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hw2 - CO 227 Homework assignment 2 Fall `10 Page 1 CO 227...

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CO 227 - Homework assignment 2 Fall ‘10 Page 1 CO 227 - Fall ‘10 Homework assignment #2: (Due at the beginning of the class, 10:30AM, on Wednesday, Oct 13th) Instructions: Please show all your work and justify your answers. Answers without proper justification will not be considered. Please list who you collaborated with. Clearly define what are your decision variables and write down your final model. Total value = 100 points Question 1 - Algorithms (20 points) Consider a general IP, where all variables are restricted to be { 0 , 1 } . min c T x s.t. Ax b x ∈ { 0 , 1 } n Now consider the following algorithm to solve this problem: For all possible values of x that satisfy Ax b and x ∈ { 0 , 1 } n , compute c T x and find the minimum among all possible choices. (a) (10 points) Give an upper bound on the running time of the algorithm (as a function of n ). (b) (10 points) Give a lower bound on the running time of the algorithm that is exponential on n , that is, provide an example of an instance for which the algorithm must make at least
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