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This paper reports on the fifth version of the Mixed Integer Programming Library. The miplib 2010 is the first miplib release that has been assembled by a large group from academia and from industry, all of whom work in integer programming. There was mutual consent that the concept of the library had to be expanded in order to fulfill the needs of the(More)
We describe an iterative refinement procedure for computing extended precision or exact solutions to linear programming problems (LPs). Arbitrarily precise solutions can be computed by solving a sequence of closely related LPs with limited precision arithmetic. The LPs solved share the same constraint matrix as the original problem instance and are(More)
We describe an iterative refinement procedure for computing extended precision or exact solutions to linear programming problems (LPs). Arbitrarily precise solutions can be computed by solving a sequence of closely related LPs with limited precision arithmetic. The LPs solved share the same constraint matrix as the original problem instance and are(More)
We present an exact rational solver for mixed-integer linear programming which avoids the numerical inaccuracies inherent in the floating-point computations adopted in existing software. This allows the solver to be used for establishing fundamental theoretical results and in applications where correct solutions are critical due to legal and financial(More)
We present an exact rational solver for mixed-integer linear programming that avoids the numerical inaccuracies inherent in the floating-point computations used by existing software. This allows the solver to be used for establishing theoretical results and in applications where correct solutions are critical due to legal and financial consequences. Our(More)
Many methods have been developed to symbolically solve systems of linear equations over the rational numbers. A common approach is to use p-adic lifting or iterative refinement to build a modular or approximate solution, then apply rational number reconstruction. An upper bound can be computed on the number of iterations these algorithms must perform before(More)