practice1_solution - CS648 Randomized Algorithms Semester...

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CS648 Randomized Algorithms Semester II, 2007-08 Motivational problem sheet Note : These problems are for those students whose expectation from this course is at least little more than just getting a good grade. More and more problems will be added to this sheet. So keep on downloading it every week at least. 1. ( * * * ) Till now we always proved low probabilty bound on positive deviation of a random variable from its expected value. This time we shall work in the other direction as well. Here is an example. We showed in an earlier class that if we throw n balls independently uniformly into n bins, the maximum load is O (log n ) with high probability. In fact, the equation ( x c ) x = n 3 we solved has exact solution x = b log n log log n for some constant b . You have to prove that this bound is tight from below too. That is, show that with high probability the maximum load is Ω( log n log log n ) . 2. (
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This note was uploaded on 11/24/2009 for the course CS CS648 taught by Professor Surenderbaswana during the Spring '08 term at University of Massachusetts Boston.

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practice1_solution - CS648 Randomized Algorithms Semester...

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