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Network Optimization by Randomization
Summer Semester 2011TU Berlin
Lectures 2-3
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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
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A (Very) Efficient Randomized Algorithm
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A (Very) Efficient Randomized Algorithm (contd.)
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Analyzing the Probability of Failure
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Analyzing the Main Choices of the Algorithm
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Generating Random Numbers
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Formalizing (Defining) Randomness
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Randomness as Frequency Stability
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Randomness as Frequency Stability (contd.)
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Randomness as Frequency Stability (contd.)
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Randomness as Incompressibility. Algorithmic Complexity
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Randomness as Incompressibility (contd.)
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PseudoRandom Number Generators
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MiddleSquare Method (von Neumann, 1949)
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Linear Congruential Generator (LCG) Method
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Simulating Discrete Uniform Distributions with a Fair Coin
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Correctness of Uniform(1,n)