Data Structures Universal Hash Functions: Definition and Example Design and Analysis of Algorithms I
Feb 19, 2016
Data Structures
Universal Hash Functions: Definition and ExampleDesign and Analysis
of Algorithms I
Tim Roughgarden
Overview of Universal Hashing
Tim Roughgarden
Universal Hash Functions
Yes, always.
No, never.
Maybe yes, maybe no (depends on the ).
Only if the hash table is implemented using chaining.
Consider a hash function family , where each hash function of maps elements from a universe to one of buckets. Suppose has the following property: for every bucket and key , a fraction of the hash functions in map to . Is universal?
Tim Roughgarden
Example: Hashing IP Addresses
Tim Roughgarden
A Universal Hash Function
Tim Roughgarden
Proof (Part I)
Tim Roughgarden
Proof (Part II)