Publications related to Integer (computer science)

Testing additive integrality gaps

Friedrich Eisenbrand, Nicolai Hähnle, Gennady Shmonin

We consider the problem of testing whether the maximum integrality gap of a family of integer programs in standard form is bounded by a given constant. This can be viewed as a generalization of the integer rounding property, which can be tested in polynomi ...

2010

Functional Performance Analysis and Optimization for the High-Frequency Magnetic Diagnostic System in ITER - II: Detailed Overview of the Analysis Method and of the Test Calculations

Jean-Marc Moret, Duccio Testa, René Chavan, Matthieu Toussaint, Jonathan Bryan Lister

The measurement performance of the baseline system design for the ITER high-frequency magnetic diagnostic system and attempts at its optimization have been performed using an innovative method based on the sparse representation of signals and the minimizat ...

American Nuclear Society2009

Extended Formulations for Packing and Partitioning Orbitopes

Yuri Faenza

We give compact extended formulations for the packing and partitioning orbitopes (with respect to the full symmetric group) described and analyzed in Kaibel and Pfetsch [Kaibel, V., M. E. Pfetsch. 2008. Packing and partitioning orbitopes. Math. Programming ...

2009

Proving non-termination

Andrey Rybalchenko, Ashutosh Kumar Gupta

The search for proof and the search for counterexamples (bugs) are complementary activities that need to be pursued concurrently in order to maximize the practical success rate of verification tools. While this is well-understood in safety verification, th ...

2008

Parametric integer programming in fixed dimension

Friedrich Eisenbrand, Gennady Shmonin

We consider the following problem: Given a rational matrix

A \in \mathbb{Q}^{m \times n}

and a rational polyhedron

Q \subseteq \mathbb{R}^{m+p}

, decide if for all vectors

b \in \mathbb{R}^m

, for which there exists an integral

z \in \mathbb{Z}^p

suc ...

2008

On defect groups for generalized blocks of the symmetric group

In a paper of 2003, Kulshammer, Olsson and Robinson defined l-blocks for the symmetric groups, where l > 1 is an arbitrary integer. In this paper, we give a definition for the defect group of the principal l-block. We then check that, in the Abelian case, ...

2008

The generic Gröbner walk

The Gröbner walk is an algorithm for conversion between Gröbner bases for different term orders. It is based on the polyhedral geometry of the Gröbner fan and involves tracking a line between cones representing the initial and target term order. An importa ...

2007

Caratheodory bounds for integer cones

Friedrich Eisenbrand, Gennady Shmonin

We provide analogues of Caratheodory's theorem for integer cones and apply our bounds to integer programming and to the cutting stock problem. In particular, we provide an NP certificate for the latter, whose existence has not been known so far. © 2005 Els ...

2006

Mapping task-graphs on distributed ECU networks: Efficient algorithms for feasibility and optimality

Friedrich Eisenbrand, Gennady Shmonin

This mapping problem has to be solved in many application scenarios. In the automotive industry, for example, the implementation of car functions involves distributed task sets running on multiple electronic control units (ECU) with bus-based inter-task co ...

2006

A linear algorithm for integer programming in the plane

Friedrich Eisenbrand

We show that a 2-variable integer program, defined by m constraints involving coefficients with at most φ bits, can be solved with O(m+φ) arithmetic operations on rational numbers of size O(φ). © Springer-Verlag 2004. ...

2005

Integer (computer science)

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Testing additive integrality gaps

Functional Performance Analysis and Optimization for the High-Frequency Magnetic Diagnostic System in ITER - II: Detailed Overview of the Analysis Method and of the Test Calculations

Extended Formulations for Packing and Partitioning Orbitopes

Proving non-termination

Parametric integer programming in fixed dimension

On defect groups for generalized blocks of the symmetric group

The generic Gröbner walk

Caratheodory bounds for integer cones

Mapping task-graphs on distributed ECU networks: Efficient algorithms for feasibility and optimality

A linear algorithm for integer programming in the plane

Extended Formulations for Packing and Partitioning Orbitopes

The generic Gröbner walk

On defect groups for generalized blocks of the symmetric group

Testing additive integrality gaps

Parametric integer programming in fixed dimension

Proving non-termination

A linear algorithm for integer programming in the plane

Caratheodory bounds for integer cones

Functional Performance Analysis and Optimization for the High-Frequency Magnetic Diagnostic System in ITER - II: Detailed Overview of the Analysis Method and of the Test Calculations

Mapping task-graphs on distributed ECU networks: Efficient algorithms for feasibility and optimality