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hw6(9) - CS 573 Graduate Algorithms Fall 2010 Homework 5...

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CS 573: Graduate Algorithms, Fall 2010 Homework 5 Practice only — Do not submit solutions 1. (a) Describe how to transform any linear program written in general form into an equivalent linear program written in slack form. maximize d j = 1 c j x j subject to d j = 1 a i j x j b i for each i = 1.. p d j = 1 a i j x j = b i for each i = p + 1.. p + q d j = 1 a i j x j b i for each i = p + q + 1.. n Z = max c · x s.t. Ax = b x 0 (b) Describe precisely how to dualize a linear program written in slack form. (c) Describe precisely how to dualize a linear program written in general form. In all cases, keep the number of variables in the resulting linear program as small as possible. 2. Suppose you have a subroutine that can solve linear programs in polynomial time, but only if they are both feasible and bounded. Describe an algorithm that solves arbitrary linear programs in polynomial time. Your algorithm should return an optimal solution if one exists; if no optimum
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