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 ...

SIAM PUBLICATIONS2018

Parametric integer programming in fixed dimension

Friedrich Eisenbrand

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

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

Friedrich Eisenbrand, Thomas Rothvoss

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 ...

2010

Testing additive integrality gaps

Friedrich Eisenbrand, Nicolai Hähnle

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 ...

Springer Berlin Heidelberg2013

Faster Algorithms for Integer Programs with Block Structure

Friedrich Eisenbrand, Kim-Manuel Klein, Christoph Hunkenschröder

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

Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik2018

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

Friedrich Eisenbrand, Martin Niemeier

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 ...

Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2010

Coloring fuzzy circular interval graphs

Friedrich Eisenbrand, Martin Niemeier

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 ...

Elsevier2012

Approximate CVPp in time 2(0.802n)

Friedrich Eisenbrand, Moritz Andreas Venzin

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 ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

Bin Packing via Discrepancy of Permutations

Friedrich Eisenbrand, Thomas Rothvoss, Doemoetoer Palvoelgyi

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 ...

Siam, 3600 Univ City Science Center, Philadelphia, Pa 19104-2688 Usa2011

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

Friedrich Eisenbrand, Thomas Rothvoss

IEEE Computer Society2008

On sub-determinants and the diameter of polyhedra

Friedrich Eisenbrand, Martin Niemeier, Nicolai Hähnle, Marco Di Summa, Nicolas Bonifas

2012

Reducibility bounds of objective functions over the integers

Friedrich Eisenbrand, Kim-Manuel Klein

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 ...

Elsevier2023

Convexly independent subsets of the Minkowski sum of planar point sets

János Pach, Friedrich Eisenbrand, Thomas Rothvoss

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) ...

American Mathematical Society2008

On largest volume simplices and sub-determinants

Friedrich Eisenbrand, Yuri Faenza, Carsten Moldenhauer, Marco Di Summa

2015

Real-time Avionics OptimizationMathematische Optimierung von Echtzeitsystemen im Flugzeugdesign

Friedrich Eisenbrand, Martin Niemeier

De Gruyter, Oldenbourg Wissenschaftsverlag GmbH2011