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)