Martin Niemeier

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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 tasks emit jobs periodically starting at their offset and then need to be executed on the machines(More)
We consider a real-time scheduling problem that occurs in the design of software-based aircraft control. The goal is to distribute tasks τi = (ci, pi) on a minimum number of identical machines and to compute offsets ai for the tasks such that no collision occurs. A task τi releases a job of running time ci at each time ai +k · pi, k ∈N0 and a collision(More)
We derive a new upper bound on the diameter of the graph of a polyhedron P = {x &#8712; R<sup>n</sup> : Ax &#8804; b}, where A &#8712; Z<sup>m&#215;n</sup>. The bound is polynomial in n and the largest absolute value of a sub-determinant of A, denoted by &#916;. More precisely, we show that the diameter of P is bounded by O(&#916;<sup>2</sup> n<sup>4</sup>(More)
We consider several real-time scheduling problems on heterogeneous multiprocessor platforms, in which the different processors share a common memory pool. These include (i) scheduling a collection of implicit-deadline sporadic tasks with the objective of meeting all deadlines; and (ii) scheduling a collection of independent jobs with the objective of(More)
We provide the currently fastest randomized (1+epsilon)-approximation algorithm for the closest lattice vector problem in the infinity-norm. The running time of our method depends on the dimension n and the approximation guarantee epsilon by 2<sup>(O(n))</sup> (log(1/epsilon))<sup>(O(n))</sup> which improves upon the (2+1/epsilon)<sup>(O(n))</sup> running(More)
Given a graph G with nonnegative node labels w, a multiset of stable sets S1, . . . , Sk ⊆ V (G) such that each vertex v ∈ V (G) is contained in w(v) many of these stable sets is called a weighted coloring. The weighted coloring number χw(G) is the smallest k such that there exist stable sets as above. We provide a polynomial time combinatorial algorithm(More)
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