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Title: Operations Research in Land Exchange
With geometric modeling techniques, one can represent the feasible solutions of problems in operations research as objects in high-dimensional space. The properties of these objects reveal information about the underlying problems and lead to algorithms. We model an application in land exchange as a clustering problem where the clusters have to adhere to prescribed cluster sizes. In this approach, we connect least-squares assignments, cell complexes, and the studies of polyhedra. Further, we report on how these results were implemented in an R&D project of the Bavarian State.