Kim-Manuel Klein

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Makespan scheduling on identical machines is one of the most basic and fundamental packing problems studied in the discrete optimization literature. It asks for an assignment of n jobs to a set ofm identical machines that minimizes the makespan. The problem is strongly NP-hard, and thus we do not expect a (1 + ε)-approximation algorithm with a running time(More)
In this paper we develop general LP and ILP techniques to find an approximate solution with improved objective value close to an existing solution. The task of improving an approximate solution is closely related to a classical theorem of Cook et al. [7] in the sensitivity analysis for LPs and ILPs. This result is often applied in designing robust(More)
We consider the bin packing problem with d different item sizes and revisit the structure theorem given by Goemans and Rothvoß [GR14] about solutions of the integer cone. We present new techniques on how solutions can be modified and give a new structure theorem that relies on the set of vertices of the underlying integer polytope. As a result of our new(More)
We consider the relaxed online strip packing problem, where rectangular items arrive online and have to be packed into a strip of fixed width such that the packing height is minimized. Thereby, repacking of previously packed items is allowed. The amount of repacking is measured by the migration factor, defined as the total size of repacked items divided by(More)
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