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We derive a new upper bound on the diameter of the graph of a polyhedron P = {x ∈ R<sup>n</sup> : Ax ≤ b}, where A ∈ Z<sup>m×n</sup>. The bound is polynomial in n and the largest absolute value of a sub-determinant of A, denoted by Δ. More precisely, we show that the diameter of P is bounded by O(Δ<sup>2</sup> n<sup>4</sup>… (More)

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 τ i = (c i , p i) on a minimum number of identical machines and to compute offsets a i for the tasks such that no collision occurs. A task τ i releases a job of running time c i at each time a i + k · p i , k ∈ N 0 and a… (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)

—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 address a scheduling problem that arises in highly parallelized environments like modern multi-core CPU/GPU computer architectures where simultaneously active jobs share a common limited resource, e.g., memory cache. The scheduler must ensure that the demand for the common resource never exceeds the available capacity. This introduces an orthogonal… (More)

Given a graph G with nonnegative node labels w, a multiset of stable sets S 1 ,. .. , S k ⊆ 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 χ w (G) is the smallest k such that there exist stable sets as above. We provide a polynomial time combinatorial algorithm… (More)

If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is. Acknowledgements First and foremost I would like to express my deepest gratitude to my advisor Prof. Dr. Friedrich Eisenbrand. With his excellent lectures on linear and combinatorial optimization in Paderborn he sparked my interest in this… (More)

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