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Universal Hash Functions: Definition and Example

Data Structures. Universal Hash Functions: Definition and Example. Design and Analysis of Algorithms I. Overview of Universal Hashing. Universal Hash Functions.

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Universal Hash Functions: Definition and Example

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  1. Data Structures Universal Hash Functions: Definition and Example Design and Analysis of Algorithms I

  2. Overview of Universal Hashing

  3. Universal Hash Functions

  4. 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? Yes, always. No, never. Maybe yes, maybe no (depends on the ). Only if the hash table is implemented using chaining.

  5. Example: Hashing IP Addresses

  6. A Universal Hash Function

  7. Proof (Part I)

  8. Proof (Part II)

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