Abstract

Fredman, Komlós & Szemerédi [1] discovered a way to construct hash functions which are guaranteed to give no collisions for a set of input values (keys) which are defined at the time that the hash function is constructed. These hash functions can be evaluated in O(1) time and take O(n) space to store. This is called ‘static ’ hashing, as it relies on knowing the values to be hashed ahead of time. Perfect static hashing has limited uses due to the requirement of knowing all the keys in advance, but it is occasionally used for things like recognising keywords in programming languages, or recognising command line arguments. Construction: 1. Create a hash function which produces ≤ n collisions on the given keys. We can find such a hash function using only a weakly universal hash function family in a constant number of trials. 2. Take each bin bi containing multiple items (i.e., bins with collisions) and generate another hash function which gives no collisions for the items in that bin. These second level hash tables are given ni 2 space, where ni is the number of items in bin bi. This ni 2 space means that it is possible to ensure that there will be no collisions in the second level tables in another constant number of trials.

Citations