Prove the theorem Suppose that a hash function h is chosen randomly from a universal collection of hash functions and has been used to hash n keys into a table T of size m, using chaining to resolve collisions. If key k is not in the table, then the expected length E Œnh.k/ of the list that key k hashes to is at most the load factor ˛ D n=m. If key k is in the table, then the expected length E Œnh.k/ of the list containing key k is at most 1 C ˛.
Prove the theorem Suppose that a hash function h is chosen randomly from a universal collection of hash functions and has been used to hash n keys into a table T of size m, using chaining to resolve collisions. If key k is not in the table, then the expected length E Œnh.k/ of the list that key k hashes to is at most the load factor ˛ D n=m. If key k is in the table, then the expected length E Œnh.k/ of the list containing key k is at most 1 C ˛.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Prove the theorem Suppose that a hash function h is chosen randomly from a universal collection of hash functions and has been used to hash n keys into a table T of size m, using chaining to resolve collisions. If key k is not in the table, then the expected length E Œnh.k/ of the list that key k hashes to is at most the load factor ˛ D n=m. If key k is in the table, then the expected length E Œnh.k/ of the list containing key k is at most 1 C ˛.
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