universal hash functions: performance guarantees (chaining)
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 PresentationTRANSCRIPT
Data Structures
Universal Hash Functions: Performance Guarantees (Chaining)Design and Analysis
of Algorithms I
Tim Roughgarden
Overview of Universal Hashing
Tim Roughgarden
Universal Hash Functions
Tim Roughgarden
Chaining: Constant-Time Guarantee
Tim Roughgarden
Proof (Part I)
Tim Roughgarden
A General Decomposition Principle
Tim Roughgarden
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?
Tim Roughgarden
Proof (Part II)
1/𝑛2
1/𝑛❑
1/21−1/𝑛
Which of the following is the smallest valid upper bound on ?
Tim Roughgarden
Proof (Part II)