Network Optimization by Randomization

Summer Semester 2011TU Berlin

Lectures 2-3

In This Lecture

• A randomized algorithm more efficient than any deterministic algorithm

• Generating random numbers

• Some probability concepts will be used but a review shall be presented during the next lecture

A (Very) Efficient Randomized Algorithm

A (Very) Efficient Randomized Algorithm (contd.)

Analyzing the Probability of Failure

Analyzing the Main Choices of the Algorithm

Generating Random Numbers

Perception of Randomness

Formalizing (Defining) Randomness

Randomness as Frequency Stability

Randomness as Frequency Stability (contd.)

Randomness as Frequency Stability (contd.)

Randomness as Incompressibility. Algorithmic Complexity

Randomness as Incompressibility (contd.)

Pseudo­Random Number Generators 

Middle­Square Method (von Neumann, 1949)

Linear Congruential Generator (LCG) Method

Simulating Discrete Uniform Distributions with a Fair Coin

Correctness of Uniform(1,n)