$.
Example: If we pick $\delta=\frac{1}{2}$. As long as $n<\sqrt{2m}$, the chance that no two keys hash to the same slot is $\geq\frac{1}{2}$.