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We have a linear program in the standard form $Ax=b,x\geq 0$ with $A(i,j)\in\{-1,0,1\}\:\forall\,i,j$ and $b(i)\in\{0,1\}\:\forall\,i$. $A$ is not full rank. Is the time complexity of testing the feasibility of this LP any better than that of general LPs? If yes, is there an algorithm known? Thanks in advance.

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My first observation: we know how to solve your LPs in strongly polynomial time, but this is an open question for general LPs.

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