Publications by Martin Niemeier

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On Sub-determinants and the Diameter of Polyhedra

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

We derive a new upper bound on the diameter of a polyhedron , where . The bound is polynomial in and the largest absolute value of a sub-determinant of , denoted by . More precisely, we show that the diameter of is bounded by . If is bounded, then we show ...

Springer2014

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

Covering Cubes and the Closest Vector Problem

Friedrich Eisenbrand, Martin Niemeier, Nicolai Hähnle

We provide the currently fastest randomized (1+epsilon)-approximation algorithm for the closest vector problem in the infinity-norm. The running time of our method depends on the dimension n and the approximation guarantee epsilon by 2^(O(n))(log(1/epsilon ...

Acm Order Department, P O Box 64145, Baltimore, Md 21264 Usa2011

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

Scheduling periodic tasks in a hard real-time environment

Friedrich Eisenbrand, Martin Niemeier, Nicolai Hähnle

We give a rigorous account on the complexity landscape of an important real-time scheduling problem that occurs in the design of software-based aircraft control. The goal is to distribute tasks

\tau_i=(c_i,p_i)

on a minimum number of identical machines a ...

Springer-Verlag2010

Coloring Fuzzy Circular Interval Graphs

Friedrich Eisenbrand, Martin Niemeier

Computing the weighted coloring number of graphs is a classical topic in combinatorics and graph theory. Recently these problems have again attracted a lot of attention for the class of quasi-line graphs and more specifically fuzzy circular interval graphs ...

Elsevier2009

Scheduling periodic tasks in a hard real-time environment

Friedrich Eisenbrand, Martin Niemeier, Nicolai Hähnle

We give a rigorous account on the complexity landscape of an important real-time scheduling problem that occurs in the design of software-based aircraft control. The goal is to distribute tasks

\tau_i=(c_i,p_i)

on a minimum number of identical machines a ...

Springer-Verlag2010

Martin Niemeier

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On Sub-determinants and the Diameter of Polyhedra

Approximation Algorithms for Modern Multi-Processor Scheduling Problems

Coloring fuzzy circular interval graphs

Covering Cubes and the Closest Vector Problem

Partitioned real-time scheduling on heterogeneous shared-memory multiprocessors

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

Scheduling periodic tasks in a hard real-time environment

Coloring Fuzzy Circular Interval Graphs

Approximation Algorithms for Modern Multi-Processor Scheduling Problems

Partitioned real-time scheduling on heterogeneous shared-memory multiprocessors

Coloring fuzzy circular interval graphs

On Sub-determinants and the Diameter of Polyhedra

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

Covering Cubes and the Closest Vector Problem

Coloring Fuzzy Circular Interval Graphs

Scheduling periodic tasks in a hard real-time environment