05 - Spring 2010 CS530 Analysis of Algorithms Homework 5 H...

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Unformatted text preview: Spring 2010 CS530 Analysis of Algorithms Homework 5 H OMEWORK 5, DUE M ARCH 3 You must prove your answer to every question. Problems with a ( * ) in place of a score may be a little too advanced, or too challenging to most students, so I do not assign a score to them. But I will still note if you solve them. Problem 1. We talked about the maximum matching problem in class: given by a bipartite graph G = ( A B , E ) . Here A is the class of workers, B the class of jobs, and ( a , b ) E if worker a can perform job b . We introduce a variable x a , b for each ( a , b ) E : in the solution, this variable 1 if edge ( a , b ) is selected and 0 otherwise. Consider the following linear program: maximize ( a , b ) E x a , b subject to b : ( a , b ) E x a , b 1 for all a A , a : ( a , b ) E x a , b 1 for all b B , x a , b for all a , b . (a) (5pts) Show that the integer solutions of this program are just the maxi- mum matchings....
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05 - Spring 2010 CS530 Analysis of Algorithms Homework 5 H...

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