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November 16th, 2011, 01:36 AM  #1 
Newbie Joined: Nov 2011 Posts: 1 Thanks: 0  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! 
November 16th, 2011, 05:44 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  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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