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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 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 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)

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)

The class of star graphs is a popular topology for interconnection networks. However it has certain deficiencies. A class of generalization of star graphs called (n, k)-star graphs was introduced in [12] to address these issues. In this paper we will consider the vertex-connectivity of the directed (n, k)-star graph, − − → S n,k , given in [8], and show… (More)

Efficient methods for solving linear-programming problems in exact precision rely on the solution of sparse systems of linear equations over the rational numbers. We consider a test set of instances arising from exact-precision linear programming and use this test set to compare the performance of several techniques designed for symbolic sparse… (More)

This paper studies K-sublinear inequalities, a class of inequalities with strong relations to K-minimal inequalities for disjunctive conic sets. We establish a stronger result on the suffi-ciency of K-sublinear inequalities. That is, we show that when K is the nonnegative orthant or the second-order cone, K-sublinear inequalities together with the original… (More)

This tutorial surveys state-of-the-art algorithms and computational methods for computing exact solutions to linear and mixed-integer programming problems.