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)