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November 16th, 2011, 02:36 AM   #1
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Graph question: model system of inequalities as graph

Hello, this is my first post in the forum .

I have a system of inequalities deriving from pairwise comparison, for example:



The goal is to maximize the differences between each and .
I would like to model it as a graph, because I think some graph algorithm would help (maximum flow?) but I can't find a solution.

Please, can you help me?

Thanks!
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November 16th, 2011, 06:44 AM   #2
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Re: Graph question: model system of inequalities as graph

How many inequalities? How many variables? Are all of the form x_i - x_1 <= k? If not, are they all of the form x_i - x_j <= k? Are there other constraints?

I can't think of a way to express this as a graph; if you have a particular idea in mind I'll think about it. Otherwise, it seems like a standard optimization problem with objective function
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