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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.Ìý

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 practice. The devised methods lead to various tools for more general questions on big data.