Friedrich Eisenbrand

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The support of a vector is the number of nonzero components. We show that given an integral mxn matrix A, the integer linear optimization problem max {c(T) x : Ax = b, x >= 0, x is an element of Z(n)} has an optimal solution whose support is bounded by 2m ...

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 ...

In the synchronous periodic task model, a set \tau_1,...,\tau_n of tasks is given, each releasing jobs of running time c_i with relative deadline d_i, at each integer multiple of the period p_i. It is a classical result that Earliest Deadline First (EDF) i ...

We consider the problem of testing whether the maximum additive 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 ...

We consider integer programming problems max {c^Tx : A x = b, l

We report on the solution of a real-time scheduling problem that arises in the design of software-based operation control of aircraft. A set of tasks has to be distributed on a minimum number of machines and offsets of the tasks have to be computed. The ta ...

Given a graph G with nonnegative node labels w, a multiset of stable sets S_1,...,S_k\subseteq V(G) such that each vertex v \in V(G) is contained in w(v) many of these stable sets is called a weighted coloring. The weighted coloring number \chi_w(G) is the ...

A well studied special case of bin packing is the 3-partition problem, where n items of size > 1/4 have to be packed in a minimum number of bins of capacity one. The famous Karmarkar-Karp algorithm transforms a fractional solution of a suitable LP relaxati ...

We show that a constant factor approximation of the shortest and closest lattice vector problem in any l(p)-norm can be computed in time 2((0.802 + epsilon)n). This matches the currently fastest constant factor approximation algorithm for the shortest vect ...

We study the settings where we are given a separable objective function of n variables defined in a given box of integers. We show that in many cases we can replace the given objective function by a new function with a much smaller domain. Our results appl ...

Let P and Q be finite sets of points in the plane. In this note we consider the largest cardinality of a subset of the Minkowski sum S ⊆ P⊕Q which consist of convex independent points. We show that, if P and Q contain at most n points, then |S| = O(n^(4/3) ...

Friedrich Eisenbrand

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The Support Of Integer Optimal Solutions

Parametric integer programming in fixed dimension

EDF-schedulability of synchronous periodic task systems is coNP-hard

Testing additive integrality gaps

Faster Algorithms for Integer Programs with Block Structure

Solving an Avionics Real-Time Scheduling Problem by Advanced IP-Methods

Coloring fuzzy circular interval graphs

Bin Packing via Discrepancy of Permutations

Static-priority Real-time Scheduling: Response Time Computation is NP-hard

Approximate CVPp in time 2(0.802n)

On sub-determinants and the diameter of polyhedra

Reducibility bounds of objective functions over the integers

Convexly independent subsets of the Minkowski sum of planar point sets

On largest volume simplices and sub-determinants

Real-time Avionics OptimizationMathematische Optimierung von Echtzeitsystemen im Flugzeugdesign