Universal Hash Functions: Performance Guarantees (Chaining)
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Data Structures Universal Hash Functions: Performance Guarantees (Chaining) Design and Analysis of Algorithms I
description
Data Structures. Universal Hash Functions: Performance Guarantees (Chaining). Design and Analysis of Algorithms I. Overview of Universal Hashing. Universal Hash Functions. Chaining: Constant-Time Guarantee. Proof (Part I). A General Decomposition Principle. Proof (Part II). - PowerPoint PPT Presentation
Transcript of Universal Hash Functions: Performance Guarantees (Chaining)
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Data Structures
Universal Hash Functions: Performance Guarantees (Chaining)Design and Analysis
of Algorithms I
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Tim Roughgarden
Overview of Universal Hashing
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Tim Roughgarden
Universal Hash Functions
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Tim Roughgarden
Chaining: Constant-Time Guarantee
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Tim Roughgarden
Proof (Part I)
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Tim Roughgarden
A General Decomposition Principle
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Tim Roughgarden
Proof (Part II)
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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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Tim Roughgarden
Proof (Part II)
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1/𝑛2
1/𝑛❑
1/21−1/𝑛
Which of the following is the smallest valid upper bound on ?
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Tim Roughgarden
Proof (Part II)