Data Structures

Universal Hash Functions: Performance Guarantees (Chaining)Design and Analysis

of Algorithms I

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Overview of Universal Hashing

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Universal Hash Functions

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Chaining: Constant-Time Guarantee

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Proof (Part I)

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A General Decomposition Principle

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Proof (Part II)

Pr [h (𝑦 )=0]Pr [h (𝑦 )≠𝑥 ]Pr [h (𝑦 )=h(𝑥)]

Pr [h ( 𝑦 )≠h (𝑥)]

What does evaluate to?

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Proof (Part II)

1/𝑛2

1/𝑛❑

1/21−1/𝑛

Which of the following is the smallest valid upper bound on ?

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Proof (Part II)