mt2(5) - CS 473G Final Exam Questions (December 13, 2005)...

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Unformatted text preview: CS 473G Final Exam Questions (December 13, 2005) Fall 2005 You have 90 minutes to answer four of these questions. Write your answers in the separate answer booklet. You may take the question sheet with you when you leave. Chernoff Bounds: If X is the sum of independent indicator variables and = E[ X ], then the following inequalities hold for any > 0: Pr[ X < (1- ) ] < e- (1- ) 1- Pr[ X > (1 + ) ] < e (1 + ) 1+ 1. Describe and analyze an algorithm that randomly shuffles an array X [1 .. n ], so that each of the n ! possible permutations is equally likely, in O ( n ) time. (Assume that the subroutine Random ( m ) returns an integer chosen uniformly at random from the set { 1 , 2 , , . . . , m } in O (1) time.) 2. Let G be an undirected graph with weighted edges. A heavy Hamiltonian cycle is a cycle C that passes through each vertex of G exactly once, such that the total weight of the edges in C is at least half of the total weight of all edges in...
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mt2(5) - CS 473G Final Exam Questions (December 13, 2005)...

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