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A Second Course in Algorithms (Lecture 18: Five Essential Tools for Analyzing Randomized Algorithms)

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Five essential tools for the analysis of randomized algorithms (approximate and otherwise). Linearity of expectation and a 7/8-approximation for MAX 3SAT. Markov and Chebyshev inequalities. Chernoff bounds. Running example: analysis of hashing. Randomized rounding for low-congestion routing.
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