CS570_FinalExam

CS570_FinalExam - CS570 Analysis of Algorithms Spring 2005...

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CS570 Analysis of Algorithms Spring 2005 Final Exam Name: _____________________ Student ID: _________________
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1- 10 pts a) The NP-complete problem X has a polynomial time 2-approximation algorithm A. X can be reduced to problem Y. Can A be used to find a 2-approximation to Y? Answer Yes, No, or Sometimes. Then explain your answer. b) The NP-complete problem X has a polynomial time 2-approximation algorithm A. Problem Y can be reduced to X. Can A be used to find a 2-approximation to Y? Answer Yes, No, or Sometimes. Then explain your answer.
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2- 20 pts You are given an m by n matrix of real numbers such that the sum of the values in each row and each column are exact integer numbers. Design an algorithm that rounds all the entries in the matrix up or down to the closest integer value without affecting the row or column sums. An example of such a transformation is shown below. Analyze the complexity of your solution. Example: Input is the 2x3 matrix shown in the shaded area.
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CS570_FinalExam - CS570 Analysis of Algorithms Spring 2005...

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