Hw_5 - CS 573 Algorithms Fall 2009 Homework 5 due Thursday:59:59 2009 Version 1.12 Name Net ID 1 2 3 4 5 6 Total Alias Score Grader Neatly print

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CS 573: Algorithms, Fall 2009 Homework 5, due Thursday, November 19, 23:59:59, 2009 Version 1.12 Name: Net ID: Alias: # Score Grader 1. 2. 3. 4. 5. 6. Total Neatly print your name(s), NetID(s), and the alias(es) you used for Homework 0 in the boxes above. Staple this sheet to the top of your homework. If you are on campus, submit the homework by submitting it in SC 3306 (or sliding it under the door). In addition, the sirloin which I threw overboard, instead of drifting oﬀ into the void, didn’t seem to want to leave the rocket and revolved about it, a second artiﬁcial satellite, which produced a brief eclipse of the sun every eleven minutes and four seconds. To calm my nerves I calculated till evening the components of its trajectory, as well as the orbital perturbation caused by the presence of the lost wrench. I ﬁgured out that for the next six million years the sirloin, rotating about the ship in circular path, would lead the wrench, then catch up with it from behind and pass it again. – The Star Diaries, Stanislaw Lem. Required Problems 1. Slack form [10 Points] Let L be a linear program given in slack form, with n nonbasic variables N , and m basic variables B . Let N 0 and B 0 be a diﬀerent partition of N B , such that | N 0 B 0 | = | N B | . Show a polynomial time algorithm that computes an equivalent slack form that has N 0 as the nonbasic variables and b 0 as the basic variables. How fast is your algorithm? 2. Tedious Computations [20 Points] Provide detailed solutions for the following problems, showing each pivoting stage separately. 1

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(A) [5 Points] maximize 6 x 1 + 8 x 2 + 5 x 3 + 9 x 4 subject to 2 x 1 + x 2 + x 3 + 3 x 4 5 x 1 + 3 x 2 + x 3 + 2 x 4 3 x 1 ,x 2 ,x 3 ,x 4 0. (B) [5 Points] maximize 2 x 1 + x 2 subject to 2 x 1 + x 2 4 2 x 1 + 3 x 2 3 4 x 1 + x 2 5 x 1 + 5 x 2 1 x 1 ,x 2 0. (C)
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This note was uploaded on 01/22/2012 for the course CS 573 taught by Professor Chekuri,c during the Fall '08 term at University of Illinois, Urbana Champaign.

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Hw_5 - CS 573 Algorithms Fall 2009 Homework 5 due Thursday:59:59 2009 Version 1.12 Name Net ID 1 2 3 4 5 6 Total Alias Score Grader Neatly print

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