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t2009m

t2009m - COT 6401 The Analysis of Algorithms Test Due...

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COT 6401 The Analysis of Algorithms Test (March 11, 2009) Due: midnight of March 12, 2009 Name —————————————- SSN —————————————- 1. (20%) ( Greedy ) A telecom company needs to install base stations to cover all houses along a long road. These houses can be sparsely distributed along the road. Suppose the coverage of each base station is 5 miles. Design an optimal solution that covers all houses using as few base stations as possible. Prove that your algorithm is optimal. 2. (20%) ( Linear programming ) Solve the following linear program using SIMPLEX and show all the relevant steps: maximize x 1 + 2 x 2 subject to 4 x 1 - x 2 9 x 1 + x 2 8 5 x 1 - 2 x 2 ≥ - 3 x 1 , x 2 0 Provide a geometric explanation of the solution by plotting the corresponding feasible region in a 2-D space. 3. (20%) ( Divide-and-conquer ) Suppose the only way to access a database of student GPA is through a simple query k and that the system returns the k th smallest value that it contains.
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