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- Ambros M. Gleixner, Daniel E. Steffy, Kati Wolter
- ISSAC
- 2012

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)

- Fatma Kilinç-Karzan, Daniel E. Steffy
- Math. Program.
- 2016

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)

- William J. Cook, Thorsten Koch, Daniel E. Steffy, Kati Wolter
- IPCO
- 2011

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)

- Ambros M. Gleixner, Daniel E. Steffy, Kati Wolter
- INFORMS Journal on Computing
- 2016

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)

- William J. Cook, Thorsten Koch, Daniel E. Steffy, Kati Wolter
- Math. Program. Comput.
- 2013

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)

- Daniel E. Steffy, Kati Wolter
- INFORMS Journal on Computing
- 2013

We consider the problem of determining as early as possible when teams in the NHL are mathematically qualified or eliminated from the playoffs. We describe the rules outlined by the NHL and give a mixed integer program formulation to determine mathematical qualification and elimination. We also give a slightly simplified version of the MIP that is more… (More)

- William J. Cook, Daniel E. Steffy
- ACM Trans. Math. Softw.
- 2011

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)

- Daniel E. Steffy
- ACM Comm. Computer Algebra
- 2010

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)

- Eddie Cheng, William A. Lindsey, Daniel E. Steffy
- Networks
- 2005

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)