Randomization function

In computer science, a randomization function or randomizing function is an algorithm or procedure that implements a randomly chosen function between two specific sets, suitable for use in a randomized algorithm.

Randomizing functions are related to random number generators and hash functions, but have somewhat different requirements and uses, and often need specific algorithms.

Uses

Randomizing functions are used to turn algorithms that have good expected performance for random inputs, into algorithms that have the same performance for any input.

For example, consider a sorting algorithm like quicksort, which has small expected running time when the input items are presented in random order, but is very slow when they are presented in certain unfavorable orders. A randomizing function from the integers 1 to n to the integers 1 to n can be used used to rerrange the n input items in "random" order, before calling that algorithm. This modified (randomized) algorithm will have small expected running time, whatever the input order.

Requirements

these are nothing ,these are the functions written on basic of computers.

Uniformity

The uniformity requirements for a randomizing function are usually much weaker than those of hash functions and pseudo-random generators. The minimum requirement is that it maps any input of the deterministic algorithm into a "good" input with a sufficiently high probability. (However, analysis is usually simpler if the randomizing function implements each possible mapping with uniform probability.)