My Math Forum Graph question: model system of inequalities as graph

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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: $\left\{\begin{matrix} x_2 - x_1 <= 4 & & \\ x_3 - x_2 <= 9 & & \end{matrix}\right.$ The goal is to maximize the differences between each $x_i$ and $x_1$. 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 $\sum_ix_i-x_1.$

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