Algorithms for Data Science: Lecture 5

The balls-and-bins exercise that we did in Homework 1 is also useful for modeling Hashing. A hash function h from a universe U = [0, 1, .., m− 1] into a range [0, ..., n− 1] can be thought of as a way of placing items from the universe into n bins. The collection of bins is called a hash table. We can model the distribution of items in bins with the same distribution as m balls placed randomly in n bins. We are making a rather strong assumption here by presuming that our hash function maps words into bins in a fashion that appears random, so that the location of each item is independent and identically distributed. There is a great deal of theory on developing hash functions that appear random. We will not delve into that theory here, and will rather assume that our hash functions are indeed random. In other words, we assume the following holds