Network Optimization by Randomization - TU Berlin · PDF fileNetwork Optimization by...

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Transcript of Network Optimization by Randomization - TU Berlin · PDF fileNetwork Optimization by...

NetworkOptimizationbyRandomization

Summer Semester 2011TU Berlin

Lectures 2-3

InThisLecture

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)EfficientRandomizedAlgorithm

A(Very)EfficientRandomizedAlgorithm(contd.)

AnalyzingtheProbabilityofFailure

AnalyzingtheMainChoicesoftheAlgorithm

GeneratingRandomNumbers

PerceptionofRandomness

Formalizing(Defining)Randomness

RandomnessasFrequencyStability

RandomnessasFrequencyStability(contd.)

RandomnessasFrequencyStability(contd.)

RandomnessasIncompressibility.AlgorithmicComplexity

RandomnessasIncompressibility(contd.)

PseudoRandomNumberGenerators

MiddleSquareMethod(vonNeumann,1949)

LinearCongruentialGenerator(LCG)Method

SimulatingDiscreteUniformDistributionswithaFairCoin

CorrectnessofUniform(1,n)

Network Optimization by RandomizationIn This LectureA (Very) Efficient Randomized AlgorithmA (Very) Efficient Randomized Algorithm (contd.)Analyzing the Probability of FailureAnalyzing the Main Choices of the AlgorithmGenerating Random NumbersPerception of RandomnessFormalizing (Defining) RandomnessRandomness as Frequency StabilityRandomness as Frequency Stability (contd.)Slide 12Randomness as Incompressibility. Algorithmic ComplexityRandomness as Incompressibility (contd.)Pseudo-Random Number Generators Middle-Square Method (von Neumann, 1949)Linear Congruential Generator (LCG) MethodSimulating Discrete Uniform Distributions with a Fair CoinCorrectness of Uniform(1,n)