hw3 - 15-750HW 3115-750 Graduate Algorithms Spring...

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Unformatted text preview: 15-750HW 3115-750 Graduate Algorithms Spring 2009Miller and Dinitz and TangwongsanAssignment 3Due date: Wednesday, March 18Some Reminders:Read the Policies section on the course web site before you start working on this assignment. Collab-orationispermitted for this assignment; however, you must write up your own solutions.When solving these problems, you should refrain from looking up solutions from outside sources;however, you should feel free to look up, say, Markovs inequality or isoperimetric bounds. For eachproblem, state whether you have seen it before. If you have questions, contact the course staff.Westronglyencourage you to type up your solutions (preferably using LaTeX). Extra-credit will begiven if we use your wonderful write-up in our solutions. You may neatly hand-write your solutions,but if we have trouble reading them, you will be required to type up future solutions.When you give an algorithm, please also explain why it is correct and analyze its running time.Start EARLY!We encourage you to start working on this assignment early and take full advantage ofoffice hours.1Duality Theory(25 pts.)Given a linear program min{c>x:Axb,x}and a solutionx, how can one decide whetherxis an optimal solution? More generally, how can one calculate agoodlower bound on such linearprograms? Duality is a key concept in linear programming that can help answer these questions.Since we did not have time in class to cover such an important topic, you will learn about dualitytheory first-hand in this problem.More concretely, suppose we are given a linear program (which we will call the primal LP)minimizec>x,subject toAxbandx.The following LP is called theduallinear program:maximizey>b,subject toA>ycandy....
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hw3 - 15-750HW 3115-750 Graduate Algorithms Spring...

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