Abstract

In this lecture, we discuss hashing as a solution to dictionary/membership problem. Various results on hashing are presented with emphasis on static perfect hashing and Cuckoo hashing. 2 Dictionary/Membership Problem In dictionary/membership problem, we want to keep a set S of items with possibly some extra information associated with each one of them. (From now on, we denote the number of elements in S by n.) For the membership problem, the goal is to create a data structure that allows us to ask whether a given item x is in S or not. For a dictionary, the data structure should also return the infomation associated with x. For example, S can be a set of Swahili words such that each of the words is associated with a piece of text which describes its meaning. (Duh!) The problems have two versions: static and dynamic. In the static version, S is predetermined and never changes. On the other hand, the dynamic version allows items to be inserted to and removed from S. 3 Hashing with Chaining Let U denote the universe of items, and let m be a positive integer. A hash function is a function from U to Zm.

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